A double large prime variation for small genus hyperelliptic index calculus
نویسندگان
چکیده
منابع مشابه
A double large prime variation for small genus hyperelliptic index calculus
In this article, we examine how the index calculus approach for computing discrete logarithms in small genus hyperelliptic curves can be improved by introducing a double large prime variation. Two algorithms are presented. The first algorithm is a rather natural adaptation of the double large prime variation to the intended context. On heuristic and experimental grounds, it seems to perform qui...
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We present a variation of the index calculus attack by Gaudry which can be used to solve the discrete logarithm problem in the Jacobian of hyperelliptic curves. The new algorithm has a running time which is better than the original index calculus attack and the Rho method (and other square-root algorithms) for curves of genus ≥ 3. We also describe another improvement for curves of genus ≥ 4 (sl...
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We consider the discrete logarithm problem (DLP) in degree 0 class groups of non-hyperelliptic curves of genus 3 over finite fields Fq. Using a recent index calculus algorithm with double large prime variation by the author, heuristically, one can solve this problem in a time of Õ(q). In this work, we study this problem from a full cost perspective. We argue that heuristically, using a 3-dimens...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2007
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-06-01900-4