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General 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	FACTORIZATION TECHNIQUES ELVIS NUNEZ AND CHRIS SHAW Abstract. The security of the RSA public key cryptosystem relies upon the computational difficulty of deriving the factors of a particular semiprime modulus. In this pa Add to Reading List Source URL: davidlowryduda.com Language: English - Date: 2016-05-25 03:59:31 Integer factorization algorithms Mathematics Cryptography Number theory Quadratic sieve Euclidean algorithm RSA Prime number Factorization Trial division General number field sieve Rational sieve
4	POST-SIEVING ON GPUs Andrea Miele1, Joppe W. Bos2, Thorsten Kleinjung1, Arjen K. Lenstra1 1LACAL, Add to Reading List Source URL: caramba.loria.fr Language: English - Date: 2016-06-13 15:37:34 Computing Computer architecture Computer hardware Graphics hardware Video cards Parallel computing GPGPU Integer factorization algorithms Fermi General number field sieve CUDA General-purpose computing on graphics processing units
5	Integer Factorization and Computing Discrete Logarithms in Maple Aaron Bradford∗, Michael Monagan∗, Colin Percival∗ , , Department of Mathematics, Simon Fr Add to Reading List Source URL: www.daemonology.net Language: English - Date: 2006-05-14 06:12:35 Cryptography Integer factorization algorithms Mathematics Abstract algebra Quadratic sieve General number field sieve Prime number Safe prime Discrete logarithm RSA Sieve of Atkin Quadratic residue
6	Innovations in Computer ScienceIdeal Forms of Coppersmith’s Theorem and Guruswami-Sudan List Decoding Henry Cohn∗ Nadia Heninger? Microsoft Research New England, One Memorial Drive, Cambridge, MA 02142 Add to Reading List Source URL: conference.itcs.tsinghua.edu.cn Language: English - Date: 2010-12-15 03:49:23 Polynomials Coding theory Field theory Error detection and correction Finite field General number field sieve Irreducible polynomial Reed–Solomon error correction Algebraic integer Abstract algebra Algebra Mathematics
7	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
8	A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic Razvan Barbulescu1 , Pierrick Gaudry1 , Antoine Joux2,3 , and Emmanuel Thomé1 1 Add to Reading List Source URL: www.loria.fr Language: English - Date: 2013-12-16 04:03:37 Finite fields Group theory Logarithms Cryptography Computational complexity theory Time complexity Polynomial General number field sieve Field extension Abstract algebra Mathematics Algebra
9	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
10	Faster deterministic integer factorisation David Harvey (joint work with Edgar Costa, NYU) University of New South Wales 25th October 2011 Add to Reading List Source URL: web.maths.unsw.edu.au Language: English - Date: 2011-10-24 19:42:20 Applied mathematics Integer factorization General number field sieve Quadratic sieve Time complexity Lenstra elliptic curve factorization Factorization Prime number Algorithm Theoretical computer science Integer factorization algorithms Mathematics