CRYPTOGRAPHIC SYSTEM CONFIGURED FOR EXTENDING A REPETITION PERIOD OF A RANDOM SEQUENCE

• US 20090110197A1
• Filed: 10/30/2007
• Published: 04/30/2009
• Est. Priority Date: 10/30/2007
• Status: Active Grant

• Current Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Original Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Inventors: Michaels, Alan J.
• Granted Patent: US 7,995,749 B2
• Time in Patent Office: Days
• US Class Current: 380/268
• CPC Class Codes: G06F 7/582 Pseudo-random number generators
• CPC Class Codes: G06F 7/729 using representation by a residue number system
• CPC Class Codes: G06F 7/766 Generation of all possible permutations
• CPC Class Codes: H04L 2209/12 Details relating to cryptographic hardware or logic circuitry
• CPC Class Codes: H04L 9/065 Encryption by serially and continuously modifying data stream elements, e.g. stream cipher systems, RC4, SEAL or A5/3

Abstract

A cryptographic system (CS) is provided. The CS (500) is comprised of a data stream receiving means (DSRM), a ring generator (RG) and an encryptor. The DSRM (602) provides a data stream (DS). The RG (400) includes a computing (404-408), converting (404-408) and permutation (410) means. The computing means is configured to perform RNS arithmetic operations to express a random number in a random number sequence as RNS residue values (RNSRV). The converting means is configured to convert each RNSRV to a relatively prime number system so that each RNSRV includes at least one digit. The permutation means is configured to generate an arbitrary permutation ordering of output sequence numbers (OSNs) using a select combination of digits associated with each RNSRV. The arbitrary permutation ordering is determined using a cyclic structure. The encryptor is configured to generate a modified data stream by combining the OSNs and DS.

Claims

1. A cryptographic system, comprising:

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

a ring generator including (a) a computing means configured for performing a plurality of RNS arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values, (b) a converting means configured for converting each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit, and (c) a permutation means configured for generating an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values, wherein said arbitrary permutation ordering is determined using a cyclic structure; and

an encryptor coupled to said data stream receiving means and said ring generator, said encryptor configured for generating a modified data stream by incorporating or combining said plurality of output sequence numbers with said data stream.

2. The cryptographic system according to claim 1, wherein said random number has a value within a range of zero to n!−

1 and said cyclic structure has n elements.

3. The cryptographic system according to claim 2, wherein each of said plurality of output sequence numbers is associated with a respective element of said n elements.

4. The cryptographic system according to claim 1, wherein said computing means is further configured for calculating said plurality of RNS residue values using relatively prime numbers as moduli, wherein said relatively prime numbers are selected to have a product equal to a decimal number defined by n!.

5. The cryptographic system according to claim 1, wherein said converting means is further configured for converting each of said plurality of RNS residue values to a different relatively prime number system.

6. The cryptographic system according to claim 1, wherein said select combination of digits are chosen so that a range of values which can be determined by said digits is equal to a number of available unselected elements in said cyclic structure.

7. The cryptographic system according to claim 1, wherein said permutation means is further configured for using a value of said select combination of digits to select an available unselected element in said cyclic structure.

8. The cryptographic system according to claim 1, wherein said permutation means is further configured for using a Chinese Remainder Theorem to combine at least two digits associated with at least two RNS residue values to obtain a digit having a different number base than said at least two digits.

9. The cryptographic system according to claim 1, wherein said permutation means is further configured for using a Chinese Remainder Theorem to combine with one or more additional cyclic ring generators.

10. The cryptographic system according to claim 9, wherein said permutation means is further configured for using said digit having a different number base to select an available unselected element in said cyclic structure.

11. 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.

12. The cryptographic system according to claim 1, wherein said encryptor is configured for performing at least one of a standard multiplication operation, a multiplication in a Galois extension field operation, an addition modulo q operation, a subtraction modulo q operation and a bitwise logic operation.

13. The cryptographic system according to claim 1, further comprising a second ring generator configured for generating a decryption sequence.

14. The cryptographic system according to claim 13, further comprising a decryptor electronically connected to said second ring generator, said decryptor configured for generating decrypted data by performing a decryption method utilizing said modified data stream and said decryption sequence.

15. A cryptographic system, comprising:

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

a first ring generator including (a) a computing means configured for performing a plurality of RNS arithmetic operations to express a random number in a random number sequence as a plurality of RNS residue values, (b) a converting means configured for converting each of said plurality of RNS residue values to a relatively prime number system so that each of said plurality of RNS residue values includes at least one digit, and (c) a permutation means configured for generating an arbitrary permutation ordering of a plurality of output sequence numbers using a select combination of digits associated with each of said plurality of RNS residue values, wherein said arbitrary permutation ordering is determined using a cyclic structure; and

a diffusion operator coupled to said data stream receiving means and said first ring generator, said diffusion operator configured for generating a diffused data stream by permuting said data stream using said arbitrary permutation ordering of a plurality of output sequence numbers.

16. The cryptographic system according to claim 15, wherein said random number has a value within a range of zero to n!−

1 and said cyclic structure has n elements.

17. The cryptographic system according to claim 16, wherein each of said plurality of output sequence numbers is associated with a respective element of said n elements.

18. The cryptographic system according to claim 15, wherein said computing means is further configured for calculating said plurality of RNS residue values using relatively prime numbers as moduli, wherein said relatively prime numbers are selected to have a product equal to a decimal number defined by n!.

19. The cryptographic system according to claim 15, wherein said converting means is further configured for converting each of said plurality of RNS residue values to a different relatively prime number system.

20. The cryptographic system according to claim 15, wherein said select combination of digits are chosen so that a range of values which can be determined by said digits is equal to a number of available unselected elements in said cyclic structure.

21. The cryptographic system according to claim 15, wherein said permutation means is further configured for using a value of said select combination of digits to select an available unselected element in said cyclic structure.

22. The cryptographic system according to claim 15, wherein said permutation means is further configured for using a Chinese Remainder Theorem to combine at least two digits associated with at least two RNS residue values to obtain a digit having a different number base than said at least two digits.

23. The cryptographic system according to claim 22, wherein said permutation means is further configured for using said digit having a different number base to select an available unselected element in said cyclic structure.

24. The cryptographic system according to claim 15, further comprising a second ring generator configured for generating a reverse diffusion sequence comprised of pseudo-random numbers or pseudo-chaotic random numbers.

25. The cryptographic system according to claim 24, further comprising a reverse diffusion operator coupled to said second ring generator, said diffusion operator configured for un-diffusing said diffused data stream by performing reverse diffusion operations utilizing said reverse diffusion sequence.