Mixed radix conversion with a priori defined statistical artifacts

• US 7,970,809 B2
• Filed: 06/07/2007
• Issued: 06/28/2011
• Est. Priority Date: 06/07/2007
• 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): Malzahn; David H
• Application Number:
  US11/759,277
• Publication Number:
  US 20080307022A1
• Time in Patent Office: 1,482 Days
• Field of Search: None
• 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 7/724 Finite field arithmetic for error detection or correction in general H03M13/00, in computers G06F11/10

Abstract

A method is presided for masking a process used in generating a random number sequence. The method includes generating a random number sequence. This step involves selectively generating the random number sequence utilizing a ring structure which has been punctured. The method also includes performing a mixed radix conversion to convert the random number sequence from a first number base to a second number base. The method further includes puncturing the ring structure by removing at least one element therefrom to eliminate a statistical artifact in the random number sequence expressed in the second number base. The first number base and second number base are selected so that they are respectively defined by a first Galois field characteristic and a second Galois field characteristic.

Claims

1. A method for masking a process used in generating a random number sequence, comprising:

generating, by at least one electronic circuit, a random number sequence;

performing, by said electronic circuit, a mixed radix conversion to convert said random number sequence from a first number base to a second number base; and

combining, by said electronic circuit, said random number sequence expressed in said second number base with a sequence of symbols defining information to be stored in a storage device or transmitted over a communications link;

wherein said generating step further comprises selectively generating said random number sequence utilizing a ring structure that has been punctured.

2. The method according to claim 1, wherein said ring structure is punctured by removing at least one element therefrom to eliminate a statistical artifact in said random number sequence expressed in said second number base.

3. The method according to claim 2, wherein said at least one element is selected to induce a chosen statistical artifact in said mixed radix conversion step.

4. The method according to claim 2, wherein said first number base and said second number base are selected so that they are respectively defined by a first Galois field characteristic and a second Galois field characteristic.

5. The method according to claim 4, wherein said first Galois field characteristic is selected so that it is mutually prime with respect to said second Galois field characteristic.

6. The method according to claim 4, wherein said second Galois field characteristic is selected to be a finite field size which is smaller as compared to a finite field size of a first Galois field.

7. The method according to claim 6, wherein said puncturing step further comprises eliminating n element(s) from said ring structure to remove at least one statistical artifact in said random number sequence expressed in said second number base, wherein n is determined based on a mathematical relation between a number of elements in said first Galois field and a number of elements in a second Galois field.

8. The method according to claim 7, wherein n is determined based on a remainder value resulting from a quotient of said number of elements in said first Galois field divided by said number of elements in said second Galois field.

9. The method according to claim 7, wherein said mixed radix conversion produces a plurality of equivalence classes in said second number base, and said n elements which are eliminated from said ring structure are selected to ensure that each equivalence class has an equal number of elements after said performing a mixed radix conversion step.

10. A system, comprising:

a generator configured for selectively generating a random number sequence utilizing a ring structure which has been punctured;

a mixed radix converter configured for performing a mixed radix conversion to convert said random number sequence from a first number base to a second number base; and

wherein said ring structure which has been punctured and said mixed radix converter are configured in combination to produce a random number sequence in said second number base which is exclusive of any statistical artifacts associated with said mixed radix conversion.

11. The system according to claim 10, further comprising a means for modifying a data stream utilizing said random number sequence expressed in said second number base.

12. The system according to claim 10, wherein said first number base and said second number base are respectively defined by a first Galois field characteristic and a second Galois field characteristic.

13. The system according to claim 12, wherein said first Galois field characteristic is mutually prime with respect to said second Galois field characteristic.

14. The system according to claim 12, wherein said second Galois field characteristic is selected as a finite field size which is smaller as compared to a finite field size of a first Galois field.

15. The system according to claim 14, wherein said ring structure has n element(s) removed therefrom to eliminate at least one statistical artifact in said random number sequence expressed in said second number base, wherein n is determined based on a mathematical relation between a number of elements in said first Galois field and a number of elements in a second Galois field.

16. The system according to claim 15, wherein n is determined based on a remainder value resulting from a quotient of said number of elements in said first Galois field divided by said number of elements in said second Galois field.

17. The system according to claim 16, wherein said mixed radix conversion produces a plurality of equivalence classes in said second number base, and said n elements which are removed from said ring structure are selected to ensure that each equivalence class has an equal number of elements after said mixed radix conversion.