Elliptic curve primality tests for Fermat and related primes

被引:6
|
作者
Denomme, Robert [2 ]
Savin, Gordan [1 ]
机构
[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA
[2] Ohio State Univ, Dept Math, Columbus, OH 43210 USA
基金
美国国家科学基金会;
关键词
D O I
10.1016/j.jnt.2007.12.009
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We use elliptic curves with complex multiplication to develop primality tests for Fermat primes and for primes of the form 3(2l) - 3(2l-1) + 1 and 2(2l) - 2(2l-1) + 1. (C) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码:2398 / 2412
页数:15
相关论文
共 50 条
  • [1] An Analysis of Non-Elliptic Curve Based Primality Tests
    Wong, William
    Alomari, Zakaria
    Lai, Hon Ching
    Li, Zhida
    Ullah, Arif
    2024 8TH INTERNATIONAL CONFERENCE ON CRYPTOGRAPHY, SECURITY AND PRIVACY, CSP 2024, 2024, : 53 - 58
  • [2] A strategy for elliptic curve primality proving
    Kiss, Gyongyver
    ACTA UNIVERSITATIS SAPIENTIAE INFORMATICA, 2015, 7 (02) : 125 - 142
  • [3] Primality tests based on Fermat's Little Theorem
    Agrawal, Manindra
    Distributed Computing and Networking, Proceedings, 2006, 4308 : 288 - 293
  • [4] Elliptic functions and the Fermat curve
    Demyanenko, VA
    MATHEMATICAL NOTES, 1996, 60 (3-4) : 453 - 456
  • [5] Primality tests and use of primes in public key systems
    Landrock, P
    LECTURES ON DATA SECURITY, 1999, 1561 : 127 - 133
  • [6] INFINITE SETS OF PRIMES WITH FAST PRIMALITY TESTS AND QUICK GENERATION OF LARGE PRIMES
    PINTZ, J
    STEIGER, WL
    SZEMEREDI, E
    MATHEMATICS OF COMPUTATION, 1989, 53 (187) : 399 - 406
  • [7] ELLIPTIC-CURVES, PRIMALITY PROVING AND SOME TITANIC PRIMES
    MORAIN, F
    ASTERISQUE, 1991, (198) : 245 - 251
  • [8] ON SUPERSINGULAR PRIMES OF THE ELKIES' ELLIPTIC CURVE
    Murabayashi, Naoki
    FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2019, 60 (01) : 41 - 59
  • [9] An elliptic curve test for Mersenne primes
    Gross, BH
    JOURNAL OF NUMBER THEORY, 2005, 110 (01) : 114 - 119
  • [10] A characterization of symplectic groups related to Fermat primes
    Ebrahimzadeh, Behnam
    Asboei, Alireza K.
    COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2021, 62 (01): : 33 - 40