On Cryptographic Schemes Based on Discrete Logarithms and Factoring

  • Marc Joye
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5888)

Abstract

At CRYPTO 2003, Rubin and Silverberg introduced the concept of torus-based cryptography over a finite field. We extend their setting to the ring of integers modulo N. We so obtain compact representations for cryptographic systems that base their security on the discrete logarithm problem and the factoring problem. This results in smaller key sizes and substantial savings in memory and bandwidth. But unlike the case of finite fields, analogous trace-based compression methods cannot be adapted to accommodate our extended setting when the underlying systems require more than a mere exponentiation. As an application, we present an improved, torus-based implementation of the ACJT group signature scheme.

Keywords

Torus-based cryptography ring ℤN discrete logarithm problem factoring problem compression ACJT group signatures 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Marc Joye
    • 1
  1. 1.Thomson R&DSecurity Competence CenterCesson-Sévigné CedexFrance

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