An analysis of the vector decomposition problem

Authors:
Steven D. Galbraith;Eric R. Verheul
Affiliations:
Mathematics Department, Royal Holloway, University of London, Egham, Surrey, United Kingdom;PricewaterhouseCoopers Advisory, Radboud University Nijmegen, Amsterdam, The Netherlands
Venue:
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Year:
2008

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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.