Patent Publication Number: US-7903820-B2

Title: Key production system

Description:
FIELD OF THE INVENTION 
     The present invention relates to key production. 
     RELATED APPLICATION INFORMATION 
     The present application claims priority from Israel Patent Application S/N 178488 of NDS Limited, filed Oct. 5, 2006. 
     BACKGROUND OF THE INVENTION 
     By way of introduction, content issued by a content provider is typically encrypted using a cryptographic key. The cryptographic key is typically changed periodically and frequently, every cryptoperiod, in order to prevent key attacks leading to gaining unauthorized access to the content. In order to efficiently store a collection of keys that change over time, it is generally necessary to generate the keys by deriving a series in a one-way manner. As will be explained in more detail below, only the last issued key needs to be retained by the content consuming device and previous keys can then be derived from the last issued key. An example of key generation is described in section 7.3 of a document entitled “DRM Specification, Approved Version 2.0—3 Mar. 2006” issued by the Open Mobile Alliance of 4275 Executive Square, Suite 240, La Jolla, Calif. 92037, USA or via the website at www.openmobilealliance.org. 
     Reference is now made to  FIGS. 1 and 2 .  FIG. 1  is a partly pictorial, partly block diagram view of a hash-chain  10  used in key-production.  FIG. 2  is a partly pictorial, partly block diagram view of keys  12  being issued after a subscription. 
     The hash-chain  10  has a root key  14 , which is input to the function f, thereby producing a key X i . The key X i  is in turn input to the function f, thereby producing a key X i−1 . The process is then continued until the hash-chain  10  is large enough for the needs of the application giving keys  12  (for example, but not limited to, keys X 0 , X 1 , X 2 , X 3  and so on) whereby one of the keys  12  is generally issued at a time. The function f, is typically a cryptographic one-way function. 
     The root key  14  of the series of the hash-chain  10  is generally kept by the deriving side, for example, but not limited to, a broadcasting Headend or the Rights Issuer. The Rights Issuer then issues keys periodically, typically starting from the last key in the series, X 0  in the example of  FIG. 1 , and then continuing issuing new keys back one-by-one towards the root key  14  so that the order of issuance is in the opposite direction to the order of derivation. 
     The first key issued to the subscribers is the key X 0 . The key X 0  is suitable as a decryption key for content issued in the first time period (January). Similarly, in the next time period (February), the key X 1  is issued to the subscribers to decrypt content issued in February. In the following time period (March), a key X 2  is issued to the subscribers to decrypt content issued in March, and so on. It will be appreciated that when the subscribers hold key X 1 , the subscribers no longer need to hold the key X 0 , as the key X 0  can be determined from the key X 1  using the function f. Similarly, when the subscribers hold the key X 2 , the subscribers no longer need to hold the keys X 1  and X 0 , as the keys X 1  and X 0  can be determined from the key X 2  using the function f. 
     Reference is now made to  FIG. 2 . A subscriber (not shown) subscribes in March and receives the key X 2  in March, the key X 3  in April and the key X 4  in May. 
     Reference is now made to  FIG. 3 , which is a partly pictorial, partly block diagram view of prior keys  16  being generated from a current key  18 . In June, the subscriber receives the key X 5 . The keys X 0 , X 1 , X 2 , X 3  and X 4  can all be determined from the key X 5  using the function f. The keys X 0  and X 1  allow the subscriber to decrypt content issued in January and February, respectively. However, the subscriber only began subscribing in March. Therefore, the subscriber is gaining free access to the January and February content. 
     Therefore, when derived keys are shared by many clients, for example, but not limited to, access keys to a service that is broadcast and stored, then everyone included in the subscription for a service receives all the current keys, but have the ability to derive all the past keys, even for periods for which the clients were not subscribed. 
     The following reference is also believed to represent the state of the art: 
     Israel unpublished patent application 174494 of NDS Limited entitled “Period Keys”. 
     The disclosures of all references mentioned above and throughout the present specification, as well as the disclosures of all references mentioned in those references, are hereby incorporated herein by reference. 
