Generator of chaotic sequences and corresponding generating system

• US 8,781,116 B2
• Filed: 03/28/2011
• Issued: 07/15/2014
• Est. Priority Date: 03/29/2010
• Status: Active Grant

• Current Assignee: Universite De Nantes
• Original Assignee: Universite De Nantes
• Inventors: El Assad, Safwan, Noura, Hassan
• Primary Examiner(s): Mehedi, Morshed
• Application Number:
  US13/638,126
• Publication Number:
  US 20130170641A1
• Time in Patent Office: 1,205 Days
• Field of Search: 380/44
• US Class Current: 380/44
• CPC Class Codes: G06F 7/582 Pseudo-random number generators
• CPC Class Codes: H04L 9/0861 Generation of secret information including derivation or calculation of cryptographic keys or passwords

Abstract

A generator of chaotic sequences of integer values is provided. The generator includes at least two discrete recursive filters at least of first-order, generating an output chaotic sequence of integer values, each recursive filter comprising means for implementing a nonlinear function connected via an exclusive-or gate to means for generating a perturbation sequence of integer values. The two filters are mounted in parallel. The chaotic sequence output from the generator is equal to an exclusive-or of the chaotic sequences output from the recursive filters, and in the means for implementing the nonlinear function includes a chaotic map.

Claims

1. A generator of chaotic sequences e_u(n), n being a strictly positive integer, of integer values represented on a determined number of quantification bits N, to form data encrypting keys, the generator comprising:

at least two discrete recursive filters at least of first-order generating an output chaotic sequence of integer values, each recursive filter comprising means for implementing a nonlinear function F, connected via an exclusive-or gate to means for generating a perturbation sequence Q(n) of integer values represented on a determined number of quantification bits k,

wherein the two filters are mounted in parallel, the chaotic sequence e_u(n) output from the generator being equal to an exclusive-or of the chaotic sequences output from the recursive filters, and

wherein the means for implementing the nonlinear function includes a chaotic map.

2. The generator of chaotic sequences according to claim 1, wherein the means for generating a perturbation sequence in each filter includes a maximum length feedback shift register using a primitive polynomial of degree k.

3. The generator of chaotic sequences according to claim 1 wherein the order of each recursive filter is third-order or lower.

4. The generator of chaotic sequences according to claim 1 wherein the means for implementing the nonlinear function includes a piece-wise linear chaotic map PWLCM.

5. The generator of chaotic sequences according to claim 3 wherein the sequences e_uj(n) output from each recursive filter j=1,2 are given by the equation

e_uj(n)=F(X_j(n−

1),P)⊕

Q(n)

where;

6. The generator of chaotic sequences according to claim 1 wherein the means for implementing the nonlinear function includes a chaotic map of SKEW-Tent type.

7. A system for generating chaotic sequences comprising at least one assembly of 14 generators of chaotic sequences according to claim 1, the generators being divided into two groups of 7 generators each, wherein the system comprises:

a first analogue multiplexer allowing a selection of an output of a first generator from among the generators of the first group;

a second analogue multiplexer allowing a selection of an output of a second generator from among the generators of the second group, the outputs of the two multiplexers being connected to an exclusive-or gate having an output that generates the chaotic sequence, and

means for addressing the multiplexers comprising a feedback shift register connected to a clock having a period that is a function of the length of the chaotic sequence.

8. The system for generating chaotic sequences according to claim 7, wherein the at least one assembly includes two assemblies, the first and second assembly being mounted in parallel, each assembly having 14 generators of chaotic sequences, the generated chaotic sequence output from the generating system being equal to an exclusive-or of the chaotic sequences generated at the outputs of the two assemblies of 14 generators.

9. The system for generating chaotic sequences according to claim 8, wherein primitive polynomials of the feedback shift registers of the first assembly of generators are different from primitive polynomials of the feedback shift registers of the second assembly of generators.

10. The system for generating chaotic sequences according to claim 7 further comprising means for eliminating a determined quantity of samples of chaotic sequences generated by the system.

11. The system for generating chaotic sequences according to claim 7 further comprising means for quantifying the generated chaotic sequences.

12. An encrypting system, comprising a system for generating chaotic sequences according to claim 7, the system for generating chaotic sequences being used for generating secret keys and in enciphering/deciphering procedures of the encryption system.