Cryptographic system incorporating a digitally generated chaotic numerical sequence

• US 8,180,055 B2
• Filed: 02/05/2008
• Issued: 05/15/2012
• Est. Priority Date: 02/05/2008
• Status: Active Grant

• Current Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Original Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Inventors: Chester, David B., Michaels, Alan J.
• Primary Examiner(s): Chea, Philip
• Assistant Examiner(s): MEJIA, FELICIANO S
• Application Number:
  US12/026,217
• Publication Number:
  US 20090196420A1
• Time in Patent Office: 1,561 Days
• Field of Search: 380/263
• US Class Current: 380/263
• CPC Class Codes: G06F 7/586 using an integer algorithm, e.g. using linear congruential method
• CPC Class Codes: G06F 7/72 using residue arithmetic
• CPC Class Codes: H04L 2209/20 Manipulating the length of blocks of bits, e.g. padding or block truncation
• CPC Class Codes: H04L 9/001 using chaotic signals
• 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 device (DSRD), a chaotic sequence generator (CSG) and an encryptor. The DSRD (602) is configured to receive an input data stream. The CSG (300) includes a computing means (302₀, . . . , 302_N−1) and a mapping means (304). The computing means is configured to use RNS arithmetic operations to respectively determine solutions for polynomial equations. The solutions are iteratively computed and expressed as RNS residue values. The mapping means is configured to determine a series of digits in the weighted number system based on the RNS residue values. The encryptor is coupled to the DSRD and CSG. The encryptor is configured to generate a modified data stream by incorporating or combining the series of digits with the input data stream.

Claims

1. A cryptographic system, comprising:

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

a first chaotic sequence generator including;

(a) a computing device configured for using residue arithmetic operations to respectively determine a plurality of solutions for a plurality of modular polynomial equations of a third order or higher, where a modulus and a constant zero-power coefficient of each modular polynomial equation are selected such that an irreducible form of a respective modular polynomial equation is generated, said plurality of solutions iteratively computed and expressed as residue values; and

(b) a mapping device configured for determining a series of digits in a weighted number system based on said plurality of residue values; and

an encryptor coupled to said data stream receiving device and said first chaotic sequence generator, said encryptor configured for generating a modified data stream by combining said series of digits with said input data stream.

2. The cryptographic system according to claim 1, wherein said mapping device is further configured to determine a series of digits in said weighted number system based on said plurality of residue values using a Chinese Remainder Theorem process.

3. The cryptographic system according to claim 1, wherein said mapping device is further configured to identify a number in said weighted number system that is defined by said plurality of residue values.

4. The cryptographic system according to claim 1, wherein said mapping device is further configured to identify a truncated portion of a number in said weighted number system that is defined by said plurality of residue values.

5. The cryptographic system according to claim 4, wherein said mapping device is further configured to select said truncated portion to include any serially arranged set of digits comprising a portion of said number in said weighted number system.

6. The cryptographic system according to claim 5, wherein said mapping device is further configured to select said truncated portion exclusive of a most significant digit when all possible weighted numbers represented by P bits, said P is a fewest number of bits required to achieve a binary representation of said weighted numbers.

7. The cryptographic system according to claim 1, wherein said computing device is further configured to utilize a modulus selected for each of said plurality of modular polynomial equations so that each said modular polynomial equation is irreducible.

8. The chaotic sequence generator according to claim 1, wherein said computing device is further configured to utilize a modulus selected for each of said plurality of modular polynomial equations so that solutions iteratively computed via a feedback mechanism for said plurality of modular polynomial equations are chaotic.

9. The cryptographic system according to claim 1, wherein said plurality of modular polynomial equations include at least a cubic type polynomial equation.

10. The cryptographic system according to claim 1, wherein said plurality of modular polynomial equations are identical exclusive of a constant value.

11. The cryptographic system according to claim 1, wherein said plurality of modular polynomial equations are at least one of a constant or varying function of time.

12. The cryptographic system according to claim 1, wherein said first chaotic sequence generator further comprises a feedback mechanism configured to selectively define a variable “

x”

of a polynomial equation as a solution computed in a previous iteration.

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 to perform at least one of a standard multiplication operation, a multiplication in a Galois extension field, an addition modulo q operation, a subtraction modulo q operation and a bitwise logic operation.

15. The cryptographic system according to claim 1, further comprising a second chaotic sequence generator configured to generate a decryption sequence, said decryption sequence is a chaotic sequence having a time varying value expressed in a digital form that has no discernable regularity or order.

16. The cryptographic system according to claim 15, further comprising a decryptor electronically connected to said second chaotic sequence generator, said decryptor configured to generate decrypted data by performing a decryption method utilizing said modified data stream and said decryption sequence.

17. The cryptographic system according to claim 1, wherein said input data stream is expressed in the same weighted number system as said series of digits generated by said first chaotic sequence generator.

18. A method for encrypting an input data stream, comprising:

using, by at least one computing processor, residue arithmetic operations to respectively determine a plurality of solutions for a plurality of modular polynomial equations of a third order or higher, where a modulus and a constant zero-power coefficient of each equation are selected such that an irreducible form of a respective modular polynomial equation is generated, said plurality of solutions iteratively computed and expressed as residue values;

determining, by said computing processor, a series of digits in a weighted number system based on said plurality of residue values; and

generating, by an encryption device, a modified data stream by combining said series of digits with said input data stream.

19. The method according to claim 18, wherein said using step further comprises utilizing a modulus selected for each of said plurality of modular polynomial equations so that each said modular polynomial equation is irreducible.

20. The method according to claim 18, wherein said determining step further comprises identifying a number in said weighted number system that is defined by said plurality of residue values.

21. The method according to claim 18, further comprising generating by said computing processor a decryption sequence, wherein said decryption sequence is a chaotic sequence having a time varying value expressed in a digital form that has no discernable regularity or order.

22. The method according to claim 19, further comprising generating by a decryption device decrypted data by performing a decryption method utilizing said modified data stream and said decryption sequence.

23. A device comprising a non-transitory computer readable medium, having stored thereon a computer program for generating a chaotic numerical sequence, the computer program having a plurality of code sections, the code sections executable by a computer to cause the computer to perform the steps of:

determining a plurality of solutions for a plurality of modular polynomial equations of a third order or higher using residue arithmetic operations, where a modulus and a constant zero-power coefficient of each modular polynomial equation are selected such that an irreducible form of a respective modular polynomial equation is generated, said plurality of solutions iteratively computed and expressed as residue values;

determining a series of digits in a weighted number system based on said plurality of residue values; and

generating a modified data stream by combining said series of digits with said input data stream.

24. The device according to claim 23, further comprising code sections for causing said computer to generate a decryption sequence, wherein said decryption sequence is a chaotic sequence having a time varying value expressed in a digital form that has no discernable regularity or order.

25. The device according to claim 24, further comprising code sections for causing said computer to generate decrypted data by performing a decryption method utilizing said modified data stream and said decryption sequence.