Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies

Journal of mathematical cryptology

article

Luca De Feo¹  David Jao²  Jérôme Plût¹ 

[1] Laboratoire PRiSM, Université de Versailles;University of Waterloo

关键词: Elliptic curves;    isogenies;    quantum-resistant cryptosystems;   

DOI  :  10.1515/jmc-2012-0015

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases under the isogeny in order to allow the parties to construct a shared commutative square despite the non-commutativity of the endomorphism ring. We give a precise formulation of the necessary computational assumptions along with a discussion of their validity, and prove the security of our protocols under these assumptions. In addition, we present implementation results showing that our protocols are multiple orders of magnitude faster than previous isogeny-based cryptosystems over ordinary curves. This paper is an extended version of [Lecture Notes in Comput. Sci. 7071, Springer (2011), 19–34]. We add a new zero-knowledge identification scheme and detailed security proofs for the protocols. We also present a new, asymptotically faster, algorithm for key generation, a thorough study of its optimization, and new experimental data.

【 授权许可】

CC BY|CC BY-NC-ND