An analysis of the vector decomposition problem ⋆
| Citations: | 4 - 1 self |
BibTeX
@MISC{Galbraith_ananalysis,
author = {Steven D. Galbraith and Eric R. Verheul},
title = {An analysis of the vector decomposition problem ⋆},
year = {}
}
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Abstract
Abstract. The vector decomposition problem (VDP) has been proposed as a computational problem on which to base the security of public key cryptosystems. We give a generalisation and simplification of the results of Yoshida on the VDP. We then show that, for the supersingular elliptic curves which can be used in practice, the VDP is equivalent to the computational Diffie-Hellman problem (CDH) in a cyclic group. For the broader class of pairing-friendly elliptic curves we relate VDP to various co-CDH problems and also to a generalised discrete logarithm problem 2-DL which in turn is often related to discrete logarithm problems in cyclic groups. Keywords: Vector decomposition problem, elliptic curves, Diffie-Hellman problem, generalised discrete logarithm problem. 1
Keyphrases
vector decomposition problem cyclic group computational problem pairing-friendly elliptic curve elliptic curve diffie-hellman problem generalised discrete logarithm problem computational diffie-hellman problem logarithm problem various co-cdh problem public key cryptosystems supersingular elliptic curve discrete logarithm problem