     SUMMARY OF THE INVENTION 
     The present invention seeks to provide an improved key production system. 
     The system of the present invention, in preferred embodiments thereof, includes a key production system based on two hash-chain series. The values of each hash-chain are associated with cryptoperiods such that one of the hash-chains has values (for example, Y 0 , Y 1 , Y 2 , Y 3 ) which progress via a first one-way function wherein progressive values correspond to later cryptoperiods (so that the order of issuance is in the same direction as the order of derivation) and the other hash-chain has values (for example, X 3 , X 2 , X 1 , X 0 ) which progress via a second one-way function wherein progressive values correspond to earlier cryptoperiods (so that the order of issuance is in the opposite direction to the order of derivation). For a selected cryptoperiod i, the cryptographic key (Z i ) is based on a value in each hash-chain for the selected cryptoperiod (for example, X i  and Y i ). Therefore, the values of the hash-chained are termed “key-components”. 
     The cryptographic key, Z i , is preferably, determined based on the value X i  in one hash-chain and the value Y i  in the other hash-chain, for the selected cryptoperiod. In general, the function used to determine Z i  should not allow computing the values X i  from Z i  and Y i  and preferably not Y i  from Z i  and X i , for a cryptoperiod i. 
     Therefore, when a client subscribes to a service, for example, in time-period k, the client receives a key-component from each hash-chain for the current cryptoperiod, for example, X k  and Y k . Each cryptoperiod, m, during subscription, the client receives a key-component X m  from the hash-chain which progresses toward the root for the cryptoperiod. The key-component Y m  for the cryptoperiod for the hash-chain which progresses away from the root can be determined by the client based on the originally issued key-component, Y k . The cryptographic key Z m  is determined using the appropriate key-components of each hash-chain, namely, X m  and Y m . 
     Therefore, the client can generally only calculate the cryptographic key Z, for cryptoperiods later than or equal to k, but earlier than or equal to m. 
     There is thus provided in accordance with a preferred embodiment of the present invention a key production system to determine a cryptographic key for a selected cryptoperiod, the selected cryptoperiod being later than or equal to a cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a, and earlier than or equal to a cryptoperiod B, the cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a being different from the cryptoperiod B, the system including a first receiver to receive a first key-component associated with the cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a, the first key-component forming part of a first hash-chain having a plurality of key-components such that the first hash-chain progresses via a first one-way function, progressive ones of the key-components in the first hash-chain corresponding to later cryptoperiods, a second receiver to receive a second key-component associated with the cryptoperiod B, the second key-component forming part of a second hash-chain having a plurality of key-components such that the second hash-chain progresses via a second one-way function, progressive ones of the key-components in the second hash-chain corresponding to earlier cryptoperiods, a first key component determination module to determine one of the key-components in the first hash-chain for the selected cryptoperiod, a second key component determination module to determine one of the key-components in the second hash-chain for the selected cryptoperiod, and a key determination module to determine the cryptographic key based on the one key-component in the first hash chain for the selected cryptoperiod and the one key component in the second hash-chain for the selected cryptoperiod. 
     Further in accordance with a preferred embodiment of the present invention the first key component determination module is operative to determine the one key-component in the first hash-chain for the selected cryptoperiod based on applying the first one-way function, at least once, to the first key component. 
     Still further in accordance with a preferred embodiment of the present invention the second key component determination module is operative to determine the one key-component in the second hash-chain for the selected cryptoperiod based on applying the second one-way function, at least once, to the second key component. 
     Additionally in accordance with a preferred embodiment of the present invention, the key determination module is operative to determine the cryptographic key by performing a cryptographic hash function on the concatenation of the one key-component in the first hash chain for the selected cryptoperiod with the one key component in the second hash-chain for the selected cryptoperiod. 
     Moreover, in accordance with a preferred embodiment of the present invention the first one-way function is the same as the second one-way function. 
