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Signature calculus and discrete logarithm problems. (English) Zbl 1143.11363

Hess, Florian (ed.) et al., Algorithmic number theory. 7th international symposium, ANTS-VII, Berlin, Germany, July 23–28, 2006. Proceedings. Berlin: Springer (ISBN 3-540-36075-1/pbk). Lecture Notes in Computer Science 4076, 558-572 (2006).
Summary: 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.
For the entire collection see [Zbl 1103.11002].

MSC:

11Y16 Number-theoretic algorithms; complexity
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94A60 Cryptography
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