@inproceedings{c93acd698d3342cbb8e261e1f1037abe,
title = "Improved sieving on algebraic curves",
abstract = "The best algorithms for discrete logarithms in Jacobians of algebraic curves of small genus are based on index calculus methods coupled with large prime variations. For hyperelliptic curves, relations are obtained by looking for reduced divisors with smooth Mumford representation (Gaudry); for non-hyperelliptic curves it is faster to obtain relations using special linear systems of divisors (Diem, Kochinke). Recently, Sarkar and Singh have proposed a sieving technique, inspired by an earlier work of Joux and Vitse, to speed up the relation search in the hyperelliptic case. We give a new description of this technique, and show that this new formulation applies naturally to the non-hyperelliptic case with or without large prime variations. In particular, we obtain a speed-up by a factor approximately 3 for the relation search in Diem and Kochinke{\textquoteright}s methods.",
keywords = "Algebraic curves, Curve-based cryptography, Discrete logarithm, Index calculus",
author = "Vanessa Vitse and Alexandre Wallet",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 4th International Conference on Cryptology and Information Security in Latin America, LATINCRYPT 2015 ; Conference date: 23-08-2015 Through 26-08-2015",
year = "2015",
month = jan,
day = "1",
doi = "10.1007/978-3-319-22174-8\_16",
language = "English",
isbn = "9783319221731",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "295--307",
editor = "Francisco Rodr{\'i}guez-Henr{\'i}quez and Kristin Lauter",
booktitle = "Progress in Cryptology – LATINCRYPT 2015 - 4th International Conference on Cryptology and Information Security in Latin America, Proceedings",
}