     There is also provided in accordance with still another preferred embodiment of the present invention a key production system to determine a cryptographic key for a selected cryptoperiod, the selected cryptoperiod being later than or equal to a cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a, and earlier than or equal to a cryptoperiod B, the cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a being different from the cryptoperiod B, the system including a first receiver to receive a first key-component associated with the cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a, the first key-component forming part of a first hash-chain having a plurality of key-components such that the first hash-chain progresses via a first one-way function, progressive ones of the key-components in the first hash-chain corresponding to later cryptoperiods, a second receiver to receive a second key-component associated with the cryptoperiod B, the second key-component forming part of a second hash-chain having a plurality of key-components such that the second hash-chain progresses via a second one-way function, progressive ones of the key-components in the second hash-chain corresponding to earlier cryptoperiods, a first key component determination module to determine one of the key-components in the first hash-chain for the selected cryptoperiod based on applying the first one-way function, at least once, to the first key component, a second key component determination module to determine one of the key-components in the second hash-chain for the selected cryptoperiod based on applying the second one-way function, at least once, to the second key component, and a key determination module to determine the cryptographic key based on the one key-component in the first hash chain for the selected cryptoperiod and the one key component in the second hash-chain for the selected cryptoperiod. 
     There is also provided in accordance with still another preferred embodiment of the present invention a key component production system to determine cryptographic key components for use in determining a cryptographic key for a selected cryptoperiod, the system including a first hash-chain module to determine a first key-component associated with the selected cryptoperiod such that the first key-component forms part of a first hash-chain having a plurality of key-components, the first hash-chain progressing via a first one-way function, progressive ones of the key-components in the first hash-chain corresponding to later cryptoperiods, a second hash-chain module to determine a second key-component associated with the selected cryptoperiod such that the second key-component forms part of a second hash-chain having a plurality of key-components, the second hash-chain progressing via a second one-way function, progressive ones of the key-components in the second hash-chain corresponding to earlier cryptoperiods, a key determination module to determine the cryptographic key for the selected cryptoperiod based on the first key-component and the second key-component, and a communication module to enable transfer of the first key-component and the second-key component to a plurality of devices for use in determination of the cryptographic key for the selected cryptoperiod. 
     There is also provided in accordance with still another preferred embodiment of the present invention a key production method to determine a cryptographic key for a selected cryptoperiod, the selected cryptoperiod being later than or equal to a cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a, and earlier than or equal to a cryptoperiod B, the cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a being different from the cryptoperiod B, the method including receiving a first key-component associated with the cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a, the first key-component forming part of a first hash-chain having a plurality of key-components such that the first hash-chain progresses via a first one-way function, progressive ones of the key-components in the first hash-chain corresponding to later cryptoperiods, receiving a second key-component associated with the cryptoperiod B, the second key-component forming part of a second hash-chain having a plurality of key-components such that the second hash-chain progresses via a second one-way function, progressive ones of the key-components in the second hash-chain corresponding to earlier cryptoperiods, determining one of the key-components in the first hash-chain for the selected cryptoperiod, determining one of the key-components in the second hash-chain for the selected cryptoperiod, and determining the cryptographic key based on the one key-component in the first hash chain for the selected cryptoperiod and the one key component in the second hash-chain for the selected cryptoperiod. 
     Further in accordance with a preferred embodiment of the present invention the one key-component in the first hash chain for the selected cryptoperiod is determined based on applying the first one-way function, at least once, to the first key component. 
     Still further in accordance with a preferred embodiment of the present invention the key-component in the second hash-chain for the selected cryptoperiod is determined based on applying the second one-way function, at least once, to the second key component. 
     Additionally in accordance with a preferred embodiment of the present invention, the cryptographic key is determined by performing a cryptographic hash function on the concatenation of the one key-component in the first hash chain for the selected cryptoperiod with the one key component in the second hash-chain for the selected cryptoperiod. 
     Moreover, in accordance with a preferred embodiment of the present invention the first one-way function is the same as the second one-way function. 
