On the Function Field Sieve and the Impact of Higher Splitting Probabilities - Application to Discrete Logarithms in and
نویسندگان
چکیده
In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as Lqn(1/3, 2/3) for computing arbitrary logarithms, but also in an heuristic polynomial time algorithm for finding the discrete logarithms of degree one elements. To illustrate the efficiency of the method, we have successfully solved the DLP in the finite field with 2 elements.
منابع مشابه
On the Function Field Sieve and the Impact of Higher Splitting Probabilities Application to Discrete Logarithms in F21971 and F23164
In this paper we propose a binary field variant of the JouxLercier medium-sized Function Field Sieve, which results not only in complexities as low as Lqn(1/3, (4/9) ) for computing arbitrary logarithms, but also in an heuristic polynomial time algorithm for finding the discrete logarithms of degree one and two elements when the field has a subfield of an appropriate size. To illustrate the eff...
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