Abstract:
A data cryptographer encrypts and decrypts character data of any given length using derivative equations and factors. The use of factors and derivative equations introduces the randomness required for effective encryption without the use of complex mathematics. A set of equations determined by the user is used in a manner similar to a key but with random results. Only a portion of the key is exposed to decrypt the encrypted information. The data cryptographer may be configured using either simple or complex equations and may be implemented in an unlimited number of variations. The data cryptographer is portable, and can be implemented in any programming language that supports cyclical character manipulation. The data cryptographer also supports input from a variety of sources, allowing control from the administrator side, string value side, or any other input that may be extracted from the desired programming language.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    Under 35 USC § 120, this application is a continuation application and claims the benefit of priority to U.S. patent application No. 10/672,811, filed Sep. 26, 2003, entitled “Method for Encrypting and Decrypting Data Using Derivative Equations and Factors”, all of which is incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention generally relates to cryptography, and more particularly to an encryption and decryption system that utilizes customizable equations and random values to securely encrypt and decrypt information. 
       BACKGROUND OF THE INVENTION 
       [0003]    Businesses, organizations, and individuals are becoming increasingly dependent on computers and data transmission. Consequently, large amounts of communicated data need to be secure from unauthorized access. A primary method of securing transmission of information utilizes cryptography, where a message or string of characters is transformed into a form understood only by the intended recipient. 
         [0004]    A typical conventional approach to encrypting data utilizes a cryptographic algorithm and a set of cryptographic keys. The decrypting algorithm is typically the same as the encrypting program performed in reverse order. Public-key encryption makes one key public and another key private. Both the sender and the recipient should have the keys to encrypt and decrypt the information. Security of the encrypted data using cryptographic keys depends on keeping the keys secret and protecting the keys from being determined by third-party cryptanalysis. Methods for preventing cryptanalysis comprise iterated cryptosystems and the “one time pad” cryptosystem. An example of an iterated cryptosystem is the Data Encryption Standard (DES) developed by IBM. An example of a secure public-key cryptosystem is the Rivest, Shamir, Adleman (RSA) system. 
         [0005]    The “one time pad” system utilizes a randomly selected key. This key is used only once and is equal or greater in length than the data to be encrypted. Because the key is random and used only once, the probability of decrypting the encrypted data without the knowledge of the key is very low. However, the recipient of the encrypted data requires the key to decrypt the data and the recipient requires a new key for each message. Consequently, a “one time pad” system is more appropriate for transmitting top-secret messages such as government messages than for large quantities of data. 
         [0006]    Fortunately, effective data security does not require an unbreakable code. Rather, encrypted information should be encrypted at a level such that the work involved to decipher the encryption is greater than the reward for success. 
         [0007]    Pseudo-random sequences are used to encrypt information provided the sequence is sufficiently random and secure. An adversary should not be able to predict a sequence based on past values or be able to deduce initial values. The goal of pseudo-random sequences is for the sequence to appear noise-like and non-repeating (aperiodic). 
         [0008]    Algorithms utilizing equations from chaos theory have been used to create these pseudo-random sequences. The purpose of using equations from chaos theory is to encrypt information in such a way that is aperiodic to prevent an adversary from decrypting information contained in the sequence. However, the equations and algorithms used to create these pseudo-random sequences are complex. 
         [0009]    Implementations of conventional approaches to encryption either involve storing a key that is liable to discovery by an adversary or attacker, or utilizing complex chaos theory equations. 
         [0010]    What is therefore needed is a system, a computer program product, and an associated method for an encryption process that can be customized by the user, making the encryption process unique to the user, thus providing security from adversaries. This process should be easy to implement and require minimal processing by the computer. The keys for decrypting the encrypted information should not be stored in a database or transmitted in such a manner that adversaries may be able to decrypt the information. The need for such a system and method has heretofore remained unsatisfied. 
       SUMMARY OF THE INVENTION 
       [0011]    The present invention satisfies this need, and presents a system, a computer program product, and an associated method (collectively referred to herein as “the system” or “the present system”) for encrypting character data (strings) of any given length using derivative equations and factors. The use of factors and derivative equations introduces the randomness required for effective encryption without the use of complex mathematics such as chaos theory. 
         [0012]    The present system uses for encryption a set of equations determined by the user in a manner similar to a key. Unlike conventional encryption technology using keys, the results can be random. In addition, only a portion of the key is exposed to decrypt the encrypted information. Unlike convention encryption technology using complex equations to produce randomized results, the present system uses a simple approach that may be customized by the user in an infinite variety of ways. The user may configure the present system using either simple or complex equations. 
