Abstract:
An electronic value transfer system using stored value in the form of serialized electronic coins and electronic bills, which provides efficient security monitoring without the need for full centralized accounting of each transaction. Central monitoring of the system-level security includes statistical sampling techniques coupled with efficient tracing of the transaction path of an electronic coin back to its source. Only small amounts of data storage and transmission are utilized, eliminating the need for large centralized databases of transaction records. Consumer privacy as well as flexibility in making card-to-card monetary transfers are thereby enhanced, while allowing verification of system-wide security as well as rapid detection and tracing of security breaches. Multiple editions of electronic coins permit transparent and periodic renewal of the system and re-establishment of a security baseline, and also provide for the regular reclamation of stored value lost or abandoned by consumers.

Description:
CROSS REFERENCE TO OTHER APPLICATIONS 
     This application is a continuation in part application of U.S. Ser. No. 09/050,388 filed Mar. 30, 1998 now U.S. Pat. No. 6,119,946. 
    
    
     FIELD AND BACKGROUND OF THE INVENTION 
     The present invention relates to an electronic value system having electronic stored-valued, and in particular to such a system with system-level monitoring of the stored value. 
     Smart cart technology has enabled two consumer payment applications: the charge (credit or debit) card with enhanced security (especially in off-line payment,) and the stored-value card, also called electronic purse. The two applications are complementary: the charge card is more suitable for medium-to-higher payments, while the electronic purse&#39;s arena is small payments. The potential synergy between two payment applications is described in U.S. Pat. No. 5,744,787 by the present inventors and assigned to common applicants of the present application. 
     A major concern in any payment system is security, i.e., preventing unauthorized transfer or production of money. In smart card stored-value payment, a vast number of patents, publications and implemented solutions deal with safeguarding payment and other value transfer transactions at the bank-to-consumer, consumer-to-merchant and merchant-to-bank levels. There are combinations of hardware, software and procedures believed to withstand any attack conducted for a reasonable time using known means. However, as security is so crucial to payment systems, many bankers insist on monitoring the flow of money at the system level, to reconfirm the flawless operation of the security means at the transaction levels. This security requirement has been commonly transformed into the concept of “full accountability”, i.e. recording and reporting all single stored-value transactions to a central computer, for checking and confirming that each addition of value to a first stored-value device has occurred only as the same amount had been deducted from a second stored-value device. Such accountability schemes require an enormous amount of data storage and transfer and may interfere with the privacy of consumers carrying personal payment cards. 
     OBJECTS AND BRIEF SUMMARY OF THE INVENTION 
     The main object of the present invention is to monitor centrally the stored value (hereinafter referred-to as “electronic value”) in a stored-value system, for system-level reconfirmation of transaction-level security, without recording and reporting each single transaction. Another object is to minimize the amount of data stored and transferred for such monitoring. Still another object is to enable consumer anonymity and privacy in most small payments. Additional objects include measuring the amount of stored value lost or abandoned by consumers; measuring the amount of invalid stored value (if transaction-level security has malfunctioned or has been broken); providing controlled refresh options for periodical renewal of electronic value and its security parameters; maintaining local audit trails for identifying the sources of fraudulent electronic value; supporting multiple-issuer environments; and enabling satisfactorily-monitored card-to-card transfer of electronic value. 
     The following terms will be used herein as follows: 
     1. Electronic money - value which is recorded electronically and is useful for payment. 
     2. Account - a storage of electronic value at an institution. Non-limiting examples include the storage of electronic money or debt at a financial institution, such as bank accounts and credit accounts. The accounts of interest to the present invention are consumer account and merchant account. 
     3. Value issuer - a business entity establishing and maintaining accounts of electronic value. In some embodiments of the present invention, value issuers are financial institutions, such as banks, credit companies and telephone companies. Actually, the term value issuer will usually relate to the computer system of such institutions used to store and maintain accounts and execute transactions therewith. 
     4. Charge - a consumer order to transfer electronic value from his account to another account. 
     5. Electronic value - value in a form which can be transferred to and stored in a consumer or merchant electronic storage device. The term “value” herein denotes any accumulated and transferable measure of worth, including but not limited to: money, cash, currency, or the equivalent thereof; loyalty points, airmiles, or other rewards or recognitions; barter credit or scrip; and coupons, such as discount coupons. The term “electronic cash” herein denotes an embodiment of electronic value that represents cash money or the equivalent thereof. 
     6. Stored-value device - an electronic storage device for storing electronic value. 
     7. Payment card - a consumer device for payment with electronic money. A payment card may include a charge card for generating charge orders (e.g., credit card or debit card), and/or an electronic purse or electronic coin purse, which is a consumer stored-value device or storage within a consumer stored-value device. 
     8. Smart card - a payment card designed to secure the information stored therein and the transactions made therewith. 
     9. Point of sale or POS, or point-of-sale terminal - a merchant&#39;s device for receiving payment and optionally also for determining the purchase contents and calculating the payment amount. A POS may be staffed (e.g., a supermarket cash register) or automatic (e.g., in a vending machine, public telephone or parking meter). 
     10. Electronic drawer, electronic coin drawer, or drawer - a merchant&#39;s secured electronic storage device or merchant stored-value device, usually forming part of POS, for storing electronic value (electronic value drawer) and/or charge orders (charge drawer). 
     11. Electronic value pool - a stored-value device for a financial institution or storage within a financial institution stored-value device, for storing and accounting for electronic value. 
     12. Elementary value unit, or EVU - the smallest amount of value that is relevant for transfer. In one embodiment of the present invention, the elementary value unit is a single loyalty point. In other embodiments, the elementary value unit is an elementary monetary value, or EMU, representing smallest amount of monetary value that is relevant for payment or change. An example 1¢ in the U.S. or 5 Agorot in Israel. 
     13. Serial number - data used for identification of a discrete entity and suitable for digital representation. Typical examples for serial numbers are positive integers and ASCII character strings. 
     14. Charge function - a means for making a charge. Charge functions may be coupled with a stored-value device. As a non-limiting example, the electronic coin purse of a payment card or personal network terminal may be coupled with a charge function. As another non-limiting example, a charge function may be coupled with an electronic coin drawer; the charge function of this example is herein denoted by the term “charge drawer”. 
     The present invention makes electronic value countable by devising the entity “electronic coin”, each electronic coin having a monetary value or other forms of value and a serial number. When an electronic coin moves, it moves along with its value and serial number. A percentage of random electronic coins flow through electronic coin pools of financial institutions, where forbidden repetitions or out-of-range serial numbers are sought. Such repetitions or out-of-range instances, if found, are reported to signal that there is a security leak at the transaction level and to estimate the size of the damage. 
     By creating a hierarchy of electronic coin types, each having a denomination which is a multiple of the previous denomination, the present invention supports very effective payment while minimizing storage requirements for electronic coins, especially on the payment card. The present invention teaches how to allocate tens or a couple hundred bytes of memory on the card, for storing hundreds of dollars, with 1¢ resolution, in a hundreds million card population, with a unique serial number for each electronic coin. This minimal storage requirement also implies minimal data communication requirement during transactions, which minimizes transaction time and enhances reliability. 
     The present invention also investigates the money flow in the monetary system constructed and operated according to the present invention, showing that most electronic value actually revolves between points of sale and payment cards, while the actual monetary transfer are made mainly by charge (credit or debit) transactions and/or by electronic bills, which are higher-denomination electronic coins which are allowed for manual reloading of payment cards. 
     Another aspect relates to managing local audit trails, where each stored-value device records the serial numbers of received electronic coins along with the identity of the source device. These records are kept for a limited time, and are useful to track back suspected electronic coins to identify the source devices for further investigation. 
     By changing editions periodically, the present invention teaches to refresh security parameters, recall efficiently and automatically the older edition&#39;s electronic coins, count them with accuracy of a single cent, identify security flaws precisely, and account for electronic value lost oar abandoned by card holders, i.e., electronic value not claimed by the expiration date of the old edition. 
     Other important achievements of the present invention include a very effective support for system-level-audited card-to-card electronic value transfers, and the provision of ultimate anonymity at most transactions. The invention offers flexibility in supporting different card types to populations of different needs and preferences, including the co-existence of personal cards having both charge and stored-value functions, and “white”, stored-value-only cards. Methods for accelerating the edition refreshing and enhancing the security sampling rate and reliability are also presented, including forced exchange of electronic coins and random or FIFO (first-in-first-out) electronic coin picking. 
     The present invention also teaches how to manage a multi-issuer environment, where every issuer is assigned a distinctive range of serial numbers. A semi-countable system is also presented, where higher denomination electronic coins are counted according to the present invention, while lower denominations are inspected statistically. 
     The present invention also generalizes the concept of stored-value devices. Although the payment card is an important class of stored-value device for storing, sending, and receiving electronic coins, other important devices are also possible. Non-limiting examples of generalized stored-value devices include personal network terminals, which herein denotes any electronic device available for personal use to access and interact with electronic networks. Personal network terminals include, but are not limited to personal computers (PC&#39;s) and telephonic devices, such as cellular telephones or other wireless communication deices. Other non-limiting examples of stored-value device include point-of-sale terminals, unattended point-of-sale terminals, and network servers such as are used on the Internet. Stored-value devices may exchange electronic coins in proximity with one another, as is done with payment cards and points-of-sale, but in generally stored-value devices may also exchange electronic coins remotely over a dial-up connection, via a network (such as the Internet), wireless communication, or a combination of these. 
     Specific types or classes of stored-value devices may be associated with consumers, merchants, and value issuers, such as financial institutions. Thus, consumers may have consumer stored-value devices, merchants may have merchant stored-value devices, and value issuers may have value-issuer stored-value devices. In particular, consumer stored-value devices are also herein denoted by the term “electronic coin purses”, merchant stored-value devices are also herein denoted by the term “electronic coin drawers”, and value issuer stored-value devices are also herein denoted by the term “electronic coin pools”. 
     As illustrated in FIG. 36, a merchant stored-value device in the form of a merchant server  900  interfaces via a network  910  with a consumer stored-value device in the form of a consumer PC  920 . Within a memory  922  of consumer PC  920  is an electronic coin purse  924  containing electronic coins  926 . Non-limiting examples of memory  922  include RAM, EEPROM, and hard disk storage. Likewise, within a memory  902  or merchant server  900  is an electronic coin drawer  904  containing electronic coins  906 . Similarly, non-limiting examples of memory  902  include RAM, EEPROM, and hard disk storage. 
     In general, there are value transfer transactions from a source stored-value device to a target stored-value device. There is great versatility in making value transfers according to the present invention. For example, a consumer might have a cellular telephone containing an electronic coin purse coupled with a charge function. The cellular telephone company might have an electronic coin drawer coupled with a charge drawer. In this manner, and as detailed herein, the consumer could pay for telephone service by transferring value to the telephone company, such as during the calls themselves. This transferred value could be a combination of electronic value representing both monetary value (electronic money) and other forms of value such as loyalty points, telephone credit points, and so forth. Additionally, a merchant could maintain an electronic coin drawer coupled with a charge drawer, and the consumer could use the cellular telephone to contact the merchant and exchange value therewith. Furthermore, in consideration of making monetary purchases, the merchant could transfer electronic value representing loyalty points to the consumer&#39;s stored-value device (the cellular telephone), which could then be used by the consumer to pay the telephone company for service. 
     There is considerable prior art in the field of transferring monetary value electronically, but the present invention differs significantly from prior art systems with regard to objectives, organization, utilization, and operating environment. 
     For example, the “Value Transfer System” of U.S. Pat. No. 5,440,634 and U.S. Pat. No. 5,623,547 to Jones et al. disclose a coinless purse system that requires a separate loading operation and independent account reconciliation on individually-stored transactions. This is in contrast to the system of the present invention, which utilizes electronic coins and does not necessarily require a separate loading operation or account reconciliation. 
     It should also be noted in particular that the general concept of convenient payment instruments in the form of indivisible digital tokens, sometimes referred to as “ecoins”, is likewise well known in the art. The present invention, however, differs significantly from prior art implementations of “ecoin” payment systems, with regard to its objectives, operating environment, and electronic coin transfer protocol. 
     For example, the prior art “ecoin” payment system of DigiCash BV (Amsterdam, The Netherlands) is intended to facilitate the making of payments over a possibly unreliable communication channel (such as a data network) and to reduce the risk of lost value due to storage and transmission errors. In The DigiCash system, “ecoins” are uniquely serialized, and any holder of an “ecoin” can make unlimited copies of the “ecoin” for legitimate purposes, such as backup against inadvertent loss. In fact, the copies of a DigiCash “ecoin” with a specific serial number are indistinguishable from one another, so that it is meaningless to speak of an “original” DigiCash “ecoin” as distinct from the copies of that “ecoin”. In the DigiCash system, the transfer of an “ecoin” from payer to payee consists of sending a copy of the “ecoin” from payer to payee. A copy of the “ecoin” remains with the payer, so that the “ecoin” may be sent repeatedly to the payee in the event of communications errors or other loss. The DigiCash system maintains integrity against unauthorized creation of value with a central database containing records of spent “ecoin” serial numbers, so that any given “ecoin” can be used to transfer value from any payer to any payee only once. A payee who receives an “ecoin” immediately sends a copy of the “ecoin” to the issuer (usually a bank), who records the “ecoin” serial number in the central database of spent “ecoins” and validates the payment, either by crediting the payee&#39;s account with the value or by returning a new (unspent) “ecoin” of equal value to the payee, which the payee may then spend. But subsequent attempts to transfer value from any payer to any payee using an “ecoin” that is registered in the central database as having already been “spent” will be rejected, and in this way the making of copies of “ecoins” does not impact the monetary value in the DigiCash system. 