     There is also provided in accordance with still another preferred embodiment of the present invention a key production method to determine a cryptographic key for a selected cryptoperiod, the selected cryptoperiod being later than or equal to a cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a, and earlier than or equal to a cryptoperiod B, the cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a being different from the cryptoperiod B, the method including receiving a first key-component associated with the cryptoperiod There is also provided in accordance with still another preferred embodiment of the present invention a, the first key-component forming part of a first hash-chain having a plurality of key-components such that the first hash-chain progresses via a first one-way function, progressive ones of the key-components in the first hash-chain corresponding to later cryptoperiods, receiving a second key-component associated with the cryptoperiod B, the second key-component forming part of a second hash-chain having a plurality of key-components such that the second hash-chain progresses via a second one-way function, progressive ones of the key-components in the second hash-chain corresponding to earlier cryptoperiods, determining one of the key-components in the first hash-chain for the selected cryptoperiod based on applying the first one-way function, at least once, to the first key component, determining one of the key-components in the second hash-chain for the selected cryptoperiod based on applying the second one-way function, at least once, to the second key component, and determining the cryptographic key based on the one key-component in the first hash chain for the selected cryptoperiod and the one key component in the second hash-chain for the selected cryptoperiod. 
     There is also provided in accordance with still another preferred embodiment of the present invention a key component production method to determine cryptographic key components for use in determining a cryptographic key for a selected cryptoperiod, the method including determining a first key-component associated with the selected cryptoperiod such that the first key-component forms part of a first hash-chain having a plurality of key-components, the first hash-chain progressing via a first one-way function, progressive ones of the key-components in the first hash-chain corresponding to later cryptoperiods, determining a second key-component associated with the selected cryptoperiod such that the second key-component forms part of a second hash-chain having a plurality of key-components, the second hash-chain progressing via a second one-way function, progressive ones of the key-components in the second hash-chain corresponding to earlier cryptoperiods, determining the cryptographic key for the selected cryptoperiod based on the first key-component and the second key-component, and enabling transfer of the first key-component and the second-key component to a plurality of devices for use in determination of the cryptographic key for the selected cryptoperiod. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will be understood and appreciated more fully from the following detailed description, taken in conjunction with the drawings in which: 
         FIG. 1  is a partly pictorial, partly block diagram view of a hash-chain used in key-production; 
         FIG. 2  is a partly pictorial, partly block diagram view of keys being issued after a subscription; 
         FIG. 3  is a partly pictorial, partly block diagram view of prior keys being generated from a current key; 
         FIG. 4   a  is a partly pictorial, partly block diagram view of two hash-chains for use with a key production system constructed and operative in accordance with a preferred embodiment of the present invention; 
         FIG. 4   b  is a partly pictorial, partly block diagram view of the two-hash chains of  FIG. 4   a  depicted in cryptographic period order; 
         FIGS. 5-8  are partly pictorial, partly block diagram views illustrating encryption key production in the system of  FIG. 4   a;    
         FIGS. 9-12  are partly pictorial, partly block diagram views further illustrating the system of  FIG. 4   a;    
         FIG. 13  is a block diagram view of the system of  FIG. 4   a;    
         FIG. 14  is a flow diagram of a preferred method of operation of the system of  FIG. 4   a;    
         FIG. 15  is a block diagram view of a key component production system constructed and operative in accordance with a preferred embodiment of the present invention; and 
         FIG. 16  is a flow diagram of a preferred method of operation of the system of  FIG. 15 . 
     
    
    
     DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT 
     Reference is now made to  FIG. 4   a , which is a partly pictorial, partly block diagram view of two hash-chains  20 ,  22  for use with a key production system  24  constructed and operative in accordance with a preferred embodiment of the present invention. 
     Each hash-chain  20 ,  22  has values  26 ,  30 , respectively, associated with cryptoperiods, for example, but not limited to, cryptoperiods 0, 1, 2, 3, i−1, i. 