         [0013]    The present system is a simple process involving a minimum of steps to implement. Unlike an application utilizing chaos theory equations, extensive mathematical skills are not required to implement the present system. The present system may be implemented in an unlimited number of variations; no two implementations may be the same. 
         [0014]    The present system is portable, and can be implemented in any programming language that supports cyclical character manipulation; i.e., C, C++, Java, etc. The present system also supports input from a variety of sources, allowing control from the administrator side, string value side, or any other input that may be extracted from the desired programming language. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS  
         [0015]    The various features of the present invention and the manner of attaining them will be described in greater detail with reference to the following description, claims, and drawings, wherein reference numerals are reused, where appropriate, to indicate a correspondence between the referenced items, and wherein: 
           [0016]      FIG. 1  is a schematic illustration of an exemplary operating environment in which a cryptographic system of the present invention can be used; 
           [0017]      FIG. 2  is a block diagram of the high-level architecture of the cryptographic system of  FIG. 1 ; 
           [0018]      FIG. 3  is a process flow chart illustrating a method of defining the factors, derivatives, and equations used by the cryptographic system of  FIGS. 1 and 2 ; 
           [0019]      FIG. 4  is a process flow chart illustrating a method of operation of the cryptographic system of  FIGS. 1 and 2  when used to encrypt a password; and 
           [0020]      FIG. 5  is comprised of  FIGS. 5A and 5B  and represents a process flow chart illustrating a method of operation of the cryptographic system of  FIGS. 1 and 2  when used to decrypt an encrypted password to authenticate a password entered by a user. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0021]    The following definitions and explanations provide background information pertaining to the technical field of the present invention, and are intended to facilitate the understanding of the present invention without limiting its scope: 
         [0022]    Original String: Refers to a set of characters that represent information requiring encryption. 
         [0023]    Encrypted String: Refers to a set of characters that represent information that has been encrypted such that the original string cannot easily be determined. 
         [0024]      FIG. 1  portrays an exemplary overall environment in which a system and associated method for encrypting and decrypting data using derivative equations and factors according to the present invention may be used. System  10  comprises a software programming code or a computer program product that is typically embedded within, or installed on a host server  15 . Alternatively, system  10  can be saved on a suitable storage medium such as a diskette, a CD, a hard drive, or like devices. 
         [0025]    Information in host server  15  that should be kept secure is encrypted by system  10  and stored in a database  20 . Examples of such information might be passwords, credit card numbers, etc. 
         [0026]    Users, such as remote Internet users, are represented by a variety of computers such as computers  25 ,  30 ,  35 , and can access the host server  15  through a network  40 . Computers  25 ,  30 ,  35  each comprise software that allows the user to interface securely with the host server  15 . The host server  15  is connected to network  40  via a communications link  45  such as a telephone, cable, or satellite link. Computers  25 ,  30 ,  35  can be connected to network  40  via communications links  50 ,  55 ,  60 , respectively. While system  10  is described in terms of network  40 , computers  25 ,  30 ,  35  may also access system  10  locally rather than remotely. Computers  25 ,  30 ,  35  may access system  10  either manually, or automatically through the use of an application. 
         [0027]    The present system maps each character in an original string, S 0 , to an encrypted character in an encrypted string, E 0 , using a set of equations. The original string, S 0 , is comprised of N characters, C: 
         [0000]    
       
      
       S 
       0 
       =C 
       0 
       , C 
       1 
       , C 
       2 
       , C 
       3 
       , . . . , C 
       N  
      
     
         [0000]    An implementer may use as many encryption equations as desired to obtain the level of randomness and complexity required in the encryption process. The implementer chooses a set of factors to be used in the equations. 
         [0028]    The factors comprise the following types: factors provided by the administrator, random values, or objects or values related to the original string, etc. These factors may be, for example, a number selected by the administrator, the current hour of the day, minute of the hour, or second of the minute, some other random number easily available from the operating system of host server  15 , or the length of the original string to be encrypted. In addition, the factors may be random numbers created by a function such as a random generator or an equation such as the chaos equation. 
         [0029]    In an exemplary embodiment, to create the encryption module, the implementer creates an encryption equation that is a function of the original string, S 0 , and the factors: 
         [0000]        E   0   =f ( S   0   , F   1   , F   2   , . . . , F   N    
         [0000]    where F 1 , F 2 , . . . , F N  are the factors. The implementer then creates a set of derivative equations that are functions of the factors: 
         [0000]        D   1   =f ( F   1   , F   2   , . . . , F   N ) 
         [0000]        D   2   =f ( F   1   , F   2   , . . . , F   N ) 
         [0000]        D   N   =f ( D   1   , D   2   , . . . , D   N ). 
