Welcome to the resource topic for 2014/119
Title:
Breaking `128-bit Secure’ Supersingular Binary Curves (or how to solve discrete logarithms in {\mathbb F}_{2^{4 \cdot 1223}} and {\mathbb F}_{2^{12 \cdot 367}})
Authors: Robert Granger, Thorsten Kleinjung, Jens Zumbrägel
Abstract:In late 2012 and early 2013 the discrete logarithm problem (DLP) in finite fields of small characteristic underwent a dramatic series of breakthroughs, culminating in a heuristic quasi-polynomial time algorithm, due to Barbulescu, Gaudry, Joux and Thomé. Using these developments, Adj, Menezes, Oliveira and Rodríguez-Henríquez analysed the concrete security of the DLP, as it arises from pairings on (the Jacobians of) various genus one and two supersingular curves in the literature, which were originally thought to be 128-bit secure. In particular, they suggested that the new algorithms have no impact on the security of a genus one curve over {\mathbb F}_{2^{1223}}, and reduce the security of a genus two curve over {\mathbb F}_{2^{367}} to 94.6 bits. In this paper we propose a new field representation and efficient general descent principles which together make the new techniques far more practical. Indeed, at the `128-bit security level’ our analysis shows that the aforementioned genus one curve has approximately 59 bits of security, and we report a total break of the genus two curve.
ePrint: https://eprint.iacr.org/2014/119
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .