The PEACE project

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The members of the PEACE project

Scientific goals

The discrete logarithm problem on algebraic curves is one of the rare contact points between deep theoretical questions in arithmetic geometry and every day applications. On the one side it involves a better understanding, from an effective point of view, of moduli space of curves, of abelian varieties, the maps that link these spaces and the objects they classify. On the other side, new and efficient algorithms to compute the discrete logarithm problem may have dramatic consequences on the security and efficiency of already deployed cryptographic devices. The PEACE (Parameter spaces for Efficient Arithmetic and Curve security Evaluation) project constitutes a comprehensive and coherent approach towards a better understanding of theoretical and algorithmic aspects of the discrete logarithm problem on algebraic curves of small genus. One of the anticipated outcomes of this project, is a new set of general criteria for selecting and validating cryptographically secure curves (or families of curves) suitable for use in cryptography. Instead of publishing fixed curves, as it is done in most standards, we aim at proposing generating rationales along with explicit theoretical and algorithmic criteria for their validation.
The project is divided in four main tasks:
  • Construction of parameter spaces for cryptography;
  • Relation between parameter spaces and objects;
  • Efficient and secure realisation of curve-based cryptosystems;
  • Analysis and validation of a curve in cryptography.
For more details, we refer the reader of this page to the pdf document describing all the goals of the project as well as its management.