     In contrast, the electronic coin system of the present invention is intended to facilitate the utilization of account-to-account transfers (credit or debit) for making cumulative small payments, and employs a highly reliable communication channel (a smart card or secured network session), in which the probability of a communications or storage failure of the devices themselves is negligibly small. In the system according to the present invention, electronic coins are uniquely serialized, but the transfer protocol precludes the making of copies. In the system according to the present invention, therefore, there exists at most a single electronic coin corresponding to any given serial number, and the transfer of an electronic coin from payer to payee consists of sending the electronic coin to the payee in such a way that no copy of the electronic coin remains with the payer. In the system according to the present invention, electronic coins circulate like their physical counterparts, and a particular electronic coin may therefore be spent more than once, in contrast to the prior art system, which allows only a single payment per “e-coin”. A typical transaction of the present invention distinctly involves electronic coins of different denominations moving between two stored-value devices in both ways to account for the desired value. The electronic coin pool of the present invention is furthermore distinct from the prior art central database in that the electronic coins in the electronic coil pool are still valid and may be put back into circulation for further spending, whereas the prior art central database is merely a listing of “e-coins” which are no longer valid for transactions. 
     Thus, according to the present invention, there is provided a countable electronic value system for the transfer of electronic money in amounts which are an integer multiple of an elementary value unit, the transfer of electronic money made between two selected ones from a plurality of payment cards, a plurality of points of sale and a number of financial institutions, the countable electronic value system including: 
     (a) at least one electronic coin type, each electronic coin type of the at least one electronic coin type having a denomination of an integer number of the elementary value unit; 
     (b) a plurality of electronic coins each belonging to one of the at least one electronic coin type, each electronic coin of the plurality of electronic coins having a serial number, 
     (c) a plurality of stored-value devices, each for storing electronic coins from the plurality of electronic coins, including: 
     a plurality of electronic coin purses, each included in a payment card of the plurality of payment cards; 
     a plurality of electronic coin drawers, each included in a point of sale of the plurality of points of sale; and 
     a number of electronic coin pools, each included in a financial institution of the number of financial institutions; 
     and transaction means for the transfer of a selectable number of electronic coins belonging to a selectable electronic coin type, from a source stored-value device selected from the plurality of stored-value devices to a another, second stored-value device selected from the plurality of stored-value devices, the transaction means being operative to record the serial number of each one of the transferred electronic coins in the target stored-value device and to erase this serial number from the first stored-value device. 
     Other aspects of the present invention are presented in the detailed specifications hereinbelow. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For brevity in the drawings, an electronic coin is denoted by the label “EC” and an electronic bill is denoted by the label “E-Bill” 
     FIG. 1 is a block and flow diagram describing the structure and operation of a basic embodiment of the present invention. 
     FIG. 2 is a block diagram describing the memory organization in preferred embodiments of cards and POS according to the present invention. 
     FIG. 3 is a block diagram describing the memory organization in preferred embodiments of financial institution computers according to the present invention. 
     FIG. 4 is a table calculating the memory requirements for the embodiment of FIG.  1 . 
     FIG. 5 is a block and flow diagram describing the structure and operation of a second preferred embodiment of the present invention. 
     FIG. 6 is a flowchart describing the payment procedure of the embodiment of FIG.  5 . 
     FIG. 7 is a table calculating the memory requirements for the embodiment of FIG.  5 . 
     FIG. 8 is a block diagram describing in detail the main units of the embodiment of FIG.  5 . 
     FIGS. 9,  9 A and  9 B are block diagrams describing a third preferred embodiment of the present invention. 
     FIGS. 10A and 10B are tables for calculating the memory requirements of the cases described in FIGS. 9A and 9B, respectively. 
     FIG. 11 is a block and flow diagram describing the structure and operation of a fourth preferred embodiment of the present invention. 
     FIG. 12 is a table for calculating the memory requirements for the embodiment of FIG.  11 . 
     FIG. 13 is a flowchart describing the electronic cash payment procedures in the embodiments of FIGS. 9,  11 ,  14  and  17 . 
     FIG. 14 is a block and flow diagram describing the structure and operation of a fifth preferred embodiment of the present invention. 
     FIG. 15 is a table for calculating the memory requirements for the embodiment of FIG.  14 . 
     FIG. 16 is a block diagram describing a preferred embodiment of the present invention that includes a mix of the previous preferred embodiment. 
     FIG. 17 is a block and flow diagram describing the structure and operation of a recommended preferred embodiment of the present invention. 
     FIG. 18 is a table for calculating the memory requirements for the embodiment of FIG.  17 . 
     FIGS. 19 and 20 are block diagrams describing the memory organization in various stored-value device of the present invention, where two editions of electronic cash are used simultaneously. 
     FIG. 21 is a block and flow diagram summarizing the flow of electronic money for the various transactions of the present invention. 
     FIG. 22 is a block diagram describing another embodiment of the present invention relating to a “semi-countable” feature. 
     FIG. 23 is a flowchart describing the operation of the embodiment of FIG.  22 . 
     FIG. 24 is a table calculating the memory requirements for the embodiment of FIG.  22 . 
     FIG. 25 is a diagram showing the storage of card identification data with respect to electronic bill serial numbers. 
     FIG. 26 is a diagram showing a paper confirmation receipt issued by a loading terminal. 
     FIGS. 27,  27 A,  27 B,  27 C, and  27 D are block diagrams showing the operation of a simple protocol for transferring an electronic coin. 
     FIG. 28 is a flowchart of the simple transfer protocol illustrated in FIG.  27 . 
     FIG. 29 is a flowchart and block diagram showing a failure of the simple transfer protocol in FIG.  27  and FIG. 28, resulting in the duplication of an electronic coin. 
     FIGS. 30A,  30 B,  30 C,  30 D,  30 E,  30 F,  30 G,  30 H, and  30 I are block diagrams showing the operation of a duplication-resistant protocol for transferring an electronic coin. 
     FIG. 31 is a flowchart of the duplication-resistant transfer protocol illustrated in FIGS. 30A-I. 
     FIG. 32 is a diagram showing a watchdog according to the present invention, based on continuous electronic coin sampling to detect duplicate electronic coins. 
     FIG. 33 is a diagram showing received electronic cash files and how they are used to perform an audit. 
     FIG. 34 is a flowchart showing an example of how a continuous electronic coin sampling detects the source of a bogus electronic coin. 
     FIG. 35 is a flowchart showing a recursive method for generating a transaction path for an electronic coin. 
     FIG. 36 is a diagram showing a consumer PC conducting a transaction with a merchant server. 
     FIG. 37 is a flowchart illustrating the use of coin picking criteria in returning change from a merchant server to a consumer PC. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     1. ELECTRONIC COINS AND ELECTRONIC COIN TRANSACTIONS 
     Payment is made in values that are a multiple of an elementary monetary unit (EMU). Hereinbelow the value of 1¢ is used as an example of EMU, although in other countries the practical EMU may have values such as 5, 10, or 100 units of the lowest monetary denomination. 
     A basic concept of the present invention is the electronic coin. This is an information entity, which can be stored electronically in stored-value devices, and moved between such devices. An electronic coin has a denomination that is an integer multiple of an EMU, and a serial number. Preferably, a serial number will be unique to each single electronic coin of a specific denomination; however, a small, redefined number of repetitions of the same serial number may be pre-programmed into the system and allowed. Also, it is noted that the serial number may be presented for human reading in any acceptable form such as Arabic numerals, letters, etc.; however, its computerized storage will be in a standard computer storage form, e.g. binary. 
     According to the present invention, when transferring an electronic coin from a stored-value device (the source) to another stored-value device (the target), the serial number of this electronic coin is erased from the source and written onto the target stored-value device. Thus, whenever the verbs “move” or “transfer” are mentioned hereinbelow in conjunction with an electronic coin, it should be understood that the serial number of this electronic coin is erased from and written onto the source, and target stored-value devices, respectively. However, the term “erase”, relating to digital storage, is essentially logical and should be interpreted hereinafter liberally; for instance, erasure may be implemented by a logical flag indicating that the storage space of an electronic coin serial number has been freed and is available for storage of another electronic coin serial number, while the resident “erased” serial number becomes logically inaccessible without necessarily resetting the bits representing this erased serial number. 
     Electronic coins of different denominations may coexist in the same system. In this case, electronic coins having the same denomination will be referred to hereinbelow as belonging to same “electronic coin type”. 
     2. PAYMENT SYSTEM CONFIGURATIONS 
     2.1. BASIC PAYMENT SYSTEM USING ELEMENTARY ELECTRONIC COINS ONLY (FIGS. 1-4) 
     An embodiment of a basic payment system based on the present invention, uses a single electronic coin type, having the denomination of one EMU (elementary monetary value), e.g. 1¢. This electronic coin type is called the elementary electronic coin, or electronic coin- 0 . 
     FIG. 1 is a block diagram describing the main elements of the basic form of a payment system of the present invention, generally designated  1 . A payment card  2  is one of a large plurality of payment cards used by consumers for payment. Payment card  2  is either in the well-known form of a credit-card like plastic card with an embedded chip, or in any other form, such as key-chain, toll-payment transponder, or part of a personal computer or part of a cellular telephone. Payment card  2  includes electronic coin- 0  purse  11 , which is a stored-value device containing security information and elementary electronic coins in the manner described in FIG. 2. A POS  3  is one of a plurality of points of sales used by merchants to receive payment for consumers. POS  3  can be a manned or automatic, and can also include means for determining the purchase contents and calculating the amount due for payment. POS  3  includes electronic coin- 0  drawer, which is a stored-value device containing security parameters and elementary electronic coins in the manner described in FIG.  2 . The aggregate of computer systems of financial institutions, designated  4 , includes an electronic coin- 0  pool  13 , which is a stored-value device containing security parameters and elementary electronic coins in a manner described in FIG. 3. A payment transaction  4  is executed when card  2  is inserted into POS  3  or communicates with POS  3  in any other way (e.g. over the Internet); this payment transaction moves a specified number of elementary electronic coins from electronic coin- 0  purse  11  to electronic coin- 0  drawer  12 , each elementary electronic coin transfer including the erasure of this electronic coin&#39;s serial number from purse  11  and its recording in drawer  12 . In settlement transaction  5 , POS  3  communicates with financial institutions  4 , to transfer elementary electronic coins from electronic coin- 0  drawer  12  to electronic coin- 0  pool  13  and claim their total value; the communication between POS  3  and financial institutions  4  can be made through telephone or data communication physical or cellular links, through hand-held devices or by physically transferring drawer  12  to a terminal of financial institution  4 . In load transaction  6 , card  2  communicates with financial institution computers  4 , preferable by presenting the card at a terminal connected to computers  4  (such as in a bank counter, ATM, special telephone or dedicated home unit); the consumer then pays a selected amount with any monetary instrument acceptable at that terminal, an equivalent amount of elementary electronic coins is then moved from pool  13  to purse  11 , each elementary electronic coin transfer including the erasure of this electronic coin&#39;s serial number from pool  13  and its recording onto purse  11 . 
     FIG. 2 is a block diagram illustrating the storage of electronic coins in electronic coin stored-value devices such as purse  11  or drawer  12  of FIG. 1. A register  21  contains the denomination the electronic coins stored in this stored-value device. A register  22  stores the current number of stored-value units; multiplying this number by denomination  21  yields the total value stored in this storage device. A register  23  shows the capacity of the electronic coin stored-value device, i.e. the maximum number of electronic coins which can be stored therein. Registers  24 - 1  to  24 -N include the serial numbers of the currently-stored electronic coins, preferable with a few parity bits added to each register for ensuring data integrity and security; the rest of the registers ( 24 -N+ 1  to  24 -MAXN) include the number zero, which means that no electronic coins are currently stored therein. 
     FIG. 3 shows an alternative way to store electronic coins, which is aimed at storing a vast number of units, typically at electronic coin pool  13 . A register  31  includes the denomination of the stored electronic coins. A register  32  stores the parameter FIRST, which is the lowest serial number of an issued electronic coin of said denomination (e.g. 1), while a register  33  stores the parameter LAST, which is the highest number of an issued electronic coin of said denomination. Registers  34 - 1  to  34 -M form a vector of length M=LAST-FIRST +1 composed of bits, wherein each issued electronic coin corresponds to a bit by the formula SERIAL NUMBER=BIT ADDRESS+FIRST-1. Whenever an electronic coin is removed from pool  13  (e.g. for loading purse  11 ), the corresponding bit is turned off; when a specific electronic coin is added to pool  13  (e.g. through settlement with drawer  12 ), the corresponding bit is turned on. In a configuration mentioned above where a small multiple K of each serial number is allowed, the vector is replaced by a matrix of (LAST-FIRST+1). by K dimensions. Any attempt to turn on an already-on bit, will indicate that there is an invalid electronic coin in the system. This provides a simple, low-cost, and efficient means for monitoring the sytem&#39;s security, which is a main objective of the present invention. 
     FIG. 4 presents a table with numerical calculations, relating to the embodiment under consideration, and to reasonable assumptions about nationwide implementation in the U.S. market. Assuming 150 million cards in circulation ( 41 - 1 ), and $200 in units of 1¢ being the capacity on each card ( 41 - 2 ), and assuming that the total electronic value in the system can be estimated by the total card capacity (in a realistic snapshot, most cards are only partly loaded, but money is also sorted in POS and cash pools), we obtain that the total number of 1¢ electronic coins is 3*10 12  ( 41 - 3 ). A serial number for this range requires 42 bits ( 41 - 4 ). Adding 3 bits per serial number for parity check ( 41 - 3 ) yields the need for 45 bits per each stored elementary electronic coin, when stored on payment cards  2  or POS  3  according to the storage scheme of FIG.  2 . This requires to reserve on each purse  11  (which may contain up to 20,000 electronic coins) 900,000 bits ( 41 - 7 ) or 112,500 bytes ( 41 - 8 ). Assuming that the merchant wishes to accumulate $1,000 of electronic value prior to performing a settlement transaction with a financial institution, he has to reserve in drawer  12  memory for 100,000 electronic coins ( 41 - 9 ) which requires 562,500 bytes ( 41 - 11 ) per POS. The cash pool, needing to monitor 3*10 12  electronic coins, will require (when applying the storage scheme of FIG.  3 ). the number of bits, or 375*10 9  Bytes ( 41 - 12 ), which is about 350 GB. 
