Cryptology ePrint Archive: Report 2014/996

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

Maike Massierer

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.

Category / Keywords: public-key cryptography / discrete logarithm problem, index calculus, algebraic curves, function field sieve

Date: received 13 Dec 2014

Contact author: maike massierer at inria fr

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Version: 20141218:034016 (All versions of this report)

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