A Quantum Algorithm for Computing Isogenies between Supersingular Elliptic Curves

被引：41
|
作者：
Biasse, Jean-Francois
Jao, David [1 ,2 ]
Sankar, Anirudh [2 ]
机构：
[1] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada
[2] Univ Waterloo, Dept Combinator & Optimizat, Inst Quantum Comp, Waterloo, ON N2L 3G1, Canada
来源：
PROGRESS IN CRYPTOLOGY - INDOCRYPT 2014 | 2014年 / 8885卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
Elliptic curve cryptography; Quantum safe cryptography; Isogenies; Supersingular curves;
D O I：
10.1007/978-3-319-13039-2_25
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we describe a quantum algorithm for computing an isogeny between any two supersingular elliptic curves defined over a given finite field. The complexity of our method is in (O) over tilde (p(1/4)) where p is the characteristic of the base field. Our method is an asymptotic improvement over the previous fastest known method which had complexity (O) over tilde (p(1/2)) (on both classical and quantum computers). We also discuss the cryptographic relevance of our algorithm.
引用
收藏
页码：428 / 442
页数：15
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