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Special number field sieve
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1	SMOOTH NUMBERS AND THE QUADRATIC SIEVE Carl Pomerance When faced with a large number n to factor, what do you do first? You might say “Look at the last digit,” with the idea of cheaply pulling out possible factors of Add to Reading List Source URL: www.mat.uniroma2.it Language: English - Date: 2007-11-23 17:17:47 Mathematics Integer factorization algorithms Number theory Quadratic sieve Special number field sieve Quadratic residue General number field sieve Prime number Lenstra elliptic curve factorization Sieve of Eratosthenes Euclidean algorithm Prime-counting function
2	Integer factorization, part 1: the Q sieve Integer factorization, part 2: detecting smoothness D. J. Bernstein Add to Reading List Source URL: www.mat.uniroma2.it Language: English - Date: 2006-11-12 13:56:00 Integer factorization algorithms Mathematics Number theory Integer sequences Quadratic sieve Discrete mathematics Prime number Smooth number Special number field sieve General number field sieve
3	Square Root Algorithms for the Number Field Sieve Emmanuel Thomé INRIA Nancy, Villers-lès-Nancy, France Abstract. We review several methods for the square root step of the Add to Reading List Source URL: www.loria.fr Language: English - Date: 2012-11-29 10:44:38 Integer factorization algorithms Polynomials Field theory Algebraic number theory General number field sieve Special number field sieve Algebraic number field Elliptic curve Prime number Abstract algebra Mathematics Algebra
4	Ch6_Jun14_SiteNeutralPAC.indd Add to Reading List Source URL: medpac.gov Language: English - Date: 2014-08-08 10:38:37 Health economics Healthcare Housing Nursing home Medicare Home care Prospective payment system Special number field sieve Health Medicine Geriatrics
5	A kilobit special number field sieve factorization Kazumaro Aoki1 , Jens Franke2 , Thorsten Kleinjung2 , Arjen K. Lenstra3 , and Dag Arne Osvik3 1 2 Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2007-05-31 05:26:07 Special number field sieve Integer factorization General number field sieve Factorization RSA Lenstra elliptic curve factorization Factor base Quadratic sieve Integer factorization records Integer factorization algorithms Cryptography Mathematics
6	Factorization of a 1061-bit number by the Special Number Field Sieve Greg Childers California State University Fullerton Fullerton, CAAugust 4, 2012 Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2012-08-06 19:06:43 General number field sieve Special number field sieve Integer factorization Arjen Lenstra Herman te Riele Factor base RSA Factorization Jens Franke Integer factorization algorithms Cryptography Mathematics
7	Factorization of a 768-bit RSA modulus version 1.21, January 13, 2010 Thorsten Kleinjung1 , Kazumaro Jens Franke3 , Arjen K. Lenstra1 , Emmanuel Thomé4 , Add to Reading List Source URL: www.loria.fr Language: English - Date: 2010-01-13 11:00:27 Number theory Quadratic sieve Special number field sieve General number field sieve Quadratic residue Prime number Factor base Lattice sieving RSA Integer factorization algorithms Cryptography Mathematics
8	Faster index calculus for the medium prime case Application to 1175-bit and 1425-bit finite fields Antoine Joux CryptoExperts and Universit´e de Versailles Saint-Quentin-en-Yvelines, Laboratoire PRISM, ´ Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2013-01-07 07:11:10 Orthogonal polynomials Polynomials Integer factorization algorithms Finite field General number field sieve Logarithm Special functions Mathematics Abstract algebra
9	Factorization of a 768-bit RSA modulus version 1.4, February 18, 2010 Thorsten Kleinjung1 , Kazumaro Jens Franke3 , Arjen K. Lenstra1 , Emmanuel Thomé4 , Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2010-02-18 11:19:25 Number theory Quadratic sieve Special number field sieve General number field sieve Quadratic residue Prime number Factor base Lattice sieving RSA Integer factorization algorithms Cryptography Mathematics
10	On Class Group Computations Using the Number Field Sieve Mark L. Bauer1 and Safuat Hamdy2 1 University of Waterloo Add to Reading List Source URL: www.iacr.org Language: English - Date: 2008-09-15 00:54:54 Integer factorization algorithms Quadratic sieve General number field sieve Special number field sieve Elliptic curve Polynomial Hyperelliptic curve Quadratic form Algebraic number field Abstract algebra Algebra Mathematics