Digital generation of an accelerated or decelerated chaotic numerical sequence

• US 8,145,692 B2
• Filed: 05/29/2008
• Issued: 03/27/2012
• 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.
• Primary Examiner(s): Ngo, Chuong D
• Application Number:
  US12/129,197
• Publication Number:
  US 20090327387A1
• Time in Patent Office: 1,398 Days
• Field of Search: 708/491, 708/492, 708/250, 708/254
• US Class Current: 708/250
• 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, by at least one electronic circuit, a plurality of polynomial equations constructed from an acc-dec variable v;

selecting, by said electronic circuit, 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, by said electronic circuit, 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;

determining, by said electronic circuit, a series of digits in a weighted number system based on said plurality of RNS residue values; and

combining, by said electronic circuit, said series of digits with a sequence of symbols defining information to be stored in a storage device or transmitted over a communications link.

2. The method according to claim 1, wherein said variable v is selected 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, wherein a value is selected for each of M moduli in an RNS used for solving each of said plurality of polynomial equations.

6. The method according to claim 1, wherein each said plurality of polynomial equations is selected to be identical exclusive of a constant value.

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

8. A device comprising a non-transitory computer-readable medium, having stored thereon a computer program for generating an accelerated and/or decelerated chaotic sequence, the computer program having a plurality of code sections executable by a computer to cause the computer to perform 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;

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

combining said series of digits with a sequence of symbols defining information to be stored in a storage device or transmitted over a communications link.

9. The device according to claim 8, 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.

10. The device 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 device according to claim 8, further comprising code sections for causing said computer to determine 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 device according to claim 8, wherein each said polynomial equation is irreducible.

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

14. The device 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 to

use 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,

determine a series of digits in a weighted number system based on said plurality of RNS residue values, and

combine said series of digits with a sequence of symbols defining information to be stored in a storage device or transmitted over a communications link;

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 to identify 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.