Some experiments investigating a possible L(1/4) algorithm for the discrete logarithm problem in algebraic curves

Maike Massierer 1, *
* Corresponding author
1 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : The function field sieve, a subexponential algorithm of complexity L(1/3) that computes discrete logarithms in finite fields, has recently been improved to an algorithm of complexity L(1/4) and subsequently to a quasi-polynomial time algorithm. We investigate whether the new ideas also apply to index calculus algorithms for computing discrete logarithms in Jacobians of algebraic curves. While we do not give a final answer to the question, we discuss a number of ideas, experiments, and possible conclusions.
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Submitted on : Friday, December 19, 2014 - 3:17:22 PM
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Maike Massierer. Some experiments investigating a possible L(1/4) algorithm for the discrete logarithm problem in algebraic curves. 2014. ⟨hal-01097362⟩

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