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Quadratic sieve
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21	THE ELLIPTIC CURVE METHOD PAUL ZIMMERMANN The Elliptic Curve Method (ECM for short) was invented in 1985 by H. W. Lenstra, Jr[removed]It is suited to find small — say 9 to 30 digits — prime factors of large numbers. Am Add to Reading List Source URL: www.loria.fr Language: English - Date: 2004-09-06 05:03:02 Cryptography Lenstra elliptic curve factorization Quadratic sieve Integer factorization Elliptic curve Primality test Prime number Prime factor Algebraic-group factorisation algorithm Integer factorization algorithms Abstract algebra Mathematics
22	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
23	Homework Two, for Fri[removed]CSE 101 When specifying an algorithm, please use pseudocode that is simple and unambiguous. Always justify the correctness and running time of the algorithm, unless these are obvious. Add to Reading List Source URL: cseweb.ucsd.edu Language: English - Date: 2014-10-12 01:34:34 Integer factorization algorithms Euclidean algorithm Multiplication Computational complexity theory Algorithm Time complexity Multiplication algorithm Greatest common divisor Quadratic sieve Mathematics Computational number theory Theoretical computer science
24	ADFS::HardDisc4.$.UKMT.JOS.imok.booklets.2015.PoScript Add to Reading List Source URL: www.ukmt.org.uk Language: English - Date: 2015-03-31 05:46:20 Number theory Coprime Algebraic number theory Prime number Factorization Number Ring Euclidean algorithm Quadratic sieve Mathematics Abstract algebra Integer sequences
25	T3.TG.17.Numberelationships Add to Reading List Source URL: www.smpmaths.org.uk Language: English - Date: 2009-01-20 04:04:02 Algorithms Sieve of Eratosthenes Prime number Integer factorization algorithms Happy number Multiplication Number Quadratic sieve Euclidean algorithm Mathematics Primality tests Elementary arithmetic
26	Julia & IJulia Cheat-sheet (for 18.xxx at MIT) Basics: documentation julialang.org Add to Reading List Source URL: math.mit.edu Language: English - Date: 2013-09-10 10:57:16 Linear algebra Matrix Vector space Euclidean vector Eigenvalues and eigenvectors Complex number Rotation matrix Quadratic sieve Algebra Mathematics Abstract algebra
27	Exponents, Polynomials, and Polynomial Functions Product rule: am •an = am+n Factoring Zero exponent: a°= 1, a ≠ 0 Add to Reading List Source URL: sradai.tripod.com Language: English - Date: 2013-02-12 11:40:05 Arithmetic Factorization Elementary algebra Quadratic equation Quadratic Discriminant Quadratic sieve Mathematics Polynomials Algebra
28	The Evolution of Public Key Cryptography Martin E. Hellman Crypto ’99 Santa Barbara, CA August 18, 1999 ADD: Loren Kohnfelder and certificates Add to Reading List Source URL: www.iacr.org Language: English - Date: 2011-06-15 12:59:08 Integer sequences Finite fields Public-key cryptography Cryptographic protocols Prime number Richard Schroeppel Quadratic sieve Diffie–Hellman key exchange RSA Mathematics Cryptography Abstract algebra
29	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
30	SHARK A Realizable Special Hardware Sieving Device for Factoring 1024-bit Integers Jens Franke1 , Thorsten Kleinjung1 , Christof Paar2 , Jan Pelzl2 , Christine Priplata3 , and Colin Stahlke3 1 Add to Reading List Source URL: www.iacr.org Language: English - Date: 2008-09-15 00:54:55 General number field sieve Numbers Lattice sieving Integer factorization records Sieve TWIRL Factor base Mesh Dynamic random-access memory Integer factorization algorithms Mathematics Quadratic sieve

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