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Integer factorization algorithms
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51	CS255: Cryptography and Computer Security Winter 2003 Basic number theory fact sheet Part II: Arithmetic modulo composites Add to Reading List Source URL: crypto.stanford.edu Language: English - Date: 2003-02-10 15:18:01 Modular arithmetic Public-key cryptography Finite fields Integer factorization algorithms RSA Prime number Euclidean algorithm Discrete logarithm Coprime Abstract algebra Mathematics Cryptography
52	Solutions to Homework Three CSE[removed]a) Each time you roll a die, the chance of getting a six is p = 1/6. So the expected number of rolls until you see a six is 1/p = 6. Add to Reading List Source URL: cseweb.ucsd.edu Language: English - Date: 2014-10-17 13:59:47 Abstract algebra Integer factorization algorithms Finite fields Integer sequences Modular arithmetic Euclidean algorithm Prime number Miller–Rabin primality test Solovay–Strassen primality test Mathematics Number theory Primality tests
53	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
54	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
55	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
56	. Accurate and efficient expression evaluation and linear algebra James Demmel Add to Reading List Source URL: www.cs.berkeley.edu Language: English - Date: 2010-09-24 20:40:19 Polynomials Mathematical analysis Logarithms Mathematics Integer factorization algorithms
57	Solutions to Homework Two CSE[removed]A 1000-bit number lies between 2999 and 21000 − 1; thus its length in decimal is roughly log10 21000 = 1000 log10 2 ≈ 300. Add to Reading List Source URL: cseweb.ucsd.edu Language: English - Date: 2014-10-12 01:34:36 Arithmetic Elementary arithmetic Least common multiple Recursion Fibonacci number Euclidean algorithm Greatest common divisor Mathematics Number theory Integer factorization algorithms
58	Cryptography and Computer Security CS255 Basic number theory fact sheet Part II: Arithmetic modulo composites Add to Reading List Source URL: crypto.stanford.edu Language: English - Date: 2015-01-03 18:17:27 Modular arithmetic Public-key cryptography Finite fields Integer factorization algorithms RSA Euclidean algorithm Prime number Discrete logarithm Chinese remainder theorem Abstract algebra Mathematics Cryptography
59	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
60	Fast arithmetic and pairing evaluation on genus 2 curves David Freeman University of California, Berkeley [removed] November 6, 2005 Add to Reading List Source URL: theory.stanford.edu Language: English - Date: 2008-06-06 19:27:47 Group theory Polynomial Euclidean algorithm Finite fields Elliptic curves Integer factorization algorithms Lenstra elliptic curve factorization Factorization of polynomials over a finite field and irreducibility tests Abstract algebra Mathematics Algebra