Primality testing through algebraic groups

被引：0
作者：
Alexander Gurevich
Boris Kunyavskiĭ
机构：
[1] Bar-Ilan University,Department of Mathematics
来源：
Archiv der Mathematik | 2009年 / 93卷
关键词：
Primary 11A51; 14G15; 20G30; Secondary 14G05; 11Y11; Primality testing; Group scheme; Formal group law;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We propose a deterministic primality test based on a section of a group scheme. Pépin’s test and the tests of Lucas–Lehmer type are special cases of our construction, provided the group scheme is taken to be the multiplicative group and the Waterhouse–Weisfeiler group scheme, respectively. Besides, we suggest a test involving formal completions of these schemes.
引用
收藏
页码：555 / 564
页数：9
相关论文
共 11 条
  • [1] Gross B.(2005)An elliptic curve test for Mersenne primes J. Number Theory 110 114-119
  • [2] Kida M.(2004)Primality tests using algebraic groups Experim. Math. 13 421-427
  • [3] Lehmer D.H.(1930)An extended theory of Lucas’ functions Ann. Math. 31 419-448
  • [4] Lucas É.(1876)Nouveaux théorèmes d’arithmétique supérieure C. R. Acad. Sci. Paris 83 1286-1288
  • [5] Pépin P.(1877)Sur la formule C.R. Acad. Sci. Paris 85 329-331
  • [6] Riesel H.(1969)Lucasian criteria for the primality of Math. Comp. 23 869-875
  • [7] Rosen M.(1988) =  Amer. Math. Monthly 95 855-856
  • [8] Waterhouse W.C.(1980)2 J. Algebra 66 550-568
  • [9] Weisfeiler B.(1968)−1 Math. Comp. 22 420-422
  • [10] Williams H.C.(undefined)A proof of the Lucas–Lehmer test undefined undefined undefined-undefined
12