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A New Index Calculus Algorithm for the Elliptic Curve Discrete Logarithm Problem and Summation Polynomial Evaluation [PDF]

open access: yes, 2018
The introduction of summation polynomials for elliptic curves by Semaev has opened up new avenues of investigation in index calculus type algorithms for the elliptic curve discrete logarithm problem, and several recent papers have explored their use.
Daniela Mueller, Gary McGuire
core  

Index Calculus for Abelian Varieties and the Elliptic Curve Discrete Logarithm Problem

open access: yes, 2004
We propose an index calculus algorithm for the discrete logarithm problem on general abelian varieties. The main difference with the previous approaches is that we do not make use of any embedding into the Jacobian of a well-suited curve.
Pierrick Gaudry
core  

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