DIGITAL GENERATION OF AN ACCELERATED OR DECELERATED CHAOTIC NUMERICAL SEQUENCE

• US 20090327387A1
• Filed: 05/29/2008
• Published: 12/31/2009
• Est. Priority Date: 05/29/2008
• 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 8,145,692 B2
• Time in Patent Office: Days
• US Class Current: 708/446
• 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

Abstract

A method for generating an accelerated and/or decelerated chaotic sequence. The method involves selecting a plurality of polynomial equations constructed from an acc-dec variable v. The method also involves selecting a value for the acc-dec variable v for advancing or stepping back a chaotic sequence generation by at least one cycle at a given time. The method further involves using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations using the acc-dec variable v. The solutions iteratively computed and expressed as RNS residue values. The method involves determining a series of digits in a weighted number system based on the RNS residue values.

Claims

1. A method for generating an accelerated and/or decelerated chaotic sequence, comprising the steps of:

selecting a plurality of polynomial equations constructed from an acc-dec variable v;

selecting a value for said acc-dec variable v for advancing a chaotic sequence generation by at least one cycle at a given time or stepping back said chaotic sequence generation by at least one cycle at said given time;

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

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

2. The method according to claim 1, further comprising the step of selecting said variable v to be defined by a mathematical expression c modulo m_i, where c is a number of cycles for acceleration or deceleration and m_i is a value indicating a cycle in which a chaotic sequence starts to repeat.

3. The method according to claim 1, wherein said plurality of polynomial equations are polynomial equations f₀[x((n+v+t)T)], . . . , f_M−

1[x((n+v+t)T)], where n is an index of time, v is a variable having a value selected to accelerate or decelerate a chaotic sequence generation by at least one cycle, t is a variable representing an initial time offset, and T is a discrete time interval.

4. 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.

5. The method according to claim 1, further comprising the step of selecting a value for each of M moduli in a RNS used for solving each of said plurality of polynomial equations.

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

7. The method according to claim 6, further comprising selecting said constant value so that a polynomial equation is irreducible for a predefined modulus.

8. A machine-readable medium having stored thereon instructions, which when executed by a machine, cause the machine to perform the following operations comprising:

selecting a plurality of polynomial equations constructed from an acc-dec variable v;

selecting a value for said acc-dec variable v for advancing a chaotic sequence generation by at least one cycle at a given time or stepping back said chaotic sequence generation by at least one cycle at said given time;

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

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

9. The machine-readable medium according to claim 8, wherein said variable v is defined by a mathematical expression c modulo mi, where c is a number of cycles for acceleration or deceleration and m_i is a value indicating a cycle in which a chaotic sequence starts to repeat.

10. The machine-readable medium according to claim 8, wherein said plurality of polynomial equations are polynomial equations f₀[x((n+v+t)T)], . . . , f_M−

1[x((n+v+t)T)], where n is an index of time, v is a variable having a value selected to accelerate or decelerate a chaotic sequence generation by at least one cycle, t is a variable representing an initial time offset, and T is a discrete time interval.

11. The machine-readable medium according to claim 8, further comprising instructions to cause the operation of determining a series of digits in said weighted number system by identifying a number in said weighted number system that is defined by said plurality of RNS residue values.

12. The machine-readable medium according to claim 8, wherein each said polynomial equation is irreducible.

13. The machine-readable medium according to claim 8, wherein each said plurality of polynomial equations is identical exclusive of a constant value.

14. The machine-readable medium according to claim 13, wherein said constant value is selected so that a polynomial equation is irreducible for a predefined modulus.

15. A chaotic sequence generator, comprising:

at least one processing device configured for using residue number system (RNS) arithmetic operations to respectively determine a plurality of solutions for a plurality of polynomial equations using an acc-dec variable v, said plurality of solutions iteratively computed and expressed as RNS residue values, and determining a series of digits in a weighted number system based on said plurality of RNS residue values;

wherein said plurality of polynomial equations are constructed from said acc-dec variable v, and said acc-dec variable v has a value selected for advancing a chaotic sequence generation by at least one cycle at a given time or stepping back said chaotic sequence generation by at least one cycle at said given time.

16. The chaotic sequence generator according to claim 15, wherein said variable v is defined by a mathematical expression c modulo m_i, where c is a number of cycles for acceleration or deceleration and m_i is a value indicating a cycle in which a chaotic sequence starts to repeat.

17. The chaotic sequence generator according to claim 15, wherein said plurality of polynomial equations are polynomial equations f₀[x((n+v+t)T)], . . . , f_M−

1[x((n+v+t)T)], where n is an index of time, v is a variable having a value selected to accelerate or decelerate a chaotic sequence generation by at least one cycle, t is a variable representing an initial time offset, and T is a discrete time interval.

18. The chaotic sequence generator according to claim 15, wherein said at least one processing device is further configured for identifying a number in said weighted number system that is defined by said plurality of RNS residue values.

19. The chaotic sequence generator according to claim 15, wherein said plurality of polynomial equations are identical exclusive of a constant value.

20. The chaotic sequence generator according to claim 19, wherein said constant value is selected so that a polynomial equation is irreducible for a predefined modulus.