     The numeric results of FIG. 4 show that the memory requirements are very demanding for the card and also for many types of POS. Also, payment, settlement and load transactions may take unacceptable average and worst-case times because of the large amount of dataflow. 
     The following, alternative embodiments will show ways to reduce dramatically the memory and dataflow requirements, thus simplifying, increasing the reliability and reducing the cost of the present invention&#39;s implementation. 
     2.2 A PAYMENT SYSTEM WITH CHARGE AND ONE ELECTRONIC COIN TYPE (FIGS.  5 - 8 ). 
     FIG. 5 is a block diagram describing schematically the main element of a preferred embodiment of a payment system according to the present invention. More information on the operation of this embodiment is described in U.S. Pat. No. 5,744,787 by the present inventors and assigned to common applicants of the present application. 
     Payment card  51  includes charge card  51 -C and electronic coin- 0  purse for accommodating elementary electronic coins having the value of one EMU (elementary monetary value). Similarly, POS  52  includes charge drawer  52 -C to temporarily store therein charge orders made in off-line, and electronic coin- 0  drawer  52 - 0  to store therein elementary electronic coins. The computer system of financial institutions  53  includes charge (credit and/or debit) accounts  53 -C, and electronic coin- 0  pool for accommodating elementary electronic coins. 
     Reference will now be made to both FIG.  5  and FIG. 6, to described the payment procedure with the embodiment under consideration. A primary concept relating to this embodiment is a parameter $LIMIT, usually defined by the card issuer or the merchant, to specify the minimal amount allowed for charge transactions, e.g. $25. 
     When a payment card  51  with current amount of $BALANCE in its electronic coin- 0  purse  51 - 0  interfaces with POS  52  (step  61 ) to pay an amount of $SUM, $SUM is compared to $LIMIT (step  62 ) to decide whether the payment can be made via charge card  51 -C (step  64 ). If not, payment is referred to purse  51 - 0 . In step  63 , $SUM is compared to $BALANCE to find out whether payment can be made from the amount stored in the purse (step  65 , transaction  55 ); if not (step  66 ), $LIMIT will be paid by charge card  51 -C to charge drawer  52 -C, and change of $LIMIT-$SUM is transferred from drawer  52 - 0  to purse  51 - 0  (transaction  56 ). 
     The payment procedure of FIG. 6 leads to some important, somewhat unexpected non-obvious results (see also §2.8 below for statistical analysis): 
     (a) payment can always be made for any amount, limited only by the charge card&#39;s ceiling; no manual loading of purse  51 - 0  is ever required in this embodiment; 
     (b) the value stored in purse  51 - 0  will not exceed $LIMIT, which minimizes the damage in case of loss; 
     (c) for any specific POS  52 , the average amount of electronic coin inflow through payment transaction  55 , equal the average amount of electronic coin outflow through change transaction  56 . This means that electronic coins actually revolve among cards and POS. 
     Returning now to FIG. 5, in settlement transaction  57 , charge orders received from customers through transactions of steps  64  and  66  of FIG. 66 are submitted for clearance with the respective accounts in charge accounts  53 -C. Transaction  59  provides the initial amount of electronic coins to a payment card, prior to supplying the card to the customer. In the embodiment under consideration, no additional transfer of electronic coins between financial institutions and customers is ever needed. In transaction  58 , four procedures are carried-out regarding electronic coin flow between the POS  52  and financial institution  53 : 
     (a) Priming: as electronic coin drawer  52 - 0  must always have sufficient amount of electronic coins for returning change to purse  51 - 0  (step  66  of FIG.  6 ), some amount of initial electronic coins must be supplied to the drawer before starting a business cycle (e.g. a workday); this amount is acquired by the merchant from the financial institution and transferred from pool  53 - 0  to drawer  52 - 0 . Priming with about 15% of the expected electronic coin revenue during the business cycle proves to be effective for flawless operation with very high probability. 
     (b) Adjustment: at the end of the business cycle, the amount of electronic coins in electronic coin drawer  52 - 0  is expected, statistically, to be unchanged in respect to the initial amount. However, due to statistical fluctuations, the actual amount would usually require small addition or subtraction in order to start the next business cycle with a predefined amount of electronic coins for priming. 
     (c) Monitoring: in order to check the security of the system at pool  53 - 0 , an amount of flow from drawer  52 - 0  must be ensured. The natural flow through adjustment transactions might be sufficient, or some additional exchange of electronic coins between drawer  52 - 0  and pool  52 - 0  may be initiated during the routine communication between the POS and financial institution, made for other transactions from 57 and 58. For more on monitoring see §4 below. 
     (d) Refresh: if both an old and a new edition of electronic coins are used, old electronic coins can be intentionally drained from POS to financial institution during route communication. For more on refreshing see §3 below. 
     It is noted that all transfers of electronic coins described above, through transactions  55 ,  56 ,  58  and  59  of FIG. 5, involve moving the serial number of each transferred electronic coin, as described in reference to FIG. 1 in §2.1 above. 
     FIG. 6 calculates the amount of storage and transfer of information needed for the implementation of the embodiment under consideration. The same 150 million cards ( 71 - 1 ) as in FIG. 4, now accommodate up to $25 each, which are 2500 1¢ electronic coins ( 71 - 2 ). The total number of coins is estimated as the total number of cards multiplied by each card&#39;s maximal capacity (actually, half of this amount will reside on cards, while the remainder will be in POS drawers and financial institution pools), which leads to 375 billion electronic coins ( 71 - 3 ) which require 39 bits for a unique serial number ( 71 - 4 ). Adding 3 parity bits, we obtain 42 bits per each electronic coin serial number. For 2500 electronic coins, this means 13,125 bytes per payment card. A POS accommodating up to $1000 in 1¢ electronic coins will require 525,000 bytes of memory for recording their serial numbers ( 71 - 11 ), while a cash pool allocating 1 bit per electronic coin (memory management according to FIG.  3 ), will need 48,875 million bytes ( 71 - 12 ). 
     The memory requirements represented by the results of FIG. 7 are easily acceptable to financial institutions and POS, and feasible, yet still demanding, for cards. Further reduction of the data storage and flow requirements will be presented in the embodiments in §2.3-2.5 below. 
     Reference is now made to FIG. 8, which is a block diagram describing in more detail the embodiment of FIG.  5 . Payment card  51  includes elementary electronic coin purse  51 - 0  and charge card  51 -C. Purse  51 - 0  includes an electronic coin denomination register  51 -D, a total balance register  51 -B and a memory  51 -L accommodating the serial numbers of all electronic coins currently stored in purse  51 - 0  Charge card  51 -C includes an account info register  51 -A with the information required to access and perform transactions with the respective account from charge accounts  53 -C at respective financial institution  53 . External interfacing allows card  51  to interface with points of sale  52 , through interface means which may use contact, contactless or remote communication links. POS  52  includes a card interface  52 - 2  to interface with payment card  51  and a customer interface  52 - 4  to allow the customer to key-in parameters such as a PIN code for charge transactions. A payment amount register  52 - 6  receives the payment amount from a calculation unit  52 - 6 , which determines the purchase contents and its price by receiving signals from a purchase interface  85 , which may be a keypad, barcode scanner, vending machine controller etc. An automatic transaction manager  52 - 1  performs the transaction procedure of FIG. 6 upon receiving the amount due from register  52 - 3  and the electronic coin purse parameters from card interface  52 - 2 . Automatic transaction manager  52 - 1  activates: an electronic coin payment unit  52 - 8  to receive payment from purse  51 - 0  and deposit the payment in electronic coin drawer  52 - 0 ; an electronic coin change loading unit  52 - 10  to return change to electronic coin purse  51 - 0  from drawer  52 - 0 ; and a charge transaction unit  52 - 7  to charge the respective account in charge accounts  52 -C in accordance to charge card  51 -C. Charge drawer  52 -C accommodates charge transaction orders until settled with financial institutions  52 . The computer system of financial institutions  53  maintains charge accounts  53 -C and electronic coin pools  53 - 0 , for transactions  57 ,  58  and  59  of FIG.  5 . 
     2.3. A PAYMENT SYSTEM WITH CHARGE AND TWO ELECTRONIC COIN TYPES (FIGS. 9-10) 
     The embodiment described in FIG. 9 is aimed at reducing the amount of data storage and transfer, in comparison to the embodiment of FIG. 5 (§2.2). In this case, an electronic coin purse  91 -s is subdivided into an electronic coin- 0  purse  91 - 0  containing elementary electronic coins of one EMU value, and an electronic coin- 1  purse  91 - 1  containing electronic coin- 1  coins, whose denominations a predefined integer number of EMU (elementary momentary unit). An electronic coin drawer  92 -S and an electronic coin pool  90 -S are subdivided similarly. Each sub-stored-value device can contain only the respective type of electronic coins, and electronic coin transactions between devices transfer electronic coins only between matching sub-stored-value devices. 
     The transaction procedure for multiple electronic coin type purses will be described in §2.5 below, and its statistics will be analyzed in 517 2.8 below, with the follow end results: 
     (a) The configuration of FIG. 9 will operate flawlessly, with similar efficiency as that of FIG.  5 . The purse subdivision is a technical aspect that can be transparent to the card holder and merchant. 
     (b) Each electronic coin sub-level will perform individually with a similar behavior as the single electronic coin level of FIG.  5 . Thus, the inflow and outflow of electronic coins at each sub-level are statistically equal in average. FIG. 9A describes a $25 charge transaction minimum limit (for FIG. 6 procedure) and an electronic coin purse subdivided to accommodate a maximum number of 24 $1 electronic coins and 99 1¢ electronic coins (the quantities  24  and  99  The determined by considerations described in 517 2.5 below.) FIG. 10A calculates the amount of data needed to be stored and transferred during transactions. It can be seen the card now needs only 563 bytes for electronic coin storage, the POS makes do with 8,956 bytes, and the financial institution can now use even a personal computer for storing the entire electronic coin pool status. 
     FIGS. 9B and 10B show that the memory requirements can be further reduced when using 50¢ electronic coins instead of $1 electronic coin- 1 , of FIG.  9 . 
     2.4 A PAYMENT SYSTEM WITH THREE ELECTRONIC COIN TYPES (FIGS. 11-12) 
     The embodiments of §2.2 and §2.3 have shown practical electronic coin storage, using a payment card which bears both a charge card and an electronic purse, and allowing automatic payment and change transactions at the POS according to FIG.  6 . FIG. 11 describes similar achievements with “pure” stored-value functions, i.e. without including charge functions in the transaction options. 
     The rules for establishing and operating a multiple electronic coin type system are described in §2.5 below, and their statistics is analyzed in §2.8 below FIG. 11 describes such a system, where each payment card can accommodate any amount between 0 to $199.99 in electronic coins of $10, $1 and $1¢ . (These values are not optimal; actually, for a $200 purse, electronic coins with denominations of $7.84, 28¢ and 1¢ would yield even better results but could be confusing). The results in FIG. 12 show that for 150 million cards, each carrying a maximum of almost $200, 581 bytes on the card would be sufficient for storing all electronic coins, while minimal storage requirements are expected also from the POS and financial institution computers. 
     An additional important aspect shown in FIG. 11 is the loading doctrine. Loading in a “purse” stored-value card, i.e. a card without a charge function, requires payment by any means to a terminal connected to the financial institution, and transferring electronic coins (each with its serial number) therefrom into the respective sub-purse. It is both reasonable and efficient to allow such load transactions only with the higher denominations of coins or even with the single highest denomination. Electronic coins of denominations allowed for loading will also be called electronic bills, and their respective storage device will be presented in the drawings as a rounded-corner square (see  111 - 2 ,  112 - 2  and  110 - 2  of FIG.  11 ). We&#39;ll show in §2.8 that while electronic bills revolve mostly in the circle pool-purse-drawer-pool, the lower electronic coins (not permitted for loading) revolve mostly between purses and drawers. 
     2.5 A PAYMENT SYSTEM WITH MULTIPLE ELECTRONIC COIN TYPES (FIGS.  13 - 15 ). 
     A multiple electronic coin type system is devised to allow payment of any multiple integer of EMU (elementary monetary unit), with a small number of electronic coins. Following is a description of such a system using J+1 types: electronic coin ( 0 ) . . . electronic coin(J), of different denominations $D( 0 ) . . . $D(J), assuming monotonic ascending order. All values described hereinafter are in terms of a common, minimal monetary unit, e.g. 1¢; thus $200 is actually represented as 20,000¢. 
     The following rules promise flawless operation: 
     (a) $D( 0 ) equal one EMU. 
     (b) R(I)=$D(I+1)/$D(I) is an integer&gt;1 for all 0≦I≦J−1. 
     (c) The memory space allocated in the payment card for electronic coin(I) is R(I)-1 for 0≦I≦J-1. For electronic coin(J), the allocated space is arbitrary and is the main factor determining the maximum value that can be stored on the card. 
     (d) The amount of electronic coins of each electronic coin type stored in the POS is considered to be practically infinite (actually, a small priming in addition to favorable transaction statistics, see §2.8 below, maintain sufficient supply of electronic coins for all change transactions, as needed). 
     (e) Payment with electronic coins is executed according to the procedure of FIG.  13 . 
