Signature calculus and discrete logarithm problems

Authors:
Ming-Deh Huang;Wayne Raskind
Affiliations:
Department of Computer Science, University of Southern California, Los Angeles, CA;Department of Mathematics, University of Southern California, Los Angeles, CA
Venue:
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Year:
2006

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Abstract

Index calculus has been successful in many cases for treating the discrete logarithm problem for the multiplicative group of a finite field, but less so for elliptic curves over a finite field. In this paper we seek to explain why this might be the case from the perspective of arithmetic duality and propose a unified method for treating both problems which we call signature calculus.