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Parameter spaces for Efficient Arithmetic and Curve security Evaluation – PEACE

PEACE

The discrete logarithm problem on algebraic curves is one of the rare <br />contact points between deep theoretical questions in arithmetic <br />geometry and every day applications.

Stakes and objective

On the one side it involves a <br />better understanding, from an effective point of view, of moduli space <br />of curves, of abelian varieties, the maps that link these spaces <br />and the objects they classify. On the other side, new and efficient <br />algorithms to compute the discrete logarithm problem may have dramatic consequences on the security and efficiency of already deployed cryptographic devices.

This proposal 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
proposal, 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.

Papers in peer-reviewed journals

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. This proposal 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 proposal, 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.

Project coordinator

Monsieur David LUBICZ (Institut de Recherche Mathématiques de Rennes) – david.lubicz@univ-rennes1.fr

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

Inria Inria
IRMAR Institut de Recherche Mathématiques de Rennes
CNRS DR12 _ IML Centre National de la Recherche Scientifique Délégation Provence et Corse _ Institut de Mathématiques de Luminy

Help of the ANR 138,925 euros
Beginning and duration of the scientific project: October 2012 - 36 Months

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