Team Lfant

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Section: New Results

Discrete logarithms

Participant : Andreas Enge.

In [34] , we presented for the first time an algorithm for the discrete logarithm problem in certain algebraic curves that runs in subexponential time less than L(1/2) , namely, L(1/3 + $ \varepsilon$) for any $ \varepsilon$>0 . In [27] , we lower this complexity to L(1/3) , showing that the corresponding algebraic curves (essentially Cab curves of genus g growing at least quadratically with the logarithmic size of the finite field of definition, logq ) result in cryptosystems that are as easily attacked as RSA or tradtional cryptosystems based on discrete logarithms in finite fields. We provide a complete classification of all the curves to which the attack applies. The article has been accepted by Journal of Cryptology .


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