     FIG. 13 is a flowchart describing the payment procedure in a multiple electronic coin type system constructed according to the above values. A statement  130  repeats the rules. In a step  131 , a purse containing value of $INPURSE(I) for each type I (e.g. if electronic coin( 3 ) type has the value of 300¢ and there are 7 electronic coins of this type, $INPURSE( 3 ) will have the value of 2,100.), is presented to pay an amount $AMOUNT (also expressed in 1¢ units). In a decision point  132 , the purse contents is checked to see if there is sufficient value for payment. If the answer is “no”, a step  133  checks for alternative options (e.g. if the card contains a charge card, then the payment alternatives  64  or  66  of FIG. 6 may become valid.), or payment is rejected. Otherwise, in a step  134 - 1  an artificial denomination $D(J+1) is set as infinity (to ensure proper completion of loop and stop at 138 for higher payments; actually, any value larger than $AMOUNT+$D(J) will sufficient as “infinity”) and then a loop  134  through all integer values of I from 0 to J starts. In a step  135  the payment $PAY required to be made by electronic coin(I) is calculated, by checking what amount cannot be paid by the next higher denomination $D(I+1). In a decision point  136  $PAY is compared to the available money in this type of coins $INPURSE)(I). If the available money is sufficient, this amount is paid in a step  136 - 1  by moving the corresponding amount of electronic coin(I) units (each moving with its serial number) from the payment card to the POS; if the amount is insufficient, then in a step  136 - 2  $AMOUNT is increased by the one next higher monetary electronic coin denomination $D(I+1) and in a step  136 - 3  this transaction is compensated by creating the card with an amount $D(I+1) in an equivalent amount of electronic coin(I) units; however, as $PAY still needs to be deducted, the end result is a change transaction  136 - 3 ; here, again each electronic coin moved is transferred from the POS to the card with the electronic coin serial number. In a step  137 , the payment of amount $PAY is deducted from the amount due $AMOUNT, and the procedure continues with the next higher denomination, until completion at an exit step  139  by a decision point  138 . 
     As mentioned above, in the case that the sum of all $INPURSE(I), checked at decision point  132 , is insufficient, it may still be possible to complete the payment by means of a charge transaction, as indicated in step  133 , and as also shown in step  66  (FIG.  6 ). When a charge transaction is carried out in order to make a payment less than the minimum charge amount, the charge transaction will be for the minimum charge amount, and the difference between this minimum charge amount and the desired payment will be returned to the payment card as change in the form of electronic coins. As previously mentioned, however, it is not possible to send an arbitrary number of electronic coins of arbitrary denomination to the payment card, because the capacities of the individual purses of the different electronic coin denominations are limited. For example, if the 1¢ purse is already filled, then it is not possible to send any 1¢ electronic coins to the payment card. In general, then, sending change to the payment card in the form of electronic coins involves a combination of transfers of electronic coins from the POS to the payment card coupled with transfers of electronic coins from the payment card to the POS. To calculate the correct combination of electronic coins which must be transferred in each direction, it is possible to use the same algorithm described above and illustrated in FIG. 13 as follows: 
     First, it is necessary that the minimum charge amount be equal to the largest electronic coin denomination multiplied by 1+ the number of those electronic coins which the payment card can hold. For example, if the largest electronic coin is worth $5 and the payment card can hold 4 of them, then the minimum charge amount must be $25. This is an easy condition to implement, because the minimum charge amount can easily be adjusted upwards to suit the denominations and capacities of the payment card. For example, if the largest electronic coin is worth $7 and there 5 of them, then the minimal charge would simply be set at $42. Then, to use the algorithm illustrated in FIG. 13, the charge is considered as if it were a “virtual” electronic coin sent from the payment card to the POS. Because there is this additional “virtual” electronic coin, the number of electronic coin denominations is therefore increased from J+1 to J+2, where EC(J+1) is the charge (the “virtual” electronic coin) and $D(J+1) is the minimum charge amount. With these conditions met, application of the algorithm described above and illustrated in FIG. 13 will result in a transfer of electronic coins such that the payment card will receive the proper change while observing the limits on the number of electronic coins permitted for each denomination. 
     The set of rules specified above, as well as the flawless operation of the payment procedure of FIG. 13, are based on elementary mathematical considerations. The general problem of selecting objects representing distinct integer values in such a way that their values add up to a specific sum is well-known in the mathematical literature, and is referred to as the “subset sum problem” (sometimes referred to as the “knapsack problem”). It is known that if the represented values (in this case, the denominations of the electronic coins) are predetermined randomly, then the problem is difficult to solve and may not have a solution for every desired sum. On the other hand, if the set of represented values is chosen according to certain conditions, then not only will there always be a solution, but the solution will be very easy to find. The condition which assures that the solution will be easy to find is simply that each object must represent a value greater than the sum of all smaller objects. A set conforming to this condition is known as a “superincreasing set”, and the solution, if it exists, can be quickly found by comparison and iteration (as shown in the examples following). The condition which assures that a solution will always be found is simply that each object must represent a value 1 greater than the sum of all smaller objects. A set conforming to this condition is known as a “minimal superincreasing set”. For example, the set { 1 ,  3 ,  5 ,  5 ,  5 ,  23 ,  47 } is a superincreasing set. To find the elements of the set which add up to 34 is easy. First of all, 47 is too large to be present in the subset, but 23 is in the subset. Subtracting 23 from 34 leaves 11. The it is seen that 5 must be in the subset, leaving 6. Another 5 must also be in the subset, leaving 1. Finally, 3 is too large to be in the subset, and it is seen that the final element in the subset is 1, leaving 0 left over, showing that 34 has a solution. The desired subset is then { 1 ,  5 ,  5 ,  23 }. On the other hand, there is no solution for a sum equal to 7. As another example, the set { 1 ,  1 ,  1 ,  1 ,  5 ,  10 ,  10 ,  10 ,  50 ,  100 } is a minimal superincreasing set for which solutions exist for every sum from 1 to 199. An arbitrary number in this range such as 137 can easily be expressed by the subset { 1 ,  1 ,  5 ,  10 ,  10 ,  10 ,  100 } using the same iterative steps as before. Minimal superincreasing sets are easy to generate by observing the conditions given above. It is readily seen that, in order to function properly, the electronic coin purses of a payment card must constitute a minimal superincreasing set. Some mathematical references which discuss the subset sum problem in detail include  Cipher Systems,  by Henry Beker and Fred Piper, Wiley-Interscience, 1982, pages 373-380; and  Applied Cryptography,  by Bruce Schneier, John Wiley, 1994, page 278. 
     For best results (i.e. minimal memory requirements in the system, and specifically on the card), two additional rules are preferable: 
     (f) The ratio factors R(I) would be set equal to each other (this is the reason for  10 B bettering  10 A). 
     (g) The number of purses, i.e. J+1, should be maximal but not exceeding the capacity needed to be stored on the card. 
     Combining these two rules, we obtain the most efficient configuration, which is a binary card with electronic coin denominations if 1EMU, 2EMU, 4EMU, 8EMU etc., each having a single accommodation on the payment card. The following example, in FIGS. 14 and 15 demonstrates the efficiency of a binary card. 
     FIG. 14 describes an embodiment of a payment system according to the present invention where each stored-value device includes 16 electronic coin-sub-storage-devices, for denominations of 1¢, 2¢, 4¢ . . . 32768¢. The payment card can accommodate a single electronic coin for each denomination; the POS and financial institution accommodate a plurality of each. The three highest electronic coin values are selected to have also an electronic bill function (see the end of §2.4 above), i.e. the card bearer is allowed to make manual loads for values that are an integer multiple of $81.92. When operated according to the procedure of FIG. 13, transaction statistics (see §2.8 and FIG. 21) teaches that the highest electronic coin type ($327.68) will revolve in the cycle pool-purse-drawer-pool; the other two electronic bills ($163.84 and $81.92) will revolve in this cycle with some percentage also in the purse-drawer-purse cycle, depending on the typical loading pattern of consumers (the more consumers tend to load higher electronic bill values, the more electronic bill change of smaller electronic bill values will be observed). The smaller electronic coins (1¢ to $40.96) will revolve in the cycle purse-drawer-purse. 
     FIG. 15 calculates the storage requirements for the binary scheme of FIG. 14, for 150 million cards ( 150 - 1 ). The card may accommodate up to one electronic coin of each type, which leads to the estimate of 150 million electronic coins of each type ( 150 - 3 ), requiring 28 bits for a unique serial number for each electronic coin belonging to a specific type ( 150 - 4 ). Adding 3 party bits ( 150 - 5 ), we obtain 31 bits per type ( 150 - 7 ). Multiplying this number by 16 for the 16 types, and dividing by 8 to convert from bits to bytes, the rock-bottom requirement of 62 bytes per card is obtained. Assuming that a POS is required to provide space for 100 coins of each type 6,200 bytes of memory will be required for each POS ( 150 - 11 ). As each electronic coin requires a single bit at the financial institution&#39;s pool (FIG.  3 ), 150,000,000 cards multiplied by 16 types and divided by 8 (for bit-to-byte conversion) yield the number of 300,000,000 bytes storage requirement ( 150 - 12 ) at the pool, which is easily provided by any personal computer&#39;s disk. 
     2.6. A PAYMENT SYSTEM WITH A MIXTURE OF CARD TYPES (FIG. 16) 
     A single payment system according to the present invention may serve a variety of card types. FIG. 16 describes such a payment system. A number of electronic coin types are selected for the entire system, according to the rules of §2.5 above. The highest electronic coin level is selected in this embodiment to serve also as electronic bill. That is, manual loading an integer multiple of this coin is allowed. Each POS  160  has a charge drawer and a number of electronic coin drawers according to the system-level selected electronic coin types. Another type of POS  161  omits the charge card function, e.g. for vending machine applications. A computer system of financial institution  162  has charge accounts and a number of electronic coin pools according to the system-level selected electronic coin types. The system serves a variety of payment cards, including electronic coin- 0  purses  163  (see also FIG.  1 ), combination charge/purse cards  164  with auto-reload function (see also FIGS.  5  and  9 ), multi-stage “purse” purse cards  165  where reloading is limited to the higher value electronic coins only (see also FIGS.  11  and  14 ). The system also serves payment cards  166 , where the card allows reloading by either manual reload of the electronic bill purse (such as intentional reload is important if the consumer wishes to make purchases under absolute anonymity and privacy), or automatically from his charge card according to the scheme of FIG. 6, for maximum convenience. 
     2.7. THE RECOMMENDED PAYMENT SYSTEM (FIG. 17-18) 
     The choice of a “preferred” configuration depends on the needs and preferences of specific environments. One major consideration is efficiency, the other major consideration being friendliness. For example, the most efficient binary, 16-stage system of §2.6 may be hard to understand to many, and the required reload of integer multiples of $81.92 may be strange an inconvenient. 
     FIG. 17 presents a recommended, multiple stage payment system, constructed according to rules of §2.5 above. Its operation according to FIG. 13 enables two reload options for the customer choice: automatic reload from the charge card according to FIG. 6 for maximum convenience (this will also keep the total electronic coin value under $25), or manual load with integer multiples of $25 for maximum anonymity and privacy (with a maximum purse capacity of $274.99). Although not an optimal (binary) division among the electronic coin denominations, the selected values show a very efficient performance (FIG.  18 ), while making use of denominations that are practical to use and easy to understand, as they resemble real-life denominations of conventional coins and bills. (It would be appreciated, however, that except for load transactions, the entire division into separate denominations is merely a technical aspect, which may be kept transparent to consumers and merchants). 
     FIG. 18 calculates the storage requirements for the configuration of FIG.  17 . The different electronic coin denominations are grouped in line  180 - 1  according to their multiplicity  180 - 4 , taken from 171 of FIG.  17 . The number of cards in circulation  180 - 3  is assumed to be 150 million. The total number of electronic coins is estimated as the total capacity of all cards (actually, cards are expected to accommodate abut 50% of this capacity, while the remainder being distributed among POS and financial instigation computers). Line  180 - 5  calculates the total number of electronic coins for each of the group members of line  180 - 1 , but multiplying the values from lines  180 - 3  and  180 - 4 . The number of bits needed for a unique serial number for each card type is calculated in  180 - 6 , and 3 parity bits added at  180 - 7  to yield the result at  180 - 8 . The size of each group (see  180 - 1 ) is presented in line  180 - 10 , for multiplying the numbers from line  180 - 9  to yield the total number of bits for each group. The total number of bits is summarized in line  180 - 12 , and converted to bytes in line  180 - 13 . 
     The POS calculation estimates preparing room for 100 electronic coins for each denomination, except the $25 denomination where room for 200 electronic coins is provided. Line  180 - 14  shows the room for the entire group. When multiplied by the number of bits per each electronic coin from line  180 - 8 , the number of bits is obtained in  180 - 15 , to be summarized in  180 - 16  and converted into bytes in  180 - 17 . 
     The financial institution calculation multiplies the total number of electronic coins  180 - 5  by group size  180 - 4  divided by 8 (bit-to-byte factor) to yield line  180 - 18  which is summarized in  180 - 19 . 
     The numbers derived from FIG. 18 show very reasonable data storage and transfer requirements for a system with 150,000,000 cards, which is sufficient to cover the entire U.S. needs. Expanding the same system to a mammoth 5 billion card system, will result in requiring 137 bytes per card, 3,755 bytes per POS, and about 17 GB for the financial institutions computer system; these numbers reconfirm the feasibility of the present invention for implementation in any desired scale. 
     2.8. COIN PICKING CRITERIA FOR GENERALIZED STORED-VALUE DEVICES 
     As previously noted, according to the present invention, a payment card has a memory space allocated of R(I)-1 for electronic coin(I), where 0≦I≦J−1. This condition places strict limits on the range of electronic coins which a payment card can hold and therefore places strict limits on the range of electronic coins which a payment card can pay or accept. 
