About the XL algorithm over GF(2)

  • Authors:
  • Nicolas T. Courtois;Jacques Patarin

  • Affiliations:
  • CP8 Crypto Lab, Louveciennes Cedex, France;CP8 Crypto Lab, Louveciennes Cedex, France and PRiSM, University of Versailles, Versailles Cedex, France

  • Venue:
  • CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
  • Year:
  • 2003

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Abstract

In this paper we introduce NTRUSIGN, a new family of signature schemes based on solving the approximate closest vector problem (APPR-CVP) in NTRU-type lattices. We explore the properties of general APPR-CVP based signature schemes (e.g. GGH) and show that they are not immune to transcript attacks even in the random oracle model. We then introduce the idea of using carefully chosen perturbations to limit the information that is obtainable from an analysis of a large signature transcript. In the case of NTRUSIGN this can be achieved while maintaining attractive efficiency properties.