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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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Discrete logarithm problem on elliptic curves
2020ABSTRACT DISCRETE LOGARITHM PROBLEM ON ELLIPTIC CURVES SALDAMLI, Gökay M.S., Department of Mathematics Supervisor: Prof. Dr. Ismail Ş. Güloğlu May 2000, 64 pages In this work, discrete logarithm problem on elliptic curves is studied. Supersingular curves and the reduction of discrete logarithm problem on an elliptic curve E over GF(q) to the discrete ...
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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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New Variations of Discrete Logarithm Problem
2023Mahdavi Oliaee, Mahdi +2 more
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On the discrete logarithm problem
Discrete Mathematics and Applications, 2014openaire +1 more source
Recent progress on the elliptic curve discrete logarithm problem
Designs, Codes, and Cryptography, 2015Steven D Galbraith, Pierrick Gaudry
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