Digital Generation of a Chaotic Numerical Sequence

• US 20080263119A1
• Filed: 04/19/2007
• Published: 10/23/2008
• 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.
• Granted Patent: US 7,937,427 B2
• Time in Patent Office: Days
• US Class Current: 708/446
• 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, comprising:

selecting a plurality of polynomial equations;

using residue number system (RNS) arithmetic operations to respectively determine a plurality of solutions for said plurality of polynomial equations, said plurality of solutions iteratively computed and expressed as RNS residue values; and

determining a series of digits in said weighted number system based on said plurality of RNS residue values.

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 plurality of RNS 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 plurality of RNS 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 in a RNS used for solving each of said plurality of polynomial equations.

8. The method according to claim 7, further comprising selecting each said modulus for each of said plurality of 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 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 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 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;

a computing means configured for using residue number system (RNS) arithmetic operations to respectively determine a plurality of solutions for a plurality of polynomial equations, said plurality of solutions iteratively computed and expressed as RNS residue values; and

a mapping means configured for determining a series of digits in said weighted number system based on said plurality of RNS residue values.

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

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

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

21. The chaotic sequence generator according to claim 20, wherein said mapping means 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 mapping means is further configured for selecting 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.

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

24. The chaotic sequence generator according to claim 17, wherein said computing means is further configured for utilizing a modulus selected for each of said plurality of 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 polynomial equations include at least a cubic type polynomial equation.

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

28. The chaotic sequence generator according to claim 17, wherein said plurality of 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 solution computed in a previous iteration.

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