     The term “cryptoperiod” as used in the specification and claims is defined as a period for which a cryptographic key setting is effective. Progressive cryptoperiods are typically of equal duration, for example, but not limited to, when the cryptoperiods progress in time. However, progressive cryptoperiods may be of unequal duration, such as when the cryptoperiods are associated with stages in a dynamic process which is typically event driven. By way of example, cryptoperiods may be triggered by time, for example, but not limited to, starting a new cryptoperiod every 10 seconds or every month. By way of another example, new cryptoperiods may be triggered by an event, for example, but not limited to, in a content sharing environment, new cryptoperiods may be triggered when new members are added so that old members can still access old content but the new members cannot access the old content, by way of example. 
     The hash-chain  22  has a root value, Y 0 . The other values  30  of the hash-chain  22  are determined by applying a function f 1  to the root value, Y 0  and subsequent values  30 , as necessary. The function f 1  is typically a cryptographic one-way function. In practice, a cryptographic Hash-function such as SHA-1 can be used as the function f 1 . 
     The term “one-way function” as used in the specification and claims is a function f such that for each x in the domain f, it is easy to compute f(x) (for example using current technology computation is typically in the order of seconds or less); but for essentially all y in the range of f, it is computationally infeasible to find any x such that y=f(x). The term “infeasible” as used in the specification and claims is defined as a problem that while theoretically is possible to solve, in practice is not, due to practical limitations in the amount of time and hardware available. For example only, if a problem can be solved using all the computers in existence working full time the next billion years, that might be considered computationally infeasible. An important property is that advances in technology and theory may well change the definition of what is infeasible. 
     By way of example only, it is currently believed that it is practically impossible to break the AES (Advanced Encryption Standard) via a brute force attack of exploring all 2 to the power  128  possible keys. 
     The values  30  (for example, Y 0 , Y 1 , Y 2 , Y 3 ) progress via the function f 1 , in a direction away from the root value Y 0 , wherein progressive values  30  correspond to later cryptoperiods, for example, Y 0  corresponds to cryptoperiod 0, Y 1  corresponds to cryptoperiod 1, and so on (so that the order of issuance is in the same direction as the order of derivation). 
     It will be appreciated that the value Y 1  can be determined from the value Y 0  using the function f 1 . Similarly, the value Y 2  can be determined from the value Y 1  using the function f 1 . As the function f 1  is a one-way function, it is infeasible to determine the value Y 0  from the value Y 1 , nor the value Y 1  from the value Y 2 . 
     The hash-chain  20  has a root value  28 . The other values  26  of the hash-chain  20  are determined by applying a function f 2  to the root value  28  and subsequent values  26 , as necessary. The function f 2  is typically a cryptographic one-way function. In practice, a cryptographic Hash-function such as SHA-1 can be used for the function f 2 . The values  26  (for example, X 3 , X 2 , X 1 , X 0 ) progress via the function f 2 , in a direction away from the root value  28 , wherein progressive values  26  correspond to earlier cryptoperiods, for example, X 3  corresponds to cryptoperiod 3, X 2  to cryptoperiod 2, X 1  to cryptoperiod 1 and X 0  to cryptoperiod 0 (so that the order of issuance is in the opposite direction to the order of derivation). 
     It will be appreciated that the value X 0  can be determined from the value X 1  using the function f 2 , Similarly, the value X 1  can be determined from the value X 2  using the function f 2 , and so on. However, as the function f 2  is a one-way function, it is infeasible to determine the value X 1  from the value X 0 , nor the value X 2  from the value X 1 . 
     The hash-chain values  26 ,  30  are also known as key-components, as the values  26 ,  30  are typically used in cryptographic key determination, described in more detail with reference to  FIGS. 5-14 : 
       FIG. 4   b  is a partly pictorial, partly block diagram view of the two-hash chains  20 ,  22  of  FIG. 4   a  depicted in cryptographic period order. The hash-chains  20 ,  22  progress in different directions with respect to cryptographic period order. 
     Reference is now made to  FIGS. 5-8 , which are partly pictorial, partly block diagram views illustrating encryption key production in the key production system  24  of  FIG. 4   a.    
