CRYPTOGRAPHIC SYSTEM INCLUDING A MIXED RADIX NUMBER GENERATOR WITH CHOSEN STATISTICAL ARTIFACTS

• US 20090279690A1
• Filed: 05/08/2008
• Published: 11/12/2009
• Est. Priority Date: 05/08/2008
• Status: Active Grant

• Current Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Original Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Inventors: Michaels, Alan J., Chester, David B.
• Granted Patent: US 8,320,557 B2
• Time in Patent Office: Days
• US Class Current: 380/28
• CPC Class Codes: G06F 7/58 Random or pseudo-random number generators
• CPC Class Codes: G06F 7/584 using finite field arithmetic, e.g. using a linear feedback shift register
• CPC Class Codes: G06F 7/724 Finite field arithmetic for error detection or correction in general H03M13/00, in computers G06F11/10
• CPC Class Codes: H04L 9/0662 with particular pseudorandom sequence generator

Abstract

A cryptographic system (1000) is provided. The cryptographic system includes a data stream receiving means (DSRM), a number generator (NG), a mixed radix accumulator (MRA) and an encryptor. The DSRM (1002) receives a data stream (DS). The NG (702) generates a first number sequence (FNS) contained within a Galois Field GF[M]. The MRA (750) is configured to perform a first modification to a first number (FN) in FNS. The first modification involves summing the FN with a result of a modulo P operation performed on a second number in FNS that proceeds FN. The MRA is also configured to perform a second modification to FN utilizing a modulo P operation. The MRA is further configured to repeat the first and second modification for numbers in FNS to generate a second number sequence (SNS). The encryptor (1004) is configured to generate a modified data stream by combining SNS and DS.

Claims

1. A cryptographic system, comprising:

a data stream receiving means configured for receiving an input data stream;

a number generator configured for generating a first sequence of numbers contained within a Galois field GF[M];

a mixed radix accumulator electronically connected to said number generator and configured for (1) performing a first modification to a first number in said first sequence of numbers comprising summing said first number with a result of a first modulo P operation performed on a second number of said first sequence that proceeds said first number, where M is relatively prime with respect to P, (2) subsequent to said first modification, performing a second modification to said first number comprising a second modulo P operation, and (3) repeating said first and second modification for a plurality of numbers comprising said first sequence of numbers to generate a second sequence of numbers; and

an encryptor electronically connected to said data stream receiving means and said mixed radix accumulator, said encryptor configured for generating a modified data stream by incorporating or combining said second sequence of numbers with said input data stream.

2. The cryptographic system according to claim 1, wherein said number generator comprises a pseudo-random number generator for generating a pseudo-random sequence of numbers containing statistical artifacts relating to said generation of said first sequence of numbers, and wherein said statistical artifact is eliminated by said mixed radix accumulator.

3. The cryptographic system according to claim 1, wherein said number generator is configured for exhaustively producing said first sequence of numbers by using a mapping which is periodically repeated.

4. The cryptographic system according to claim 3, wherein said mapping includes a combination of an additive mapping and a multiplicative mapping.

5. The cryptographic system according to claim 4, wherein said additive mapping and said multiplicative mapping in combination include repeated computations of an irreducible polynomial over a Galois field GF[M].

6. The cryptographic system according to claim 1, wherein a value of M is mutually prime with respect to a value of P and all of a plurality of relatively prime factors of P including p₁, p₂, p₃, . . . , p_k.

7. The cryptographic system according to claim 6, further comprising a plurality of arithmetic operator units each configured for performing a third modification on said second sequence of numbers, said plurality of arithmetic operator units generating a plurality of output number sequences from said second sequence of numbers.

8. The cryptographic system according to claim 7, wherein said third modification comprises a modulo p operation performed upon each number in said second sequence of numbers to generate said plurality of output number sequences, where p includes a plurality of values selected from the group comprising p₁, p₂, p₃, . . . , p_k.

9. The cryptographic system according to claim 1, wherein said second number precedes said first number by one position.

10. The cryptographic system according to claim 1, wherein said second number precedes said first number by N positions, where N is greater than 1.

11. The cryptographic system according to claim 1, wherein said first sequence of numbers is limited to a finite number of elements M defined by a Galois field GF[M], said second sequence of numbers has statistical artifacts that are evenly distributed over a plurality of equivalence classes of said Galois field GF[P], and wherein said plurality of equivalence classes include an equivalence class for each integer 0, 1, . . . , P−

1.

12. The cryptographic system according to claim 1, wherein said first sequence is operated upon by a filter structure configured to perform calculations inside a Galois field of equal size to the second sequence.

13. The cryptographic system according to claim 1, wherein said encryptor includes at least one of a multiplier, an adder, a digital logic device and a feedback mechanism.

14. The cryptographic system according to claim 1, wherein said encryptor is configured for performing a standard multiplication operation, a multiplication in a Galois extension field operation, an addition modulo q operation, a subtraction modulo q operation or a bitwise logic operation.

15. The cryptographic system according to claim 1, further comprising a second number generator and a second mixed radix accumulator configured in combination to generate a decryption sequence.

16. The cryptographic system according to claim 15, further comprising a decryptor coupled to said second mixed radix accumulator, said decryptor configured for producing decrypted data by performing a decryption method utilizing said modified data stream and said decryption sequence.

17. A cryptographic system, comprising:

a data stream source configured for generating an input data stream of a dynamic range M including a first sequence of numbers with a known non-uniform probability distribution;

a mixed radix accumulator electronically connected to said data stream source and configured for (1) performing a first modification to a first number in said first sequence of numbers comprising summing said first number with a result of a modulo P operation performed on a second number of said first sequence that proceeds said first number, where M is relatively prime with respect to P, (2) subsequent to said first modification, performing a second modification to said first number comprising a modulo P operation, and (3) repeating said first and second modification for a plurality of numbers comprising said first sequence of numbers to generate a second sequence of numbers.

18. The cryptographic system according to claim 17, wherein P is greater than M, P is equal to M, or P is a fixed value less than M.

19. The cryptographic system according to claim 17, wherein P is a time-varying value constrained to values greater than M, P is a time-varying value constrained to values equal to M, or P is a time-varying value less than M at a given point in time.

20. The cryptographic system according to claim 17, further comprising a decryption device coupled to said mixed radix accumulator and configured for producing decrypted data by performing a decryption method implementing a correlation-based mathematical structure.

21. The cryptographic system according to claim 20, wherein said correlation-based mathematical structure is a Hidden Markov Model.

22. A method for encrypting and decrypting an input data stream, comprising the steps of:

receiving an input data stream;

generating a first sequence of numbers contained within a Galois field GF[M];

performing a first modification to a first number in said first sequence of numbers comprising summing said first number with a result of a first modulo P operation performed on a second number of said first sequence that proceeds said first number, where M is relatively prime with respect to P;

performing a second modification subsequent to said first modification to said first number comprising a second modulo P operation;

repeating said first and second modification for a plurality of numbers comprising said first sequence of numbers to generate a second sequence of numbers; and

generating a modified data stream by combining said second sequence of numbers with said input data stream.

23. The method according to claim 22, wherein said generating step further comprises performing a standard multiplication operation, a multiplication in a Galois extension field, an addition modulo q operation, a subtraction modulo q operation, or a bitwise logic operation.

24. The method according to claim 22, further comprising generating a decryption sequence, wherein said decryption sequence is a random number sequence having chosen statistical artifacts over all equivalence classes of a Galois Field GF[P].

25. The method according to claim 24, further comprising generating a decrypted data stream by performing a decryption method utilizing said modified data stream and said decryption sequence.