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- W2152538360 abstract "We study the discrete logarithm problem for the multiplicative group and for elliptic curves over a finite field by using a lifting of the corresponding object to an algebraic number field and global duality. We introduce the textit{signature} of a Dirichlet character (in the multiplicative group case) or principal homogeneous space (in the elliptic curve case), which is a measure of the ramification at certain places. We then develop textit{signature calculus}, which generalizes and refines the index calculus method. Finally, we show the random polynomial time equivalence for these two cases between the problem of computing signatures and the discrete logarithm problem." @default.
- W2152538360 created "2016-06-24" @default.
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- W2152538360 date "2007-10-11" @default.
- W2152538360 modified "2023-09-27" @default.
- W2152538360 title "Global duality, signature calculus and the discrete logarithm problem" @default.
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