       FIG. 5  depicts a subscription of a consumer (not shown) starting in March and receiving, by a device (not shown) of the consumer, a plurality of key-components  36 , namely X 2  and Y 2 . X 2  is from the hash-chain  20  and Y 2  is from the hash-chain  22 . A content decryption key  34  for decrypting a plurality of encrypted content items  32  issued in March is Z 2 . Z 2  is determined from X 2  and Y 2  using a function f 3 . In general, the function f 3  should not allow computing the values X i  from Z i  and Y i  and preferably not Y i  from Z i  and X i , for a cryptoperiod i. By way of example only, in practice a cryptographic hash function that takes the concatenation of X i  with Y i  as input is a good candidate for the function f 3 . In the example of  FIG. 5 , the function f 3  uses X 2  and Y 2  as inputs. 
     Previous values of the key-components in the hash-chain  20 , namely X 1  and X 0  can be derived from X 2  by applying the function f 2  to X 2 . However, since it is infeasible to determine the previous values of the key components in the hash-chain  22  namely Y 1  and Y 0  (not shown) from Y 2  as the function f 1  is a one-way function, the content decryption keys Z 0  and Z 1  cannot generally be determined and therefore a plurality of content items  38  issued in January and February encrypted using Z 0  and Z 1 , respectively, cannot generally be decrypted by the device. 
     Reference is now made to  FIG. 6 . In April, a new key-component  40 , namely X 3 , is issued to the device of the consumer for the hash-chain  20 . To save storage space, the client only stores X 3  and Y 2 . X 2  is derived from X 3  using the function f 2  applied to X 3 . Y 3  is derived from Y 2  using the function f 1  applied to Y 2 . The content decryption key Z 2  is determined from X 2  and Y 2  using the function f 3  and a content decryption key Z 3  is determined from X 3  and Y 3  using the function f 3 . Therefore, the encrypted content items  32  issued in March and a plurality of encrypted content items  42  issued in April may be decrypted by the device using the content decryption keys Z 2  and Z 3 , respectively. As described with reference to  FIG. 5  the content  38  cannot generally be decrypted as Z 0  and Z 1  cannot generally be determined. 
     Reference is now made to  FIG. 7 . In May, a new key-component  44 , namely X 4 , is issued to the device of the consumer for the hash-chain  20 . To save storage space, the device only stores X 4  and Y 2 . X 2  and X 3  are derived from X 4  using the function f 2 . Y 3  and Y 4  are derived from Y 2  using the function f 1 . Therefore, the content decryption keys Z 2 , Z 3  and a content decryption key Z 4  can be determined from the respective values of X and Y. Therefore, the encrypted content items  32 ,  42  and a plurality of encrypted content items  46  issued in May can be decrypted by the device using content decryption keys Z 2 , Z 3  and Z 4 , respectively. 
     Reference is now made to  FIG. 8 . The consumer decided not to renew the subscription for June. Therefore, the device of the consumer does not receive any new key-components for June. It is possible to derive a plurality of key components  48 , namely, Y 5  and Y 6 , in the hash-chain  22  for June and July, respectively, from Y 2  using the function f 1 . However, as the function f 2  is a one-way function, it is infeasible to derive the key-components X 5  and X 6  (not shown), in the hash-chain  20  for June and July, respectively, from X 4 . Therefore, decryption keys Z 5  and Z 6  for decrypting a plurality of encrypted content items  50  issued in June and July, respectively, generally cannot be determined. 
     As described above with reference to  FIG. 7 , the encrypted content items  32 ,  42 ,  46  can still be decrypted, as the decryption keys Z 2 , Z 3  and Z 4  can be determined using the key-components Y 2  and X 4 , as well as from the key-components X 2 , X 3 , Y 3 , Y 4  derived from Y 2  and X 4 . 
     Reference is now made to  FIGS. 9-12 , which are partly pictorial, partly block diagram views further illustrating the key production system  24  of  FIG. 4   a.    