     For example, suppose a payment system with an EMU of 1¢ has multiple electronic coin types as follows: 1¢, 10¢, and $1. As provided above, the payment card will have memory space allowed for 9 of the 1¢ electronic coins and 9 of the 10¢ electronic coins. 
     Now consider a situation where the payment card contains only the following electronic coins: eight of the 1¢ electronic coins and one $1 electronic coin, for a total value of $1.08. In this example, the payment card must make a payment of 83¢. This amount is less than the value contained in the payment card, but the payment card does not have the payment amount in the specific electronic coins to make the payment exactly, and so it will be necessary to pay the $1 electronic coin and receive smaller electronic coins as change. If, however, the payment card pays on the $1 electronic coin, the change returned would be only 10¢ electronic coin and seven 1¢ coins. But although there is capacity for the payment card to accept the 10¢ electronic coin, there is insufficient memory to accept seven 1¢ electronic coins, because the payment card already has eight such coins with a maximum capacity of nine. Thus, the payment card must pay the $1 electronic coin plus three 1¢ electronic coins, and receive two 10¢ electronic coins as change. 
     For generalized stored-value devices, however, there are no such strict limitations on the number of electronic coins of each type which may be held. The memory available for storing electronic coins in a generalized stored-value device is not so severely constrained and may be made arbitrarily large. Thus, large numbers of electronic coins may be held in stored-value devices other than payment cards. 
     In the example presented above (a payment system with an EMU of 1¢ and having multiple electronic coin types as follows: 1¢, 10¢, and $1), a general stored-value device (other than a payment card), can have memory space allocated for large numbers of each of the electronic coin types. Thus, if such a stored-value device were to contain eight of the 1¢ electronic coins and one $1 electronic coin, for a total value of $1.08, and must make a payment of 83∞, there are a number of different options for doing so, including but not limited to: 
     (i) The general stored-value device could apply the same rules that are in effect for a payment card. In this example, the device would pay the $1 electronic coin plus three 1¢ electronic coins, and receive two 10¢ electronic coins as change. 
     (ii) The general stored-value device could simply pay the smallest available electronic coin(s) that equal or exceed the payment amount and receive change with the smallest number of coins. In this case, the device would pay the $1 electronic coin and receive one 10¢ electronic coin and seven 1¢ electronic coins as change. After such a transaction, the device would contain one 10¢ electronic coin and 15 of the 1¢ electronic coins. This would cause no difficult in the device, because there is sufficient memory allocated to accommodate these 15 electronic coins. 
     (iii) The general stored-value device could simply pay the smallest available electronic coin(s) that equal or exceed the payment amount and receive change in the smallest electronic coin type. In this case, the device would pay the $1 electronic coin and receive 17 of the 1¢ electronic coins. 
     Option (c) is illustrated in the flowchart of FIG. 37, where a consumer PC makes a payment to a merchant server. In a step  950 , the consumer PC with $BALANCE in the purse interfaces with the merchant server to pay $SUM, where $SUM does not exceed $BALANCE. In step  952 , a coin picking criterion is employed by which electronic coins of the purse are chosen to pay the smallest value that is not less than $SUM (the existence of a set of electronic coins in the purse that meets this criterion is assured, because the available $BALANCE in this case is not less than $SUM). The value of the selected electronic coins is denoted as $AMOUNT in step  952 . Finally, in a step  954 , the merchant server returns change equal to the difference between $AMOUNT and $SUM. The coin picking criteria used in the making of change is that $AMOUNT-$SUM, if non-zero, is returned to the purse in the form of electronic coins having the denomination of the EMU. If the purse has the proper electronic coins to pay $SUM exactly ($AMOUNT=$SUM), the $AMOUNT-$SUM=0 and no change need be returned. 
     2.9 TRANSACTION STATISTICS 
     In the specifications relating to FIGS. 5,  9 ,  11 ,  14  and  17 , it has been stated that the amount of electronic coins of a specified value flowing from cards to a POS as payment, equal in average to the amount of similar electronic coins flowing from same POS to cards as change. 
     Reference will be made now to FIGS. 5 and 6, recalling also the rules of §2.2 above, the focus being on decision  63  and transactions  65 ,  66 . 
     A first important conclusion is that the amount of stored value ($BALANCE) will be maintained smaller than $LIMIT. Even if initially $BALANCE is of a larger value, transactions  65  will deplete the purse until the purse contents is smaller than $BALANCE. Then, in the next transaction, $BALANCE will be either further depleted by  65 , or increased by adding change through transaction  66 . However, an amount of ($LIMIT-$SUM), added to $BALANCE in  66 , equals $LIMIT-($SUM-$BALANCE), which is smaller than $LIMIT under condition  63 . 
     A second important point is that, after a large number of transactions with many purses and many POS (and since neither the consumer nor the merchant have any influence or preference regarding $BALANCE), the value will be a random number evenly distributed between zero and 1 EMU less than $LIMIT. 
     Therefore, the decision in  63  will yield probability of $SUM/$LIMIT (which is the probability of  63  to be false) to transfer ($LIMIT-$SUM) from the POS to the card, and probability of (1-$SUM/$LIMIT) to transfer $SUM from the card to the POS. The expected value of both directions (obtained by multiplying the transferred value by its probability) is identical, which proves the claim that, on average, pay  55  and charge  56  equal each other. 
     An analogous discussion with FIG. 13 yields similar results, based upon an analogy between: FIGS.  13 =&gt; 6 ; decisions  136 =&gt; 63 ; transfers  136 - 1 =&gt; 65  and  136 - 3 =&gt; 66 ; and values $PAY=&gt;$SUM, $D(I+1)=&gt;$LIMIT and $INPURSE(I)=&gt;$BALANCE; respectively. This explains why electronic coins actually revolve between electronic coin purses and electronic coin drawers of the same denominations, in all transaction levels of FIGS. 9,  11 ,  14  and  17  which do not allow manual reload. 
     3. EDITIONS OF ELECTRONIC COINS (FIGS. 19-20) 
     One of the well-known attacks on security schemes is through repetitive attempts to guess the security parameters. The present invention provides an effective countermeasure: issuing a new edition of electronic coins, with a new set of security parameters, periodically (say, each six months), setting an expiration date of the previous edition for a reasonable time after the new edition issues (say, another four months), and devising means at all transaction levels to drain payment cards and POS from electronic coins of the previous edition during all transaction types. These electronic coins are directed into the respective edition&#39;s cash pool, where each electronic coin is counted and accounted for. At the expiration date of the edition, the value of all electronic coins that have not been claimed (i.e. all old edition&#39;s electronic value that has been lost or abandoned by card holders) is counted and can be accounted for accurately, which is another object of the present invention. 
     FIG. 19 demonstrates data organization in an electronic coin purse for sharing the allocated memory for a specific electronic coin type between two electronic coin editions. A register  192  stores the denomination of the electronic coin type, while register  193  stores the maximum number of electronic coins of the respective type, which can be stored in the card. Referring to the two editions as “A” and “B”, registers  194  and  197  contain the security parameters (passwords, signatures, etc.) related to the two editions, registers  195  and  198  include the respective expirations dates while registers  196  and  199  contain the number of electronic coins currently stored from each edition. Registers  190 - 1  to  190 -NA and  191 - 1  to  191 -NB contain the serial numbers for the electronic coins currently stored in the purse. In this way, a minimal memory space (even for a single electronic coin, such as for 50¢ ELECTRONIC coins in card  171  of FIG. 17) can be effectively divided between two editions effectively. At the POS drawer level, a similar technique can be used to divide the memory space between the two editions, while at the financial institution pool, the two editions are preferably managed separately. FIG. 20 shows a two-edition electronic coin storage of 1¢ electronic coins (register  200 ), similar to the storage technique of FIG.  3 . Registers  201 ,  202 ,  205  and  206  contain the limits of issued electronic coins for each edition, registers  203  and  207  contain the security parameters for each edition, and registers  204  and  208  include the respective expiration dates. 
     Preferably, whenever electronic coins have to be transferred between cards and POS or between POS and financial institutions, those from the older edition will be selected first, while transfers in the opposite directions, will prefer electronic coins from the newer edition. This will effectively refresh the electronic value in circulation by draining cards and POS from the older edition&#39;s electronic coins and moving them to the electronic coin pools. 
     4. MONEY FLOW AND SYSTEM-LEVEL CONTROL (FIG. 21) 
     Preferably, when a monetary system of the present invention is established, all electronic value will be generated and deposited in one or more electronic coin pools. Then, prior to supplying a new payment card to a consumer, this card will be preloaded by transferring electronic coins from an electronic coin pool to the card. A POS joining the system, will be initially primed with a specified amount of electronic coins, to ensure its flawless operation. After theses initializations, electronic money will flow through various transactions as described below. 
     The way money flows in the system of the present invention is demonstrated in FIG. 21, in reference to the embodiment of FIG.  17  and the payment procedures of FIGS. 6 and 13. 
     An electronic bill flow  210  from a pool to a purse occurs when a manual reload of electronic bills (i.e., higher-denomination electronic coins allowed for manual reload) is executed by the user. An electronic coin pool-to-purse load  211  for lower-denomination electronic coins occurs only once per each card, prior to supplying the preloaded card to the user. An electronic bill flow  212  and a charge orders flow  213  from card to POS take place to pay for higher-cost purchases or to automatically purchase smaller-denomination electronic coins (blocks  66  in FIG.  6  and  136 - 2  &amp;  136 - 3  in FIG.  13 ). The POS will communicate from time to time with the financial institution, to initiate a charge order flow  219  and an electronic bill flow  218 , for settlement. Electronic coins of smaller denomination than electronic bills, actually revolve between cards and POS: at each small purchase, electronic coins flow from the card to the POS as payment ( 214 ) or from the POS to the card as change ( 215 ). It has been shown in §2.8 that statistically, for each electronic coin denomination, the average flows in both direction are equal, which explains the usage of the term “revolve”. 
     Electronic coins flow ( 217  and  216 ) between POS and financial institutions for various purposes: 
     (a) Priming the POS, before staring a business cycle, with a sufficient amount of each electronic coin type, for having sufficient change to compensate for statistical fluctuations (see  58  in FIG.  5 ). 
     (b) Emptying the POS from electronic value at the end of a business day, if so desired by security consideration or required by law. 
     (c) Adjusting the amount of electronic coins in the POS between the end of a business cycle and the beginning of the following one; this may be required if the POS is not emptied at the end of a business cycle, to compensate for statistical fluctuations which may cause the amount of electronic coins of each denomination to be substantially below or above the desired amount at the beginning of the next business cycle. 
     The two electronic coin cycles ( 214 / 215  and  216 / 217 ), although transferring on the average a zero monetary value, cause a continuous diffusion and mixing of electronic coins among financial institutions, POS and cards. This mixing process has two very important roles: 
     (a) Security: the mixing process allows a continuous sampling, at the financial institutions&#39; electronic coin pools, of the electronic coins in circulation, to identify invalid electronic coins of each type. Such invalid electronic coins are identified by finding serial numbers out of the issued range ( 32  and  33  of FIG.  3 ), or by finding a forbidden repetition of the same serial number. When finding such invalid electronic coins, the mixing process reveals either a system malfunction or a breakdown of security. Also, the number of such invalid electronic coins and the size of the sample, provide a reliable estimate to the overall damage size. 
     (b) Refreshing: the mixing process allows effectively replacing an older electronic coin edition with a newer one by preferring flow of older electronic coins in the direction of the financial institution. 
     To enhance the effectiveness of the electronic coin mixing at both the card-POS and POS-financial institution levels, the purse-drawer and drawer-pool transaction procedures will preferably include also the following routines: 
     (a) The picking of each electronic coin of certain edition and type for transfer from one stored-value device to another, will be made according to preselected picking criteria, such as first-in-first-out of random-picking. 
     (b) A forced-exchange mode will allow exchange of an equal, selectable number of electronic coins of a selected denomination between two communicating stored-value devices; this will allow the system operator, during normal, routine transactions and transparently to consumers and merchants, to accelerate the draining of an older edition and/or to increase the efficiency and reliability of the security sampling process described above. When used for accelerating the refreshing, such forced exchange will move a selectable number of an old-edition electronic coins of a selected denomination from a purse to a drawer or from a drawer to a pool, while moving the same number of a new-edition electronic coins of the same denomination, from the drawer to the purse or form the pool to the drawer, respectively. When refreshing, devices establish a priority of the transfer of electronic coins of a first edition with respect to the transfer of electronic coins of a second edition, where the priority depends on the direction of transfer with respect to the financial institution. If a first device makes a transfer to refresh a second device that is more “distant” (in terms of the device hierarchy) from the financial institution, the first device sends a new electronic coin to the second device and receives an old electronic coin in exchange. In this way, the old electronic coins have a preferred movement back to the financial institution, where they are collected and retired from circulation. In contrast, when used for accelerating the mixing, a selectable number of electronic coins of the same edition and denomination will be exchanged between a purse and a drawer or a drawer and a pool, on a first-in-first out or random picking basis at each stored-value device. 
     Following is an example of forced exchange, with respect to the embodiment of FIG. 17 with the procedure of FIG.  13 . Suppose that a payment card performing a payment transaction currently accommodates two old and two new 10¢ electronic coins (“old” and “new” referring to editions,) and two old and two new $1 electronic coins, and according to the procedure of FIG. 13, one 10¢ electronic coin and no $1 electronic coins have to be transferred to the POS. According to criteria downloaded to the POS from the financial institution during a previous transaction, the POS now takes from the card two old and one new 10¢ electronic coins, and returns two new 10¢ electronic coins; the POS also takes from the card one old and one new $1 electronic coin, and returns two new $1 electronic coins. By these forced exchanges, both edition refreshing and coin mixing are accelerated. Similar forced exchanges are executed during routine transactions between POS and financial institutions. 
