GPS (cryptography)

GPS , abbreviation of Girault - Poupard/Straws - Stern is a algorithm of Authentification and numerical Signature with key public, based on the problem of the discrete Logarithme in any multiplicative group. It was conceived by Jacques Stern, Guillaume Poupard, Marc Girault and Jean-Claude Paillès.

The speed of this protocol makes it available to components low costs, like a Smart card without Cryptoprocesseur, which can be authenticated/sign in a few milliseconds, with a safety which can be equivalent or higher than that of RSA.

At the time of the phase of authentification itself, calculation is limited to an extremely simple operation: $y = has \ cdot x-b ~$ (nonmodular operation).

This prowess holds in the fact that the largest part of calculations can be carried out in advance and stored in the form of coupons. Thus even a component of low costs can prove that it is neither a counterfeit, nor a clone, and that in a few milliseconds.

Standardization

GPS received certification NESSIE (European project of evaluation of cryptographic primitives).
the diagram of authentification is standardized in the ISO under ISO/IEC 9798-5: “Entity authentication - Mechanisms using technical zero-knowledge”
the diagram of signature is in the course of standardization in the ISO: ISO/IEC 14888-2

GPS is declined in several alternatives. One of it makes it possible to use keys of the type RSA while offering same safety. Another alternative functions on the elliptic curved .

See too

DIGITAL Signature Algorithm
digital Elliptic curve signature algorithm

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