Digital generation of a chaotic numerical sequence

• US 7,937,427 B2
• Filed: 04/19/2007
• Issued: 05/03/2011
• Est. Priority Date: 04/19/2007
• Status: Active Grant

• Current Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Original Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Inventors: Michaels, Alan J., Chester, David B.
• Primary Examiner(s): Ngo; Chuong D
• Application Number:
  US11/737,459
• Publication Number:
  US 20080263119A1
• Time in Patent Office: 1,475 Days
• Field of Search: 708/250, 708/252, 380/46
• US Class Current: 708/250
• CPC Class Codes: G06F 7/584 using finite field arithmetic, e.g. using a linear feedback shift register
• CPC Class Codes: G06F 7/72 using residue arithmetic

Abstract

A method is provided for generating a chaotic sequence. The method includes selecting a plurality of polynomial equations. The method also includes using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations. The solutions are iteratively computed and expressed as RNS residue values. The method further includes determining a series of digits in a weighted number system (e.g., a binary number system) based on the RNS residue values. According to an aspect of the invention, the method includes using a Chinese Remainder Theorem process to determine a series of digits in the weighted number system based on the RNS residue values. According to another aspect of the invention, the determining step comprises identifying a number in the weighted number system that is defined by the RNS residue values.

Claims

1. A method for generating a chaotic sequence in a communication system, comprising the steps of:

concurrently solving, by said communication system, a plurality of different polynomial equations to obtain a plurality of solutions, each of said plurality of different polynomial equations having chaotic properties in Galois field arithmetic and having an input variable with a value equal to a residue value computed using a previous solution therefore;

concurrently performing, by said communications system, a plurality of arithmetic operations to express said plurality of solutions as residue values;

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

combining, by said communication system, said series of digits with a sequence of symbols defining information to be transmitted from said communication system.

2. The method according to claim 1, further comprising using a Chinese Remainder Theorem process to perform said determining step.

3. The method according to claim 1, wherein said determining step further comprises identifying a number in said weighted number system that is defined by said residue values.

4. The method according to claim 1, wherein said determining step further comprises identifying a truncated portion of a number in said weighted number system that is defined by said residue values.

5. The method according to claim 4, further comprising selecting said truncated portion to include any serially arranged set of digits comprising a portion of said number in said weighted number system.

6. The method according to claim 5, further comprising selecting said truncated portion exclusive of a most significant digit comprising said number in said weighted number system.

7. The method according to claim 1, further comprising selecting a value for each of N moduli used to compute said residue values.

8. The method according to claim 7, further comprising selecting each said modulus for each of said plurality of different polynomial equations so that each said polynomial equation is irreducible.

9. The method according to claim 7, further comprising selecting each said modulus for each of said plurality of different polynomial equations so that solutions iteratively computed via a feedback mechanism for said polynomial equations are chaotic.

10. The method according to claim 1, further comprising selecting said plurality of different polynomial equations to include at least a cubic type polynomial equation.

11. The method according to claim 1, further comprising selecting each of said plurality of different polynomial equations to be identical exclusive of a constant value.

12. The method according to claim 11, further comprising selecting said constant value so that a polynomial equation is irreducible for a predefined modulus.

13. The method according to claim 1, further comprising selecting said polynomial equation to be at least one of a constant or varying function of time.

14. The method according to claim 1, further comprising iteratively computing said plurality of solutions using a feedback mechanism.

15. The method according to claim 14, further comprising selecting said feedback mechanism to include selectively defining a value of a variable of a polynomial equation for each solution iteratively computed, said value based on a previous iteratively computed solution of said polynomial equation.

16. The method according to claim 1, wherein said weighted number system is a binary number system.

17. A chaotic sequence generator, comprising:

at least one electronic circuit configured for

concurrently solving a plurality of different polynomial equations to obtain a plurality of solutions, each of said plurality of different polynomial equations having chaotic properties in Galois field arithmetic and having an input variable with a value equal to a residue value computed using a previous solution therefore,

concurrently performing a plurality of arithmetic operations to express said plurality of solutions as residue values,

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

combining said series of digits with a sequence of symbols defining information to be transmitted from said communication system.

18. The chaotic sequence generator according to claim 17, wherein said electronic circuit is further configured for determining a series of digits in said weighted number system based on said residue values using a Chinese Remainder Theorem process.

19. The chaotic sequence generator according to claim 17, wherein said electronic circuit is further configured for identifying a number in said weighted number system that is defined by said residue values.

20. The chaotic sequence generator according to claim 17, wherein said electronic circuit is further configured for identifying a truncated portion of a number in said weighted number system that defined by said residue values.

21. The chaotic sequence generator according to claim 20, wherein said electronic circuit is further configured for selecting said truncated portion to include any serially arranged set of digits comprising a portion of said number in said weighted number system.

22. The chaotic sequence generator according to claim 21, wherein said electronic circuit is further configured for selecting said truncated portion exclusive of a most significant digit when all possible weighted numbers are represented by P bits, said P is a fewest number of bits required to achieve a binary representation of said weighted numbers.

23. The chaotic sequence generator according to claim 17, wherein said electronic circuit is further configured for utilizing a modulus selected for each of said plurality of different polynomial equations so that each said polynomial equation is irreducible.

24. The chaotic sequence generator according to claim 17, wherein said electronic circuit is further configured for utilizing a modulus selected for each of said plurality of different polynomial equations so that solutions iteratively computed via a feedback mechanism for said polynomial equations are chaotic.

25. The chaotic sequence generator according to claim 17, wherein said plurality of different polynomial equations include at least a cubic type polynomial equation.

26. The chaotic sequence generator according to claim 17, wherein said plurality of different polynomial equations are identical exclusive of a constant value.

27. The chaotic sequence generator according to claim 26, wherein said constant value is selected so that a polynomial equation is irreducible for a predefined modulus.

28. The chaotic sequence generator according to claim 17, wherein said plurality of different polynomial equations are at least one of a constant or varying function of time.

29. The chaotic sequence generator according to claim 17, further comprising a feedback mechanism configured for selectively defining a variable “

x’

of a polynomial equation as a residue value computed in a previous iteration.