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MapReduce for Elliptic Curve Discrete Logarithm Problem
2016 IEEE World Congress on Services (SERVICES), 2016Elliptic curve based cryptography has attracted a lot of attention because these schemes usually require less storage than those based on finite field. It is also used to construct bilinear pairing, which is an essential tool to construct various cryptography schemes.
Zhimin Gao +2 more
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The Discrete Logarithm Problem
1999The public key cryptosystems presented in Chapter 1 rely on the difficulty of solving the discrete logarithm problem in certain groups: An adversary who could efficiently compute discrete logarithms in the group underlying such a cryptosystem would be able to break the system. So to judge the security of the proposed cryptosystems we must have a closer
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A Rigorous Proof of the Waterloo Algorithm for the Discrete Logarithm Problem
Designs, Codes and Cryptography, 2002The index calculus attack is a sub-exponential algorithm to compute discrete logarithms in finite fields. For fields of small characteristic, especially \(\mathbb{F}_{2^n}\), \textit{D. Coppersmith}'s variant [IEEE Trans. Inf. Theory 30, 587-594 (1984; Zbl 0554.12013)] is (heuristically) most efficient.
Michael Drmota, Daniel Panario
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Local Duality and the Discrete Logarithm Problem
2011It is shown that the computational complexity of Tate local duality is closely related to that of the discrete logarithm problem over finite fields. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered.
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Multiple Discrete Logarithm Problems with Auxiliary Inputs
2015Let g be an element of prime order p in an abelian group and let $$\alpha _1, \dots , \alpha _L \in {\mathbb Z}_p$$ for a positive integer L. First, we show that, if $$g, g^{\alpha _i}$$, and $$g^{\alpha _i^d}$$$$i=1, \dots , L$$ are given for $$d \mid p-1$$, all the discrete logarithms $$\alpha _i$$'s can be computed probabilistically in $$\widetilde ...
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Practical Solving of Discrete Logarithm Problem over Prime Fields Using Quantum Annealing
Lecture Notes in Computer Science, 2022Michał Wroński
exaly
On the discrete logarithm problem
Discrete Mathematics and Applications, 2014openaire +1 more source