     4.1. DUPLICATION-RESISTANT ELECTRONIC COIN TRANSFER PROTOCOL 
     Throughout the embodiments of the present invention there is the principle that electronic coins may not be created within a payment card or POS, and, as described herein, the system has features that statistically monitor the electronic coin pools to detect duplicate electronic coins. If no duplicates are detected, the system is assumed to be functioning properly. Otherwise, the system permits the tracing of duplicates back to their point of origin for investigation and corrective action. It is desirable, however, to have an electronic coin transfer protocol that precludes the possibility of a duplication of value. An embodiment of such a transfer protocol is presented herein. 
     Duplicate electronic coins can be the result of deliberate attempts to create unauthorized value (“counterfeiting”), or could be the result of simple transaction failures. For example, consider the case where an electronic coin is to be transferred from a payment card to a POS using a simple transfer protocol, as illustrated in FIG.  27  and FIG. 28. A payment card  500  contains an electronic coin  500 - 1  that is to be transferred to a POS  502  (FIG.  27 A). The transfer consists of making a copy electronic coin  502 - 1  of original electronic coin  500 - 1  within POS  502  in a copy operation  504  (FIG.  27 B), and then deleting original electronic coin  500 - 1  in payment card  500  with a deletion operation  506  (FIG.  27 C). Both copy operation  504  and deletion operation  506  are supervised by a transaction manager  501 . After completion of this protocol, original electronic coin  500 - 1  in payment card  500  has been transformed into copy electronic coin  502 - 1  in POS  502  (FIG.  27 D). Because copies of electronic coins are indistinguishable from original electronic coins in this system, this procedure has the net effect of transferring an electronic coin from the payment card to the POS. The steps of this simple protocol are shown in FIG.  28  and consist of a copy operation  504  followed by a deletion operation  506 , as also illustrated in FIG.  27 B and FIG. 27C, respectively. Unfortunately, this simple protocol suffers from a weakness in that if anything interrupts the completion of the protocol, there is the possibility that multiple copies of a single electronic coin will exist. For example, suppose payment card  500  is disconnected from transaction manager  501  after copy operation  504  has taken place, but before deletion operation  506  has taken place. This could happen through a number of natural and possible events. In addition to a genuine power failure which disables transaction manager  501 , a consumer might suddenly withdraw his payment card from the POS prior to the execution of the deletion operation, either innocently without realizing the effect, or deliberately with the intent to induce such failure. In any case, the result would be that POS has received an electronic coin credit, but the payment card still has the electronic coin available to be spent again (FIG.  29 ). In certain prior art implementations of this simple protocol, the electronic coin is “flagged” by the payment card prior to transfer and retains the internal flag in the event of such a failure. This could conceivably prevent the electronic coin from being erroneously considered as a spendable coin, but the information contained in the flag is insufficient to enable an interrupted transfer to be completed. 
     To eliminate such problems, a transfer protocol can be employed which is fundamentally resistant to electronic coin duplication. One such protocol is illustrated in FIG.  30  and FIG. 31, also in terms of a transfer from a payment card to a POS, although the protocol is general and would apply equally well in the reverse direction. As with the simple transfer protocol illustrated above, there is a transaction manager, but for clarity in the drawings the transaction manager is not shown in FIG. 30 or FIG.  31 . It should first be noted that a monetary transfer is generally defined as a “transaction ” in which one account is credited with a certain amount and another account is debited with the exact same amount. Transactions are “atomic” or “indivisible” in that (ideally) either the entire transaction is executed or no part of the transaction is executed. In on-line systems, for example, a provision is made either to “commit” the transaction (to transform both accounts to the state of the executed transaction) or to “roll back” the transaction (to return both accounts to the state they were in prior to the initiation of the transaction). Traditionally, in the event of an interruption of the transaction (such as by a power failure), the “roll back” option is taken, in which case the transfer was unsuccessful. The transfer could be attempted again, or it could be left unperformed with both accounts as they originally were. The “commit” option is taken only upon the successful completion of the transaction. In either event, the integrity of the system and the accounts involved is protected. In the present case of payment cards and electronic coins, provision for “commit” and “roll back” options would serve to guarantee that the transfer of an electronic coin would be performed completely or not performed at all, and would therefore insure that electronic coins are neither created nor destroyed in the course of transfers or attempted transfer. Unfortunately, current embodiments of the “commit” and “rollback” features require a central administrator (such as a central on-line computer) to oversee the transaction, and this is difficult or impossible to provide in the fluid environment of transfers between payment cards and points-of-sale. Accordingly, in an embodiment of the present invention, cryptographic techniques are employed in the transfer protocol to approximate, as closely as possible within the system of the present invention, a “commit” and a “roll back” option. 
     In this protocol, payment card  500  has a public-private keypair consisting of a public key  500 - 3  and a private key  500 - 5  (FIG.  30 A). Likewise, POS  502  has a public-private keypair consisting of a public key  502 - 3  and a private key  502 - 5 . This protocol can utilize any of the suitable public key encryption methods well known in the art. For purposes of this protocol, public keys need not be certified or authenticated, and so either party involved in a transfer may obtain the public key of the other party to the transfer by a simple request to that party. In this protocol, public key encryption serves as a one-way function from the perspective of the sender of an electronic coin, to prevent that electronic coin from inadvertently becoming available for spending a second time by the sender. The coin, however, is not immediately destroyed, but remains for a time with the sender in encrypted form for controlled recovery in the event that a “roll back” is needed. 
     In this particular embodiment of the protocol, public key  500 - 3  and private key  500 - 5  are not utilized in the transfer of electronic coin  500 - 1  from payment card  500  to POS  502 , but they are shown here because they would be needed for transfer of an electronic coin form POS  502  to payment card  500 . 
     In the first step of the transfer protocol, payment card  500  obtains public key  502 - 3  from POS  502  in a key-exchange operation  510  (FIG.  30 B). In the second step, payment card  500  encrypts electronic coin  500 - 1  with public key  502 - 3  to obtain an encrypted electronic coin  500 - 2  in an encryption operation  512  (FIG.  30 C). In a preferred embodiment, this encryption is done “in place” so that electronic coin  500 - 1  is replaced by encrypted electronic coin  500 - 2 . Thereafter, as far as payment card  500  is concerned, electronic coin  500 - 1  has been effectively “destroyed” so that no copy of it exists which can be used by payment card  500  for any purpose other than the intended transfer to POS  502 . Electronic coin  500 - 1 , however, still exists and can be recovered in the event of failure even through it is unavailable of use by payment card  500 . In the third step, payment card  500  deletes the local copy of public key  502 - 3  in a deflection operation  514  (FIG.  30 D). In the fourth step, payment card  500  sends a copy  502 - 2  of encrypted electronic coin  500 - 2  to POS  502  in a copy operation  516  (FIG.  30 E). At this point, two copies of the original electronic coin exist, but neither is immediately usable, since both are encrypted with public key  502 - 3 . In the fifth step, POS  502  decrypts encrypted electronic coin  502 - 2  with private key  502 - 5  in a decryption operation  518  to obtain a valid electronic coin  502 - 4 , which is the same as original electronic coin  500 - 1  (FIG.  30 G). In the sixth step of the protocol, POS  502  notifies payment card  500  that it has electronic coin  502 - 4 , in a notification operation  520  (FIG.  30 G). In the seventh and final step of the protocol, payment card  500  deletes encrypted electronic coin  500 - 2  in a deletion operation  522 , thereby completing the transfer (FIG.  30 H). After completion of the protocol, payment card  500  no longer has electronic coin  500 - 1 , and POS  502  has electronic coin  502 - 4  (FIG. 30 I). 
     An important property of this duplication-resistant protocol is that at no time does the transferred electronic coin exist in unencrypted form in both the payment card and the POS. This means that inadvertent or deliberate replication of the electronic coin cannot occur. Furthermore, although multiple copies of the encrypted electronic coin may exist simultaneously for a brief period, there are usable only to the intended recipient and cannot create a liability to the system if they happen to persist after the transaction is completed. These encrypted electronic coins could be sent multiple times only to the original intended recipient, and the serial number of the electronic coin can, in principle, can identify multiple transfer of the same coin to the recipient, should this occur, in which case the recipient would ignore the extraneous transfers. 
     It should be noted that this duplication-resistant transfer protocol assumes that both the sender and the recipient (the payment card and the POS) are trusted, secure devices. This duplication-resistant transfer protocol by itself does not provide protection against duplication of electronic coins by an attack in which an attacker impersonates an authorized sender, such as by presenting a counterfeit or compromised payment card. In such a case, the attacker is clearly not bound by the requirement of the protocol, for example, that the electronic coin be encrypted “in place”, and can therefore maintain multiple copies of the same electronic coin in unencrypted form, or may otherwise make unlimited copies of electronic coins. Additional security measures are needed to protect against such attacks, and this transfer protocol should be conducted within a suitable secure environment. For example, the entire session between the payment card and the POS can (and should) be encrypted according to methods well known in the art. The purpose of the transfer protocol illustrated herein is to provide a basis for treating an electronic coin transfer as a transaction in the context of secure devices whose interconnectivity and/or power-dependent operability cannot be guaranteed. 
     Once the electronic coin that is to be transferred has been encrypted with the public key of the intended recipient, it becomes permanently unavailable for any purpose other than sending to the intended recipient. For this reason, although this duplication-resistant transfer protocol provides better recovery from error conditions than the simple transfer protocol illustrated above (FIG.  27  and FIG.  28 ), true “commit” and “roll back” operations are not directly provided. Rather, the duplication-resistant transfer protocol retains an interrupted transfer in a state that is resumable, and which may be completed at some future time; subsequent procedures can effectively implement the “commit” and “roll back” operations. FIG. 31 illustrates the flow of the duplication-resistant transfer protocol as shown in FIG. 30, with some added features pertaining to maintaining the integrity of the transaction in the event of interruption. For example, after copy operation  516 , a decision point  517  checks to determine if the copy has been successful. If not, copy operation  516  is retried. It is important to note that the retry need not be attempted immediately, but that an arbitrary time can elapse before the retry is made. For example, suppose a customer puts a payment card into a POS (such as a vending machine), but the transfer of the electronic coin from payment card to POS is somehow interrupted, such that the payment card encrypts the electronic coin but the electronic coin is not copied to the POS and therefore remains with the payment card. At a future time, the customer can return to the same POS and complete the transaction or obtain a refund. Suppose, however, that the encrypted electronic coin is successfully copied to the POS but the transfer protocol is interrupted before the encrypted coin can be deleted from the payment card. In that case, if the customer returns to the same POS to resume the transaction, decision point  519  (FIG.31) checks to determine if the electronic coin has been previously transferred. If so, the POS deletes the decrypted electronic coin (this electronic coin is a duplicate) and signals the payment card to do likewise. If the electronic coin has not been previously transferred, the transaction resumes and completes normally. 
     It should also be noted that, although it is unsatisfactory for duplicate electronic coins to be created within the system of the present invention, the occasional loss of an electronic coin is considered to be a tolerable condition. If, for some reason, a transfer is interrupted as described above, but the POS becomes permanently inaccessible to the payment card, there will generally be no way to recover or use the encrypted electronic coin, and thus the electronic coin could be effectively lost. It is possible, however, for the issuer of the POS to maintain a copy of the private key of the POS and thereby make it possible to recover the lost electronic coin from the payment card to take account of such possibilities. 
     5. SEMI-COUNTABLE ELECTRONIC MONETARY SYSTEM (FIGS. 22-24) 
     In the statistical analysis of §2.8 and its symbolic summary at FIG. 21, it has been shown that lower-denomination electronic coins (i.e. electronic coins of denomination which is not allowed for manual purse loading) revolve between cards and POS and between POS and financial institutions, with no net long-term effect on the system-level money flow. The money flow has been shown there to take place through transfers of electronic bills (i.e., electronic coins of higher denomination allowed for manual reload) and of charge orders. This behavior allows further simplification of the system of the present invention, by defining the “semi-countable” concept. 
     “Electronic penny” will be defined as an electronic monetary instrument having the value of one EMU (elementary monetary unit). The electronic penny (herein denoted in the drawings as an “E-Penny” for convenience) is similar to an elementary electronic coin in its payment capability; however, an electronic penny has no serial number, and therefore cannot be traced individually. Its storage is essentially in counter devices, which count the number of electronic pennies stored therein. Transfer of an electronic penny from a source counter device to a target counter device involves incrementing the count in the target counter device, while decrementing the count in the source counter device. 
     FIG. 22 describes schematically a semi-countable embodiment of the present invention. A financial institution  220  includes charge accounts  220 -A, and an electronic bill pool  220 -B storing electronic coins of, say $25 each, which are allowed for manual load into electronic bill purses of payment cards. An electronic penny pool  220 -P is a counter device, for having therein the number of pennies (e.g. of 1¢ value) currently stored at financial institution  220 . A POS  221  includes a charge drawer  221 -A for storing therein charge orders received from payment cards. POS  221  has an electronic value purse  221 -C which includes an electronic bill drawer  221 -B to store therein $25 electronic coins received from payment cards, and an electronic penny drawer  22 -P which is a counter device having the number of 1¢ pennies currently stored therein. 
