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
  • [41] RANK PARITY FOR CONGRUENT SUPERSINGULAR ELLIPTIC CURVES
    Hatley, Jeffrey
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (09) : 3775 - 3786
  • [42] Simultaneous supersingular reductions of CM elliptic curves
    Aka, Menny
    Luethi, Manuel
    Michel, Philippe
    Wieser, Andreas
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2022, 2022 (786): : 1 - 43
  • [43] Minimal CM liftings of supersingular elliptic curves
    Yang, Tonghai
    PURE AND APPLIED MATHEMATICS QUARTERLY, 2008, 4 (04) : 1317 - 1326
  • [44] Arithmetics of elliptic curves with supersingular reduction at P
    Perrin-Riou, B
    EXPERIMENTAL MATHEMATICS, 2003, 12 (02) : 155 - 186
  • [45] Iwasawa theory for elliptic curves at supersingular primes
    Kobayashi, S
    INVENTIONES MATHEMATICAE, 2003, 152 (01) : 1 - 36
  • [46] A Post-quantum Digital Signature Scheme Based on Supersingular Isogenies
    Yoo, Youngho
    Azarderakhsh, Reza
    Jalali, Amir
    Jao, David
    Soukharev, Vladimir
    FINANCIAL CRYPTOGRAPHY AND DATA SECURITY, FC 2017, 2017, 10322 : 163 - 181
  • [47] An elementary proof for the number of supersingular elliptic curves
    Finotti, Luis R. A.
    SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2020, 14 (02): : 531 - 538
  • [48] Iwasawa theory for elliptic curves at supersingular primes
    Shin-ichi Kobayashi
    Inventiones mathematicae, 2003, 152 : 1 - 36
  • [49] An elementary proof for the number of supersingular elliptic curves
    Luís R. A. Finotti
    São Paulo Journal of Mathematical Sciences, 2020, 14 : 531 - 538
  • [50] Fast point multiplication on elliptic curves through isogenies
    Brier, E
    Joye, M
    APPLIED ALGEBRA, ALGEBRAIC ALGORITHMS AND ERROR-CORRECTING CODES, PROCEEDINGS, 2003, 2643 : 43 - 50
12345