         [0030]    To create the decryption module, the implementer uses the derivative values and factor decryption equations to solve for the factors F 1 , F 2 , . . . , FN: 
         [0000]        F   1   =f ( D   1   , D   2   , . . . , D   N ) 
         [0000]        F   2   =f ( D   1   , D   2   , . . . , D   N ) 
         [0000]        F   N   =f ( D   1   , D   2   , . . . , D   N ) 
         [0000]    The implementer then uses the encryption equation and the factors to solve for the original string: 
         [0000]        S   D   =f (E 0   , F   1   , F   2   , . . . , F   N ) 
         [0031]    The values stored in database  20  are the encrypted string E 0  and the derivatives. The encryption equation and derivative equations are written as programming code within the encryption module. The decryption equation and factor decryption equations are written as programming code within the decryption module. 
         [0032]    The encrypted string is created by encrypting each character of the original string individually and concatenating the encrypted characters to the encrypted string in order. Provided to the decryption module are the encrypted string and the derivatives. Unless an adversary or attacker is able to access the encryption code, the adversary is unable to determine the relation between the characters in the string and the derivatives. In another feature of system  10 , additional derivatives may be provided that are not actually used to determine the factors; the presence of these false derivatives provide an additional level of security in the encryption method of system  10 . 
         [0033]    The high-level architecture of system  10  is illustrated by the diagram of  FIG. 2 . An input  205  to an encryption module  210  comprises an original string  215  (S 0 ) and factors  220  (F 1 , F 2 , . . . , F N ). An output  225  from the encryption module  210  comprises derivatives  230  (D 1 , D 2 , . . . , D N ) and an encrypted string  235  (E 0 ). A decryption module  240  decrypts output  225  to produce a decrypted string  245  (S D ). The decrypted string  245  is equal to the original string  215 . 
         [0034]    A method  300  illustrating the process of developing the encryption module  210  and the decryption module  240  is illustrated by the process flow chart of  FIG. 3 . At block  305 , an implementer such as a system administrator selects or defines factors  220 . For example, the implementer may choose a number, 7, the minute of the hour, and the length of the string: 
         [0000]      F 1 =7 
         [0000]      F 2 =minute of the hour 
         [0000]      F 3 =length of the string. 
         [0035]    Administrative keys form a subcategory of factors. The only requirement is that factors exist. Therefore, a set of factors using all random factors (i.e., another subcategory) is acceptable so long as the derivatives can be uniquely related to the factors. 
         [0036]    The implementer then creates an encryption equation at block  310  that describes the encryption equation as a function of a character in the original string  215  and factors  220  (i.e., F 1 , F 2 , F 3 ). For example, the implementer may create the following equation that maps a character in the original string  215 , S 0  (C), to a character in the encrypted string  235 , E 0 (C): 
         [0000]        E   0 ( C )=S 0 ( C )+ F   1   +F   2   *F   3 /2. (1) 
         [0000]    The encryption equation may be as complex as the implementer requires, as long as the implementer can create derivative equations that can be solved by the decryption module  240  to determine factors  220 . 
         [0037]    The implementer creates a set of derivative equations at block  315 . The number of derivative equations required is greater or equal to the number of factors  220  selected by the implementer. For example, the implementer may define derivatives  230  as follows: 
         [0000]        D 1 =F 1+ F 2 −F 3 (2) 
         [0000]        D 2 =F 1−2 F 2+3 F 3 (3) 
         [0000]        D 3 =F 3− F 1+2 (4) 
         [0000]    The encryption module  210  is comprised of the encryption equation, factors  220 , and the derivative equations. The derivative equations may be as complex as desired provided that an equation for factors  220  may be written in terms of derivatives  230 . Additional derivative equations may be created to act as decoys within the encryption and decryption process. Because derivatives  230  are defined in terms of factors  220 , factors  220  may change from encryption to encryption, allowing the use of random values based on time values such as the value the minute of the hour when the encryption is performed, for example. 
         [0038]    The decryption module  240  comprises a set of factor decryption equations and a decryption equation. The decryption equation uses factors  220  derived from the factor decryption equations and the encrypted string  235  to obtain the decrypted string  245 , S D , that is equivalent to the original string  215 , S 0 . The implementer solves the decryption equations for factors  220  at block  320 , obtaining the factor decryption equations that map derivatives  230  to factors  220 . For example, by using standard algebraic manipulation the implementer may solve the exemplary factors  220  in terms of derivatives  230  (i.e., D 1 , D 2 , and D 3 ): 
         [0000]        F   1 =0.5 D   1 +0.25 D   2 −0.25 D   3 +0.5 (5) 
         [0000]        F   2   =D   1   +D   3 −2 (6) 
         [0000]        F   3 =0.5 D   1 +0.25 D   2 +0.75  D   3 −1.5 (7) 
         [0000]    The implementer then solves the encryption equation E 0  to obtain the decryption equation (block  325 ). For example, equation (1) solved for the original string  215 , S 0 , yields: 
         [0000]        S   D ( C )= S   0 ( C )= E   0 ( C )− F   1   −F   2   *F   3 /2 (8) 
         [0039]    At block  330 , the implementer converts the encryption equation and derivative equations into programming code for the encryption module  210 ; the factor decryption equations and the decryption equations are converted into programming code for the decryption module  240 . For example, equations (1), (2), (3), and (4) are converted into programming code for the encryption module  210  and equations (5), (6), (7), and (8) are converted into programming code for the decryption module  240 . 
