Welcome to the resource topic for 2003/058
Title:
An Elliptic Curve Trapdoor System
Authors: Edlyn Teske
Abstract:We propose an elliptic curve trapdoor system which is of interest in
key escrow applications. In this system, a pair
(E_{\rm s}, E_{\rm pb}) of elliptic curves over \F_{2^{161}} is constructed with the following properties: (i) the Gaudry-Hess-Smart Weil descent attack reduces the elliptic curve discrete logarithm problem (ECDLP) in E_{\rm s}(\F_{2^{161}}) to a hyperelliptic curve DLP in the Jacobian of a curve of genus 7 or 8, which is computationally feasible, but by far not trivial; (ii) E_{\rm pb} is isogenous to E_{\rm s}; (iii) the best attack on the
ECDLP in E_{\rm pb}(\F_{2^{161}}) is the parallelized Pollard rho method.\
The curve E_{\rm pb} is used just as usual in elliptic curve cryptosystems. The curve $E_{\rm s} is submitted to a trusted authorityfor the purpose of key escrow. The crucial difference from other key escrow scenarios is that the trusted authority has to invest a considerable amount of computation to compromise a user’s
private key, which makes applications such as widespread wire-tapping
impossible.
ePrint: https://eprint.iacr.org/2003/058
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