       FIG. 9  depicts a consumer  52  having a device  54  for consuming a plurality of content items  56 . The device  54  may be any suitable consuming device, for example, but not limited to, a portable music player, portable TV, desktop computer, portable computer, a set-top box, or any other suitable portable or non-portable device. 
     In January, the consumer  52  starts subscribing to a service for receiving the content items  56 . The content items  56  issued in January are encrypted using a key Z JAN . The device  54  downloads, from a server  58 , a plurality of key components, namely X JAN  and Y JAN , associated with the hash-chain  20  ( FIG. 4   a ) and the hash-chain  22  ( FIG. 4   a ), respectively. The device  54  also downloads, from the server  58 , the content items  56  issued in January. The key Z JAN  is determined by the device  54  from X JAN  and Y JAN . The key Z JAN  is then used to decrypt the content items  56 . 
     Encrypted content issued prior to January cannot generally be decrypted, as it is infeasible to determine values earlier than Y JAN  as the function f 1  is a one-way function. 
     Reference is now made to  FIG. 10 . In February, the device  54  downloads, from the server  58 , a key component X FEB  and the content items  56  issued in February encrypted with a key Z FEB . The key Z FEB  is determined by the device  54  based on X FEB  and Y FEB  which is derived from Y JAN  using the function f 1 . Even though X FEB  and Y JAN  are the only key-components still being stored by the device  54 , Z JAN  can still be determined by deriving X JAN  from X FEB  using the function f 2 . Therefore, both the content items  56  issued in January and February can be played by the consumer  52  on the device  54 . 
     Reference is now made to  FIG. 11 . In March, the device  54  downloads, from the server  58 , a key component X MAR  and the content items  56  issued in March encrypted with a key Z MAR . The key ZMAR is determined by the device  54  from X MAR  and Y MAR  which is derived from Y JAN  using the function f 2 . 
     Reference is now made to  FIG. 12 . The consumer  52  decided not to renew the subscription in April. Nevertheless, the user downloads, from the server  58 , the content items  56  issued in April encrypted with a key Z APR . Although the device  54  may determine Y APR  based on Y JAN  using the function f 1 , it is infeasible for the device  54  to determine X APR  from X MAR  as the function f 2  is a one-way function. Therefore, the device  54  cannot generally determine Z APR  nor decrypt the content items  56  issued in April. 
     In the above examples of  FIGS. 5-12 , the subscribers are restricted to accessing content encrypted using keys associated with the subscription period. However, access to content encrypted prior to the encryption period may be allowed by supplying the subscribers with earlier keys in the hash-chain  22  for example, by supplying the consumer  52  of  FIGS. 9-12  with a key component before Y JAN  or supplying the subscriber of  FIGS. 5-8  with the key component Y 0  or Y 1 , by way of example only. 
     It should be noted that it is desirable to start a new chain in place of the hash-chain  22  occasionally, as hackers may try to combine key-components that they receive in order to be able to construct keys for cryptoperiods for which the users are not subscribed. 
     Reference is now made to  FIGS. 13 and 14 .  FIG. 13  is a block diagram view of the key production system  24  of  FIG. 4   a .  FIG. 14  is a flow diagram of a preferred method of operation of the key production system  24  of  FIG. 4   a.    
     The key production system  24  is preferably operative to determine a cryptographic key for a selected cryptoperiod. The selected cryptoperiod is typically later than, or equal to, a cryptoperiod A and earlier than, or equal to, a cryptoperiod B. The cryptoperiod A may be the same as, or different from, the cryptoperiod B. 
     The key production system  24  preferably includes a first receiver  60 , a second receiver  62 , a first key component determination module  64 , a second key component determination module  66  and a key determination module  68 . 
     The first receiver  60  is preferably operative to receive a first key-component associated with the cryptoperiod A. The first key-component typically forms part of a first hash-chain having a plurality of key-components such that the first hash-chain progresses via a first one-way function. Progressive key-components in the first hash-chain correspond to later cryptoperiods (block  70 ). 
