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Periodic autocorrelation of sequences

Florian Caullery, Eric F Érard, François Rodier

TL;DR

It is shown that the same is true for the evaluation of the periodic autocorrelations of random binary sequences as for the evaluation of the periodic autocorrelations of random Boolean functions.

Abstract

The autocorrelation of a sequence is a useful criterion, among all, of resistance to cryptographic attacks. The behavior of the autocorrelations of random Boolean functions (studied by Florian Caullery, Eric Férard and François Rodier [4]) shows that they are concentrated around a point. We show that the same is true for the evaluation of the periodic autocorrelations of random binary sequences.

Periodic autocorrelation of sequences

TL;DR

It is shown that the same is true for the evaluation of the periodic autocorrelations of random binary sequences as for the evaluation of the periodic autocorrelations of random Boolean functions.

Abstract

The autocorrelation of a sequence is a useful criterion, among all, of resistance to cryptographic attacks. The behavior of the autocorrelations of random Boolean functions (studied by Florian Caullery, Eric Férard and François Rodier [4]) shows that they are concentrated around a point. We show that the same is true for the evaluation of the periodic autocorrelations of random binary sequences.

Paper Structure

This paper contains 9 sections, 22 theorems, 68 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of theorem \ref{['theo']}
  4. Appendix : proof of the proposition \ref{['prop_P(Cu_cap_Cv)']}
  5. Even sequences.
  6. Upper bound for $\xi$-partitions
  7. Decomposition of $\xi$-partitions.
  8. Bound on the number of $\xi$-partitions.
  9. Proof of proposition \ref{['prop_P(Cu_cap_Cv)']}.

Key Result

Theorem 1

Theorems & Definitions (41)

  • Theorem 1
  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Lemma 2
  • Proposition 2
  • proof
  • Proposition 3
  • Lemma 3
  • ...and 31 more