On Cryptographic Schemes Based on Discrete Logarithms and Factoring

Authors:
Marc Joye
Affiliations:
Thomson R&D, Security Competence Center, Cesson-Sééévigné Cedex, France 35576
Venue:
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Year:
2009

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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.