         [0040]    A method  400  of the encryption module  210  of system  10  is illustrated by a process flow chart of  FIG. 4 , using an example of a user registering for a service such as a paid subscription to a database. The user registers for access to the database at block  405  by entering a user name and a password. System  10  calls the encryption module  210  to encrypt the password at block  410 . The encryption module  210  generates factors  220  as required by the encryption module  210  and calculates derivatives  230  (block  415 ). Some of factors  220  used by the encryption module  210  may be constant values provided by the administrator when the encryption module  210  is created. Other factors  220  may be random values generated by the encryption module  210  at the time the password is encrypted. 
         [0041]    The encryption module  210  selects a character such as, for example, the first character in the password at block  420  and encrypts that character using the encryption equation at block  425 . The encrypted character is appended to the encrypted string  235  at block  430 . System  10  determines at decision block  435  whether additional characters remain to be encrypted in the password. If additional characters remain to be encrypted, system  10  proceeds to block  440  and selects the next character in the password. Blocks  425  through  440  of method  400  are repeated until no more characters remain for encryption (decision block  435 ). 
         [0042]    System  10  then stores the encrypted string  235  and derivatives  230  generated at block  415  with the user name in a database record of database. While the encrypted password is stored with derivatives  230  in database  20 , no information is stored that can be used to determine how to decrypt the password. The equations used to decrypt the password are programming code in the encryption module  210 . To decrypt the password, an adversary would have to identify the appropriate equations in the encryption module  210  and then use derivatives  230  appropriately to decrypt the password; this is a very difficult task. 
         [0043]    A method  500  for decrypting the encrypted string  235  is illustrated by the process flow chart of  FIG. 5  ( FIGS. 5A and 5B ), using the example of authenticating a user login to a subscription database with the stored encrypted password created by method  400 . A user logs onto the subscription database at block  505  with their user name and password. For the username provided by the user (block  510 ), system  10  retrieves the encrypted password and derivatives  230  from the database  20 . 
         [0044]    System  10  then calls the decryption module  240  to decrypt the encrypted password at block  520 . At block  525 , the decryption module  240  calculates factors  220  from derivatives  230  using the factor decryption equations in the decryption module  240 . 
         [0045]    System  10  selects a character such as, for example, the first character in the encrypted password for decryption (block  530 ). The decryption module  240  decrypts the encrypted character at block  535  ( FIG. 5B ) using factors  220  and the decryption equation. 
         [0046]    At block  540 , system  10  appends the decrypted character to the decrypted string  245 . System  10  determines at decision block  545  whether any additional characters remain to be decrypted. If yes, system  10  proceeds to block  550  and selects the next character in the encrypted string  235 . System  10  repeats blocks  535  through  550  until no characters in the encrypted string  235  remain to be decrypted. 
         [0047]    After all the characters in the encrypted string  235  have been decrypted, system  10  compares the decrypted string  245  with the password provided by the user at log-on (block  560 ). If system  10  determines at decision block  565  that the decrypted string  245  is identical to the password provided by the user, system  10  authenticates the user at block  570 , allowing the user access to the subscription database. If the decrypted string  245  is not identical to the password provided by the user, system  10  returns an error to the user and denies the user access to the subscription database. 
         [0048]    It is to be understood that the specific embodiments of the invention that have been described are merely illustrative of certain applications of the principle of the present invention. Numerous modifications may be made to system and method for encrypting and decrypting data using derivative equations and factors invention described herein without departing from the spirit and scope of the present invention. 
         [0049]    In addition, while the present invention has been described in view of a single dimension of sets of factors and derivative equations, it should be understood that the sets of factors and derivative equations could be subsets of higher level sets of factors and derivative equations, respectively, with indicators that identify the higher level sets of factors and derivative equations that have been selected. 
         [0050]    Moreover, while the present invention is described for illustration purpose only in relation to the WWW, it should be clear that the invention is applicable as well to, for example, to any application where data is encrypted.