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
相关论文
共 50 条
  • [21] Post-Quantum Cryptography on FPGA Based on Isogenies on Elliptic Curves
    Koziel, Brian
    Azarderakhsh, Reza
    Kermani, Mehran Mozaffari
    Jao, David
    IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2017, 64 (01) : 86 - 99
  • [22] Identifying supersingular elliptic curves
    Sutherland, Andrew V.
    LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2012, 15 : 317 - 325
  • [23] On oriented supersingular elliptic curves
    Onuki, Hiroshi
    FINITE FIELDS AND THEIR APPLICATIONS, 2021, 69
  • [24] Pseudorandom number generator based on supersingular elliptic curve isogenies
    Yan Huang
    Fangguo Zhang
    Zhijie Liu
    Haibo Tian
    Science China Information Sciences, 2022, 65
  • [25] Class pairings and isogenies on elliptic curves
    Buell, Duncan A.
    Call, Gregory S.
    JOURNAL OF NUMBER THEORY, 2016, 167 : 31 - 73
  • [26] ESTIMATING ISOGENIES ON ELLIPTIC-CURVES
    MASSER, DW
    WUSTHOLZ, G
    INVENTIONES MATHEMATICAE, 1990, 100 (01) : 1 - 24
  • [27] Computing isogenies between Jacobians of curves of genus 2 and 3
    Milio, Enea
    arXiv, 2017,
  • [28] Efficient Algorithm for Computing Odd-Degree Isogenies on Montgomery Curves
    Kodera, Kenta
    Cheng, Chen-Mou
    Miyaji, Atsuko
    INFORMATION SECURITY APPLICATIONS, WISA 2020, 2020, 12583 : 258 - 275
  • [29] On the Iwasawa μ-invariants of supersingular elliptic curves
    Saikia, Anupam
    ACTA ARITHMETICA, 2020, 194 (02) : 179 - 186
  • [30] ON THE SUPERSINGULAR REDUCTION OF ELLIPTIC-CURVES
    MURTY, MR
    PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 1987, 97 (1-3): : 247 - 250
12345