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On Cryptographic Schemes Based on Discrete Logarithms and Factoring

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Cryptology and Network Security (CANS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5888))

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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.

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Author information

Authors and Affiliations

  1. Thomson R&D, Security Competence Center, 1 avenue de Belle Fontaine, 35576, Cesson-Sévigné Cedex, France

    Marc Joye

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  1. Marc Joye
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Editor information

Editors and Affiliations

  1. AT&T Labs Research, Florham Park, NJ, USA

    Juan A. Garay

  2. Japan Advanced Institute of Science and Technology (JAIST), Nomi, Ishikawa, Japan

    Atsuko Miyaji

  3. National Institute of Advanced Industrial Science and Technoloy (AIST), Tokyo, Japan

    Akira Otsuka

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Joye, M. (2009). On Cryptographic Schemes Based on Discrete Logarithms and Factoring. In: Garay, J.A., Miyaji, A., Otsuka, A. (eds) Cryptology and Network Security. CANS 2009. Lecture Notes in Computer Science, vol 5888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10433-6_3

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  • DOI: https://doi.org/10.1007/978-3-642-10433-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10432-9

  • Online ISBN: 978-3-642-10433-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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