Integer factoring

被引：37

作者：

Lenstra, AK ^{[1
]}

机构：

[1] Citibank NA, Mendham, NJ 07945 USA

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2000年 / 19卷 / 2-3期

关键词：

integer factorization; quadratic sieve; number field sieve; elliptic curve method; Morrison-Brillhart approach;

D O I：

10.1023/A:1008397921377

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Using simple examples and informal discussions this article surveys the key ideas and major advances of the last quarter century in integer factorization.

引用

页码：101 / 128

页数：28

共 38 条

[1]

ADLEMAN LM, 1991, P 23 ANN ACM S THEOR, P64

[2]

BRENT RP, 1981, MATH COMPUT, V36, P627, DOI 10.1090/S0025-5718-1981-0606520-5

[3] ON A PROBLEM OF OPPENHEIM CONCERNING FACTORISATIO NUMERORUM [J].

CANFIELD, ER ;

ERDOS, P ;

POMERANCE, C .

JOURNAL OF NUMBER THEORY, 1983, 17 (01) :1-28

[4] Computing pi(x): The Meissel, Lehmer, Lagarias, Miller, Odlyzko method [J].

Deleglise, M ;

Rivat, J .

MATHEMATICS OF COMPUTATION, 1996, 65 (213) :235-245

[5]

Dodson B, 1995, LECT NOTES COMPUT SC, V963, P372

[6]

GOLLIVER R, 1994, LECT NOTES COMPUTER, V877, P18

[7] COMPUTING PI-(X) - THE MEISSEL-LEHMER METHOD [J].

LAGARIAS, JC ;

MILLER, VS ;

ODLYZKO, AM .

MATHEMATICS OF COMPUTATION, 1985, 44 (170) :537-560

[8]

LAMACCHIA BA, 1991, LECT NOTES COMPUT SC, V537, P109

[9] THE FACTORIZATION OF THE 9TH FERMAT NUMBER [J].

LENSTRA, AK ;

LENSTRA, HW ;

MANASSE, MS ;

POLLARD, JM .

MATHEMATICS OF COMPUTATION, 1993, 61 (203) :319-349

[10] FACTORING WITH 2 LARGE PRIMES [J].

LENSTRA, AK ;

MANASSE, MS .

MATHEMATICS OF COMPUTATION, 1994, 63 (208) :785-798

← 1 2 3 4 →