Factorization of a 768-bit RSA modulus

Factorization of a 768-bit RSA modulus (2010)

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by Thorsten Kleinjung , Kazumaro Aoki , Jens Franke , Arjen K. Lenstra , Emmanuel Thomé , Pierrick Gaudry , Peter L. Montgomery , Dag Arne Osvik , Herman Te Riele , Andrey Timofeev , Paul Zimmermann, et al.

Citations:

9 - 3 self

BibTeX

@MISC{Kleinjung10factorizationof,
    author = {Thorsten Kleinjung and Kazumaro Aoki and Jens Franke and Arjen K. Lenstra and Emmanuel Thomé and Pierrick Gaudry and Peter L. Montgomery and Dag Arne Osvik and Herman Te Riele and Andrey Timofeev and Paul Zimmermann and et al.},
    title = {Factorization of a 768-bit RSA modulus},
    year = {2010}
}

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Abstract

This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA.

Citations

2506	A method for obtaining digital signatures and public-key cryptosystems - Rivest, Shamir, et al.
216	Shift-register synthesis and BCH decoding - Massey - 1969
108	The development of the number field sieve - Lenstra, Lenstra - 1993
49	The quadratic sieve factoring algorithm - Pomerance - 1985
47	The factorization of the ninth Fermat number - Lenstra, Lenstra, et al. - 1994
47	Analysis and comparison of some integer factoring algorithms - Pomerance - 1982
46	Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm - Coppersmith - 1994
32	A tale of two sieves - Pomerance - 1996
25	Factoring a 512-bit RSA modulus - Cavallar, Dodson, et al.
24	Solving linear equations over gf(2): block Lanczos algorithm. Linear Algebra and its Applications - Coppersmith - 1993
22	A method of factorization and the factorization of F7 - Morrison, Brillhart - 1975
20	Factoring numbers using singular integers - Adleman
14	Subquadratic computation of vector generating polynomials and improvement of the block Wiedemann algorithm - THOMÉ
13	Lattice sieving and trial division - Golliver, Lenstra, et al. - 1994
12	Asymptotically fast factorization of integers - Dixon - 1981
11	Strategies in filtering in the number field sieve - Cavallar - 2000
11	et al., Factoring a 512-bit RSA modulus - Cavallar, Dodson, et al. - 2000
11	Computing a square root for the number field sieve, The development of the number field sieve - Couveignes - 1993
10	A kilobit special number field sieve factorization - Aoki, Kleinjung, et al. - 2007
10	A Montgomery-like Square Root for the Number Field - Nguyen - 1998
10	The lattice sieve - Pollard
9	Factoring estimates for a 1024-bit RSA modulus - Lenstra, Tromer, et al. - 2003
8	Algorithms in number theory, chapter 12 in Handbook of theoretical computer science, Volume A, algorithms and complexity - Lenstra, Lenstra - 1990
4	Cofactorisation strategies for the number field sieve and an estimate for the sieving step for factoring 1024 bit integers - Kleinjung
3	Technical report implementing the number field sieve - Buhler, Montgomery, et al. - 1994
3	On Polynomial Selection For The General Number Field Sieve - Kleinjung - 2006
3	Improved polynomial selection for the number field sieve, extended abstract for the conference on the mathematics of public-key cryptography - Montgomery, Murphy
2	Continued fractions and lattice sieving - Franke, Kleinjung - 2005
2	Square roots of products of algebraic numbers, http://ftp.cwi.nl/pub/pmontgom/ sqrt.ps.gz - Montgomery
1	Liniensieben und Quadratwurzelberechnung für das Zahlkörpersieb - Bahr - 2005
1	A world wide number field sieve factoring record: on to 512 bits - Elkenbracht-Huizing, Lenstra, et al. - 1996
1	Polynomial selection, talk presented at the CADO workshop on integer factorization - Kleinjung - 2008
1	Computational methods in public key cryptology, pp. 175–238 in: H. Niederreiter, Coding theory and cryptology - Lenstra - 2002
1	Modelling the Yield of Number Field Sieve - Murphy - 1998