     The second receiver  62  is preferably operative to receive a second key-component associated with the cryptoperiod B. The second key-component typically forms part of a second hash-chain having a plurality of key-components such that the second hash-chain progresses via a second one-way function. Progressive key-components in the second hash-chain correspond to earlier cryptoperiods (block  72 ). 
     When the selected cryptoperiod is not equal to the cryptoperiod A, the first key component determination module  64  is preferably operative to determine the key-component in the first hash-chain for the selected cryptoperiod based on applying the first one-way function, at least once (as many times as necessary), to the first key component (block  74 ). 
     When the selected cryptoperiod is not equal to the cryptoperiod B, the second key component determination module  66  is preferably operative to determine the key-component in the second hash-chain for the selected cryptoperiod based on applying the second one-way function, at least once (as many times as necessary), to the second key component (block  76 ). 
     The first one-way function may be the same as, or different from, the second one-way function. 
     The key determination module  68  is preferably operative to determine the cryptographic key based on the key-component in the first hash chain for the selected cryptoperiod and the key component in the second hash-chain for the selected cryptoperiod (block  78 ). 
     In accordance with a most preferred embodiment of the present invention, the key determination module  68  is preferably operative to determine the cryptographic key using a function (for example the function f 3  described with reference to  FIG. 5 ) with the key-component in the first hash chain for the selected cryptoperiod and the key component in the second hash-chain for the selected cryptoperiod as input. 
     By way of introduction, the key components for a selected cryptoperiod received by the subscriber devices (for example, the device  54  of  FIGS. 9-12 ) are typically determined by a server (for example, the server  58  of  FIGS. 9-12 ). The key components are then generally broadcast or pushed by the server or downloaded from the server by the subscriber devices. The server typically includes a key component production system  80 , which is now described in more detail with reference to  FIGS. 15 and 16 .  FIG. 15  is a block diagram view of the key component production system  80  constructed and operative in accordance with a preferred embodiment of the present invention.  FIG. 16  is a flow diagram of a preferred method of operation of the system  80  of  FIG. 15 . 
     The key component production system  80  preferably includes a first hash-chain module  82 , a second hash-chain module  84 , a communication module  86  and a key determination module  94 . 
     The first hash-chain module  82  is preferably operative to determine a first key-component associated with the selected cryptoperiod such that the first key-component forms part of a first hash-chain having a plurality of key-components (block  88 ). The first hash-chain progresses via a first one-way function. Progressive key-components in the first hash-chain correspond to later cryptoperiods. 
     The second hash-chain module  84  is preferably operative to determine a second key-component associated with the selected cryptoperiod such that the second key-component forms part of a second hash-chain having a plurality of key-components. The second hash-chain progresses via a second one-way function. Progressive ones of the key-components in the second hash-chain correspond to earlier cryptoperiods (block  90 ). 
     The communication module  86  is preferably operative to enable transfer of the first key-component and the second-key component to a plurality of devices for use in determination of the cryptographic key for the selected cryptoperiod. The communication module  86  typically broadcasts or pushes the key-components to the devices (for example, but not limited to, sending the key-components in an SMS message to mobile subscriber devices) or allows the key-components to be downloaded by the devices (block  92 ). 
     The key determination module  94  is preferably operative to determine the cryptographic key for the selected cryptoperiod based on the first key-component and the second key-component. The cryptographic key is then typically used to encrypt content for consumption by the subscriber devices (block  96 ). 
     It is appreciated that present invention may be implemented in software, ROM (read only memory) form, or hardware, if desired, using conventional techniques, or any suitable combination thereof. 
     It will be appreciated that various features of the invention which are, for clarity, described in the contexts of separate embodiments may also be provided in combination in a single embodiment. Conversely, various features of the invention which are, for brevity, described in the context of a single embodiment may also be provided separately or in any suitable sub-combination. It will also be appreciated by persons skilled in the art that the present invention is not limited by what has been particularly shown and described hereinabove. Rather the scope of the invention is defined only by the claims which follow.