     Payment cards  222 ,  223  and  224  represent three types which may co-exist in the system. Payment card  222  includes a charge card  222 -A, having a minimum charge limit of $25 (the charge limit and the electronic bill value are preferably equal, to simplify the operation of the procedure of FIG.  23 ;) thus payment cards  222 ,  223 , and  224  can be used to pay amounts of $25 or more; these payment cards also include an electronic penny purse  222 -P, which is a counter device having the number of 1¢ pennies currently stored therein. Payment card  223  includes an electronic bill purse  223 -B for manually loading thereto and paying therefrom $25 electronic coins; payment card  223  also includes an electronic penny purse  223 -P. Payment card  224  includes charge card  224 -A, and also has an electronic value purse  224 -C that includes an electronic bill purse  224 -B and an electronic penny purse  224 -P. 
     FIG. 23 describes the operation of the embodiment of FIG. 22, for paying an amount $SUM with a payment card having $BALANCE in its purse, wherein $BALANCE is the sum of the contents of both the electronic bill purse and the electronic penny purse included in the payment card. At a decision point  232 , the feasibility of electronic value payment is checked. If an affirmative decision is found, then in a step  233  $SUM is paid by electronic value, by any or both electronic bills and electronic pennies with the possibility of payment with electronic bills and receiving change by electronic pennies (for guidance see FIG.  13 ). At a decision point  234 , payment has been found unfeasible for the current electronic value in the purse, and therefore payment by charge is checked, i.e. to verify that the payment card is of type  222  or  224 , but not of type  223 ; if charge in not available, then in a step  235  the user is instructed to reload his card manually with a number of electronic bills, or else the payment is rejected. At a decision point  236 , a decision is made to pay $SUM through the charge card, or receive $25 via the charge card and return $25-$SUM in electronic pennies to the electronic penny purse. 
     Analysis of this procedure, according to the statistical consideration of §2.8, yields the following results: 
     (a) the amount of electronic pennies stored in electronic penny purse  222 -P,  223 -P or  224 -P will be a random number, evenly distributed in the range zero (inclusive) and $25 (exclusive); 
     (b) the average electronic penny flow into POS  221  equals the average electronic penny flow out of POS  221 , so there is no net effect on the money flow. 
     Consumers are allowed to select three payment cards:  222  for ultimate convenience (no reload option),  223  for unbanked consumers, and  224  for consumers who wish to have both ultimate convenience through incorporating charge card  224 -A, but will manually load their electronic bill purse  224 -B with sufficient amount of electronic value, prior to making a purchase where privacy is desired (electronic bill payment is not traceable, while charge payment is traceable). 
     Bankers may like the present embodiment because of minimal storage and data transfer requirement for both cards and POS. Because memory is allocated only for electronic coin storage of electronic bills (an electronic penny purse counting 2500¢ makes do with a two-byte counter), and assuming the storage of 40 or 80 $25 electronic bills, for accommodating up to $1,000 or $2,000 in each card or POS respectively, FIG. 24 shows that 180 bytes on the card ( 241 - 8 ) and 360 bytes in each POS ( 241 - 11 ) are sufficient. If, however, instead of 40 $25 electronic bills the card will accommodate 1 electronic bill of each $25, $50, $100 and $200 denomination and two $400 electronic bills, the required storage on the card, for an equivalent performance, becomes 24 bytes only. 
     The security behind the semi-countable concept is based on counting electronic bills as before, while monitoring the electronic penny transaction statistics between each POS and financial institutions, expecting zero average over a long period. Any POS substantially deviating from zero average will indicate a possible flaw in the system&#39;s security. 
     6. MULTI-ISSUER ENVIRONMENT 
     More than one financial institution may be involved in issuing electronic value. In such a situation, a plurality of electronic coin pools shall be maintained in the same system of the present invention. In such situations, a range of separate serial numbers will be allocated to each financial institution. When electronic coins are to be moved from POS to financial institutions (transactions  217  and  218  of FIG.  21 ), they will be routed to the respective financial institution according to their serial number. This sorting and routing will take place either at the POS level, or at the level of intermediate processing centers (not shown in FIG.  21 ), similarly to the techniques used commonly to route charge transactions to the respective financial institutions ( 219  in FIG.  21 ). 
     7. CARD-TO-CARD TRANSFER 
     Card-to-card transfer is a desirable feature in any electronic value system, for enabling person-to-person (e.g. parent to child) transactions. Such transactions were in conflict with “accountable” systems of the prior art, but are supported effectively under the present invention. When two cards interface through a transaction device (essentially similar to purse-to-drawer interface), transfer of electronic coins (each with its serial number) will maintain the integrity of the system under the present invention. 
     It should be noted, however, that, unlike in the case of card-to-POS transaction where the POS is primed with a sufficient amount of electronic coins of each denomination to enable flawless payment of any amount, card-to-card transactions are limited according to the electronic coins actually stored in both cards; thus a parent having a card of FIG. 17 currently having only two $5 electronic coins, will be able to transfer to his child&#39;s card currently sorting a single $1 electronic coin, only an amount of $4, $5, $9 and $10. 
     8. ANONYMITY AND PRIVACY 
     It would be appreciated that while there is a tight monitoring on each individual electronic coin in the system, this monitoring does not involve tracking of individual cards or car bearers, thus preserving customer anonymity and privacy, which is an important object of the present invention. 
     9. RECOVERING THE VALUE STORED IN LOST OR DAMAGED CARDS (FIGS. 25-26) 
     Referring to FIG. 16, card types  165  and  166  allow manual reload of electronic bills. Practically, such manual reloads may reach substantial values, e.g., $500 to $1,000. If a card is lost, stolen or broken, substantial damage may occur to the card owner. According to an aspect of the present invention, such damage may be minimized by recording the serial numbers of electronic bills loaded onto a payment card, and recovering the value of unused electronic bills when these electronic bills expire. Thus, when approaching a loading terminal, e.g. a special ATM, for a manual reload, paying for the loaded electronic bills with nay monetary instrument acceptable at this terminal (cash, any charge card, etc.), the serial numbers of the loaded electronic bills are recorded for further possible claims. 
     FIG. 25 (see also FIG.  20  and the related text) describes a preferred embodiment, where the user identifies himself at the loading terminal, e.g. by his credit card. The user identification data is transferred to the appropriate electronic bill pool related to each loaded electronic bill, where a user ID  257 -i is recorded in respect to serial number i, while a status bit  256 -i is turned to 0, signaling that the corresponding electronic bill has been moved from the electronic bill pool to an electronic bill purse. 
     FIG. 26 described another preferred embodiment, where the serial numbers of the loaded electronic bills  262  are recorded on paper slip  260  by the loading terminal along with a loading date  261 ; a confirmation code  263  is supplied by the terminal or the electronic value pool, to authenticate the entire slip&#39;s information. 
     Upon the expiration date, unused electronic bills (i.e. electronic bills that have not been returned to the respective electronic bill pool), can be identified automatically by an embodiment of the present invention. In the embodiment of FIG. 25, the original latest ownership of each unused electronic bill with serial number i can be identified from the respective register  257 -i; in the embodiment of FIG. 26, such original latest ownership can be determined by the user who presents a slip  260  having the latest loading date  261 . Upon receiving a claim for the value of a lost or damaged card, the financial institution may pay the user the value of the unused electronic bills. 
     To enhance security in the situation under consideration, a PIN may be required for any transaction that involves spending electronic bills. In this way, the electronic bills in a lost or stolen card will remain unusable, and therefore recoverable on the expiration date. 
     10. GENERAL COMMENTS 
     It will be appreciated that, for both payment cards and POS units, whenever a plurality of storage devices is mentioned, the present invention relates to logical memory management, and not necessarily to separate chips. For instance, a single hardware chip on a payment card can accommodate a charge card and a number of electronic coin purses. 
     It would be also be appreciated that whenever an apparatus (payment card, POS or financial institution computer) is described to include separate units to perform separate functions, such separation is basically logic, and several or all functions can be actually executed by a single microprocessor; also, in some cases when two apparatuses are described to interact to execute a mutual function such as transfer of money from one apparatus to another, some of the units described to be included in one apparatus can actually be moved to the other apparatus to perform their function from there. 
     The parity bits added to each electronic coin&#39;s serial number can take into account also the electronic coin&#39;s edition and denomination, thus enhancing the system&#39;s security and reliability. 
     The term “serial number” should be interpreted broadly, as any recordable data included in an electronic coin, identifying it and moving with it. It may contain electronic representation of any relevant identification data, such as issuer identification, issue date, expiration date, etc. 
     11. EXTENDED SECURITY MONITOR 
     The present invention can be expanded and extended to offer a comprehensive electronic value security scheme as follows (reference is made to FIG.  21 ): 
     a. Each electronic bill  210  flowing from bank to card, each electronic bill  212  flowing from card to POS, and each electronic bill  212  flowing from POS to financial institution, including the transaction path via all sorted-value devices involved, is reported to the electronic bill pool at the financial institution. Any mismatch is easily interrogated by the data available in the electronic pool the term “transaction path” denotes the sequence of devices that have engaged in successive transactions with a specific instance of electronic value, wherein the sequence of devices terminates at a financial institution. The term “intersection”, when used with reference to a transaction path, denotes any device which is in common with two or more transaction pather. 
     b. Card-to-card transfer of electronic bills is allowed for one transfer (ore a small number of transfers) only. In this case, the identity of the first card will be concatenated to the serial number, and flow with the serial number up to the electronic bill pool, thus maintaining a complete transaction path tracking. 
     c. Each POS and each intermediate computer in the settlement chain (normally, transaction information flows from a POS to central banks via several intermediate computers, e.g. local, regional, etc., not shown in FIG.  21 ), records each received electronic coin along with the identity of the source device which has supplied this electronic coin. This data is kept, normally passively, for about one month, and then its memory space if freed for further data recording. The embodiments according to the present invention which utilize this data are discussed in detail below. 
     d. Each link in the settlement chain maintains a “statistical trap”, to measure statistical moments of electronic coins flowing therethrough. Since electronic coin flow statistics are predictable, abnormalities (i.e. exceeding predefined statistical thresholds) will trigger an accelerated refreshing rate at all intermediate computers and POS below the device operating the respective alerting statistical trap. 
     e. Any electronic coins having an out-of-range or duplicate serial number that are found in the electronic coin pool, will trigger automatically a systematic query, wherein each device identified as supplying the electronic coin will be queried to provided information on the previous supplier of the electronic coin, down to the respective POS identifying the payment card. The reconstructed path will be used for human interrogation and intervention. The term “invalid electronic coin” herein denotes any electronic coin having an out-of-range serial number or a serial number which is identical to another electronic coin currently in circulation. 
     11.1. A CONTINUOUS ELECTRONIC COIN SAMPLING WATCHDOG 
     It will be appreciated that the security scheme described above incorporates complete electronic bill accountability and, at the electronic coin level, a combination of distributed, localized, passive data collection which is normally dormant, with very alert watchdogs (continuous electronic coin sampling; statistical traps). When the watchdog barks, a highly efficient, systematic query identifies the exact transaction path of invalid electronic coins for human intervention. An embodiment of a method according to the present invention for auditing the system to discover the presence and source of invalid electronic coins is described below. The auditing aspects of the method can also be applied to tracing the origin of any electronic value, including electronic bills, but are illustrated for electronic coins only. 
     During a certain period of time, a number of transactions involving the spending of electronic coins takes place. It is desired to detect if, during this time period, any of the electronic coins in circulation are duplicates or are out-of range, and, if so, what is the source of these invalid electronic coins. While duplicate or our-of-range electronic coins, representing unauthorized creation of value, are not permitted under the system of the present invention, an occasional invalid electronic coin is not a cause for alarm, as the values of electronic coins are low enough to limit the risk exposure which such electronic coins pose. Furthermore, because electronic coin editions according to the present invention have a limited lifetime, invalid electronic coins are automatically removed from circulation at regular intervals. Moreover, it is anticipated that the normal attrition of electronic coins due to losses (such as in lost or damaged payment cards) will always exceed the number of invalid electronic coins that may come into existence through natural stochastic processes (such as normal data errors). Counterfeit electronic coins, however, are invalid electronic coins that are intentionally created by attackers in an effort to cheat the system, and thereby pose a threat to the system&#39;s integrity. If counterfeit electronic coins occur at all, the occurrences would be more than just occasional, so it is important to be able to race counterfeit electronic coins to their source. The term “bogus electronic coin” herein denotes an invalid electronic coin which appears to be counterfeit electronic coin, but has not yet been confirmed by investigation to be a counterfeit electronic coin. The purposes of the continuous electronic coin sampling watchdog according to the present invention are therefore: 
     1. to determine if bogus electronic coins are in circulation; 
     2. if bogus electronic coins are not in circulation, to confirm this and thereby to establish a degree of confidence in the integrity of the system; 
     3. if bogus electronic coins are in circulation, to determine if the occurrences are serious enough to warrant further investigation; and 
     4. if the occurrences of bogus electronic coins warrant further investigation, to provide information leading directly to the source of the bogus electronic coins. 
     The continuous electronic coin sampling watchdog must work efficiently and be enabled at all times, yet not impose an undue burden of data processing on the system, that is, the continuous electronic coin sampling watchdog should operate invisibly in the background. This goat is attained by the present invention, as illustrated below for a case involving a bogus electronic coin in the form of an invalid electronic coin that has been put into circulation twice by the same payment card. 
     It should first be noted that there is nothing inherently wrong in having a payment card spend the same electronic coin more than once. Because electronic coins according to the present invention circulate, it is to be expected that a payment card will occasionally receive change that includes an electronic coin which was previously spent by that same payment card. A problem arises, however, when a payment card (or other device) spends an electronic coin that is presently in circulation elsewhere in the system, for this represents a duplication of value. The method according to the present invention of detecting such an invalid electronic coin at the electronic coin pool is both efficient and economical, and furthermore is able to identify the sources or sources of the duplicate electronic coins. The method can also be applied to detecting the sources of out-of-range electronic coins. 
