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

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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

Source URL: www.mat.uniroma2.it

• 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

Integer factorization, part 1: the Q sieve Integer factorization, part 2: detecting smoothness D. J. Bernstein

Source URL: www.mat.uniroma2.it

• Integer factorization algorithms
• Mathematics
• Number theory
• Integer sequences
• Quadratic sieve
• Discrete mathematics
• Prime number
• Smooth number
• Special number field sieve
• General number field sieve

Integer factorization, part 1: the Q sieve D. J. Bernstein Sieving small integers using primes:

Source URL: www.mat.uniroma2.it

• Mathematics
• Integer factorization algorithms
• Number theory
• Integer sequences
• Integer factorization
• Prime number
• Prime factor
• Factorization
• Quadratic sieve
• Congruence of squares

The Million-Key Question—Investigating the Origins of RSA Public Keys Petr Švenda, Matúš Nemec, Peter Sekan, Rudolf Kvašňovský, David Formánek, David Komárek, and Vashek Matyáš, Masaryk University https://www

Source URL: www.usenix.org

• Cryptography
• Integer sequences
• Integer factorization algorithms
• Primality tests
• Safe prime
• Finite fields
• RSA
• Prime number
• Strong prime
• Blum integer
• Trial division
• Quadratic sieve

Implicit Factoring: On Polynomial Time Factoring Given Only an Implicit Hint ∗ Alexander May, Maike Ritzenhofen Horst Görtz Institute for IT-security Faculty of Mathematics Ruhr-University of Bochum, 44780 Bochum, Ger

Source URL: www.cits.rub.de

• Cryptography
• Integer factorization algorithms
• Computational hardness assumptions
• E-commerce
• RSA
• Quadratic sieve
• Lattice
• Integer factorization

International Mathematical Olympiad Preliminary Selection Contest 2004 — Hong Kong Outline of Solutions Answers:

Source URL: web.hku.hk

• Integer sequences
• Integer factorization algorithms
• Prime number
• Algebraic number theory
• Field theory
• Quadratic sieve
• Wieferich prime

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

Source URL: davidlowryduda.com

• Integer factorization algorithms
• Mathematics
• Cryptography
• Number theory
• Quadratic sieve
• Euclidean algorithm
• RSA
• Prime number
• Factorization
• Trial division
• General number field sieve
• Rational sieve

Integer Factorization and Computing Discrete Logarithms in Maple Aaron Bradford∗, Michael Monagan∗, Colin Percival∗ , , Department of Mathematics, Simon Fr

Source URL: www.daemonology.net

• 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

A kilobit special number field sieve factorization Kazumaro Aoki1 , Jens Franke2 , Thorsten Kleinjung2 , Arjen K. Lenstra3 , and Dag Arne Osvik3 1 2

Source URL: eprint.iacr.org

• 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