Inferring Sequences Produced by Nonlinear Pseudorandom Number Generators Using Coppersmith’s Methods

  • Aurélie Bauer
  • Damien Vergnaud
  • Jean-Christophe Zapalowicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7293)

Abstract

Number-theoretic pseudorandom generators work by iterating an algebraic map F (public or private) over a residue ring ℤ N on a secret random initial seed value v 0 ∈ ℤ N to compute values \(v_{n+1} = F(v_n) \bmod{N}\) for n ∈ ℕ. They output some consecutive bits of the state value v n at each iteration and their efficiency and security are thus strongly related to the number of output bits. In 2005, Blackburn, Gomez-Perez, Gutierrez and Shparlinski proposed a deep analysis on the security of such generators. In this paper, we revisit the security of number-theoretic generators by proposing better attacks based on Coppersmith’s techniques for finding small roots on polynomial equations. Using intricate constructions, we are able to significantly improve the security bounds obtained by Blackburn et al..

Keywords

Nonlinear Pseudorandom number generators Euclidean lattice LLL algorithm Coppersmith’s techniques Unravelled linearization 

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Copyright information

© International Association for Cryptologic Research 2012

Authors and Affiliations

  • Aurélie Bauer
    • 1
  • Damien Vergnaud
    • 2
  • Jean-Christophe Zapalowicz
    • 3
  1. 1.Agence Nationale de la Sécurité des Systèmes d’InformationParis 07France
  2. 2.École Normale Supérieure – C.N.R.S. – I.N.R.I.A.Paris Cedex 05France
  3. 3.INRIA Rennes – Bretagne AtlantiqueRennesFrance

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