     A preferred embodiment of the present invention for detecting duplicate electronic coins in a system of electronic cash is illustrated in FIG. 32, to which reference is now made. Payment cards  600 ,  610 ,  620 ,  630 , and  640  spend electronic coins  680 ,  682 ,  684 ,  686 , and  688 , respectively. Payment card  600 , however, spends electronic coin  680  more than once, and thus electronic coin  680  appears as a duplicate electronic coin. For example, payment card  600  might be defective, or might have been compromised by an attacker in order to produce and spend counterfeit electronic coins. In any case, electronic coin  680  is spent at a POS  650  and also, during the same general time period, at a POS  660 . (Payment card  600  and electronic coin  680  are emphasized in FIG. 32 to more readily distinguish them.) For the purpose of this example, it is assumed that electronic coin  680  is a counterfeit electronic coin, rather than merely a invalid electronic coin that has arisen incidentally from natural stochastic processes, such as data errors. However, the fact that electronic coin  680  is an intentional counterfeit cannot be absolutely determined without a thorough investigation, and therefore electronic coin  680  is referred to as a bogus electronic coin for this example. 
     In general, a stored-value device can maintain a received electronic value file whose records contain an electronic value identification field for specifying the electronic coins received from another stored-value device, along with a device identification field for specifying the identity of the other stored-value device form which the electronic coins were received. In this embodiment of the present invention, the electronic value is equivalent to monetary value, and thus the received electronic value file is denoted as a received electronic cash file. 
     POS  650  maintains a received electronic cash file  655  and POS  660  maintains a received electronic cash file  665 . As illustrated in FIG. 33, and as detailed below, a received electronic cash file contains records of each item of electronic cash received by a device during the course of a particular time period. In particular, the transaction records of received electronic cash file  660  and received electronic ash file  665  contain the serial number of each electronic coin which the POS has received during the time period along with the identity of the transferring device that supplied the electronic coin, which, in this case, will be a payment card. As noted previously, this data is kept passively by the POS for a limited time. A certain amount of memory is allocated for these transaction records, and once the memory is full, new transaction records systematically replace the transaction records corresponding to the transactions having the earliest transaction date. The amount of time a specific received electronic cash file is retained can be increased by increasing the memory allocated in the POS for the received electronic cash file, and should be sufficient to retain a specific transaction record long enough that the electronic coin of the transaction will circulate back to the financial institution for statistical verification, as described below. In general, a received electronic cash file contains transaction records with an electronic cash identification field corresponding to arbitrary forms of received electronic cash, such as electronic bills as well as electronic coins. In general, also, a received electronic cash file contains transaction records with a transferring device identification field which contains the identifier for the device that transferred the electronic cash. Transferring devices include, but are not limited to, payment cards, points of sale, and intermediate stored-value devices as noted below. 
     Returning to FIG. 32, subsequent to the initial transactions at POS  650  and POS  660 , the process of normal circulation augmented by the mixing and refreshing processes according to the present invention, causes electronic coins  680 ,  682 ,  684 ,  686 , and  688  from POS  650  and POS  660  to reach a financial institution  670  via optional one or more intermediate stored-value devices between financial institution  670  and the level of POS  650  and POS  660 . Intermediate stored-value devices include computers, servers, and special-purpose devices used to collect or transfer electronic cash from one device to another. Some generic intermediate stored-value devices (hereinafter referred to simply as “intermediate devices ”) are illustrated in FIG. 32 as an intermediate device  652  and an intermediate device  662 , with ellipsis ( . . . ) indicating the option of additional intermediate devices in the chain. Intermediate device  652  maintains a received electronic cash file  657  and intermediate device  662  maintains a received electronic ash file  667 . Because electronic coin  680  has been spent twice during the specified time interval (even at different POS terminals), there is a high probability that the two copies of electronic coin  680  will subsequently be found at financial institution  670  at overlapping times. The presence of the duplicate will be detected immediately by financial institution  670  at overlapping times. The presence of the pool is update, since the presence of a coin in the electronic coin pool is indicated by the setting of a bit corresponding to the serial number of electronic coin  680 . Financial institution  670  maintains a received electronic cash file  675  which lists each electronic coin and the identity of the transferring device (such as a point of sale or intermediate device) which supplied the electronic coin to financial institution  670 . In general, the transferring device can be any device which is appropriate to transfer electronic cash to the receiving device, including payment cards as well as points of sale and intermediate devices. 
     FIG. 33 shows the details of received electronic cash file  675 , received electronic cash file  665 , and received electronic cash file  655 . For simplicity, FIG. 33 shows the chain of electronic coin transfers to be from POS  650  and POS  660  directly to financial institution  670  (FIG.  32 ), without intervening devices, such as device  652  and device  662  (FIG.  32 ). Therefore, received electronic cash file  675  shows POS  650  and POS  660  as the devices from which financial institution  670  received the electronic coins in question. The method presented herein is general, however, and operates effectively regardless of what devices, if any, are in the chain between the POS and the financial institution. The method is illustrated for the general case in the flowchart of FIG. 35, which is described in detail below. Returning to FIG. 33, a transaction record  675 - 1  has fields specifying the date of the transaction, the electronic coin serial number and value, and the device from which the electronic coin was obtained. When financial institution  670  (FIG. 32) detects a duplicate of electronic coin  680  in the electronic coin pool, received electronic cash file  675  is consulted to determine the immediate sources of electronic coin  680  (FIG.  33 ). It is seen that transaction record  675 - 1  and another transaction record  675 - 2  both show the arrival of electronic coin  680 . Transaction record  675 - 1  shows that the first duplicate of electronic coin  680  came from POS  650 , and transaction record  675 - 2  shows that the second duplicate of electronic coin  680  came from POS  660 . At this point, POS  650  is queried to obtain selected data from received electronic cash file  655 , and POS  660  is queried to obtain selected data from received electronic cash file  665 . In both cases, the selected data consists of relevant records from the respective received electronic cash files, as illustrated by the example of FIG.  33 . It is next seen that received electronic cash file  655  contains a transaction record  655 - 1  which shows that the first duplicate of electronic coin  680  originally came from payment card  600 , and that received electronic cash file  665  contains a transaction record  665 - 1  which shows that the second duplicate of electronic coin  680  also originally came from payment card  600 . At this point, the source of the duplicate electronic coins has been pinpointed and the relevant information can be reported and used for further investigation, if warranted. 
     In the manner shown above, the original source of a bogus electronic coin can be quickly and economically determined. Note that this method does not require the storage and preservation of a vast quantity of archival data concerning transactions, but only a modest amount of data concerning relatively recent transactions. Moreover, this data is distributed thorughout the system, does not need to be centralized, and can be acquired and maintained by devices already present in the system at negligible cost. Furthermore, unless there is a need to do so, no analysis is performed on the transaction data, and even when there is a need, the analysis is relatively simple. Thus, according to the present invention, the keeping of transaction data and the analysis as needed does not place any undue burden on the system, but is immediately responsive to any conditions that warrant attention. 
     The general procedures for obtaining information about the source of a bogus electronic coin that arrives at the electronic coin pool of a financial institution are illustrated in FIG.  34  and FIG.  35 . These methods are illustrated for locating the source of a bogus electronic coin but also apply to locating the source of a genuine electronic coin. In FIG. 34, the financial institution merely maintains an alert for incoming bogus electronic coins. As noted previously, an electronic coin in the electronic coin pool is represented as a set bit in a serial number vector, so if a duplicate electronic coin or out-of-range electronic coin arrives at the electronic coin pool, it will be immediately detected using negligible effort, without the need for any data searching or comparisons. This alert for incoming bogus electronic coins is represented in FIG. 34 by a decision point  700 , which loops back upon itself if no bogus electronic coin is detected. If a bogus electronic coin is detected, then in a step  710 , the transaction records for that electronic coin are retrieved from the received electronic coin received electronic cash file of the electronic coin pool. Following this is a loop starting at a loop start  720  and ending at a loop end  740 , containing a step  730  in which the transaction path corresponding to each of the retrieved records is added to a list of transaction paths. When loop end  740  reaches the final record of the records retrieved in step  710 , the loop exists, and the list of transaction paths is processed in a step  750  to find intersections in the transaction paths. Finally, a report output procedure  760  issues a report for human use by investigators, who can pursue the manner as necessary. 
     A recursive method of deriving a transaction path for an electronic coin in the electronic coin pool is illustrated in the flowchart of FIG.  35 . The method starts by setting the current device of the financial institution&#39;s electronic coin pool in a step  800 . Next, in a step  810 , the received electronic coin received electronic cash file of the current device is obtained. At the beginning of this recursive method, this means the received electronic coin received electronic ash file of the electronic coin pool will be obtained. As the recursion proceeds, however, the current device will change. Next, the serial number of the subject electronic coin (the electronic coin whose transaction path is desired) is input as data  820 , and in a step  830  the device that previously handled the subject electronic coin is obtained, and in a step  840  the previous device is added to the transaction path. At a decision point  860 , it is determined whether the previous device has a received electronic coin received electronic cash file. If the previous device does not have a received electronic coin received electronic cash file (for example, a payment card does not maintain a received electronic coin received electronic cash file), the method is complete and a transaction path  870  is output. If, however, the previous device does have a received electronic coin received electronic cash file, a step  850  sets the current device to the previous device and loops back to step  810 . 
     In general, the method of locating the source of bogus electronic coins according to the present invention is therefore to compile the transaction paths for a number of bogus electronic coins and examine the transaction paths for intersections with the same device or devices. Devices which appear at or near such intersections are likely sources for the bogus electronic coins and should be investigate further. 
     It is noted that human investigation is ultimately needed because there are several different electronic coin tracing scenarios possible when dealing with bogus electronic coins, and the automated information obtained as described above may not in itself be conclusive, but may only provide indicia of a source of bogus electronic coins. For example, it is conceivable that POS  650  (FIG. 32) might have dispensed electronic coin  680  to another payment card  605  (not shown), which later sent electronic coin  680  to financial institution  670 . In this case, there will be no record at financial institution  670  that POS  650  was ever involved with the transaction path of electronic coin  680 . When financial institution  670  traces the path of electronic coin  680  back to original sources, the result will only show that payment card  600  spent one of the duplicates at POS  660 , and that payment card  605  spent another of the duplicates at POS  652 . This is not sufficient information to identify payment card  600  as the source of both duplicates. However, if a payment card is the source of a large number of bogus electronic coins, there is a reasonable probability that the payment card will appear in a statistically significant number of transaction paths involving the bogus electronic coins, and can therefore be detected. 
     It is also noted that payment cards are not the only suspects when tracing down the source of bogus electronic coins. A POS, for example, could also be a source of bogus electronic coins if it were somehow compromised by a dishonest merchant. In such a case, it would be expected that the POS would issue its bogus electronic coins as change, rather than send them directly up to the financial institution. In this way, the bogus electronic coins would be spent by unknowing customers at a variety of other (also innocent) POS devices before finding their way to the financial institution and being detected. The result would be that the compromised POS generating and distributing the bogus electronic coins would not appear in any transaction path. Instead, it should be expected that there would be a set of transaction paths for the bogus electronic coins that would be localized in the vicinity of the compromised POS. To uncover the identity of the compromised POS, it would be necessary for human investigators to deduce a connection between the various payment cards at the base of the transaction paths. This connection would be the compromised POS, and while automated tools could assist in this investigation, human intervention would be necessary to guide the investigation. 
     12. AGGREGATION OF TRANSACTIONS BY MERCHANT 
     FIG. 21 describes the relations between a single POS, cards and financial institutions, showing how revenues are carried by charges and electronic bills while electronic coins revolve via payment, change, adjustment and refreshing, with zero average effect. It would be appreciated that a merchant operating a plurality of POS units (e.g. a supermarket,) may actually consolidate the various POS drawers of the same function (e.g. see  172  in FIG.  17 ), each into a single, merchant-level drawer, maintaining a similar statistical behavior as in a single POS. Thus, FIG. 21 represents also a case where the “POS” block is replaced by a “MERCHANT” block actually representing the flow of electronic bills, charges and electronic coins through a consolidated plurality of POS. 
     13. A CENTRAL ELECTRONIC COIN ISSUER AND MULTIPLE ELECTRONIC BILL ISSUERS 
     As has been demonstrated in FIG. 21, revenues are actually carried by electronic bills and charge orders, while electronic coins revolve, with average zero net, between cards POS and between POS and financial institutions. The function of electronic coins thus becomes mostly technical, to enable small payments by larger-value charges and electronic bills. It might be preferable, in some systems, to have the smaller electronic coins issued by a single source, e.g. the system operator or coordinator, while electronic bills can be issued by and settled with a plurality of issuers. Thus, smaller electronic coins will be originated in and flow through a single electronic coin pool for adjustment and refreshing, while electronic bills will be purchases from issuers to be loaded into electronic purses, and late directed from points of sale to the respective issuers&#39; pools for settlement. 
     14. EDITIONS OF ELECTRONIC PENNIES 
     FIGS. 22-24 have introduced electronic pennies, which are actually counters of EMU value units. It is noted that if a new edition is issued (§3 above and FIGS.  19 - 20 ), new electronic pennies will also be issued. New and old electronic pennies will be stored and moved separately among separate partitions in all stored-value devices (similarly to FIGS.  19  and  20 ), with preference of moving old electronic pennies (via payment, change, adjustment and refreshing) toward the pools and new electronic pennies toward purses, just effectively draining the system from old electronic pennies. Old electronic pennies will be accumulated in an “old ” partition at the electronic penny pool, and on the expiration date they will be counted, with a precision of 1 EMU, to effectively confirm the security and integrity of the payment system. It is noted, however, that this method is less accurate with electronic pennies than with electronic coins, since unused electronic pennies may unnoticeably compensate for counterfeit electronic pennies.