Modular Methods in CoCoA What are modular methods? When you have to do a quick calculation on the back of an envelope, you might calculate the sum or product of two (small) polynomials, and you would most likely use a di

Source URL: cocoa.dima.unige.it

• Polynomials
• Computer algebra
• Finite fields
• Euclidean algorithm
• Factorization of polynomials
• Integer factorization algorithms
• Greatest common divisor
• Prime number
• Algebraic number field
• Mathematics
• Abstract algebra
• Algebra

Certicom ECC Challenge Abstract Certicom is pleased to present the Certicom Elliptic Curve Cryptosystem (ECC) Challenge. The first of its kind, the ECC Challenge has been developed to increase the industry’s understand

Source URL: www.certicom.com

• Finite fields
• Computational hardness assumptions
• Group theory
• Key management
• Elliptic curve cryptography
• Elliptic curve
• Integer factorization
• Key size
• Elliptic Curve DSA
• Abstract algebra
• Cryptography
• Mathematics

Integer Factorization Per Leslie Jensen DIKU[removed]kl. 10:15

Source URL: pgnfs.org

Pollard’s p 1 Factoring Algorithm As a quick review, Pollard’s p 1 factoring algorithm is efficient only in the case where one of the primes, say p, has the property that p 1 is a product of small primes (such a p 1

Source URL: www.untruth.org

• Prime number
• Factorization
• Finite fields
• Integer factorization algorithms
• Mathematics
• Algebra

Integer Factorization Per Leslie Jensen Master Thesis D I K U

Source URL: pgnfs.org

• Abstract algebra
• Integer factorization
• Quadratic sieve
• General number field sieve
• RSA
• Prime number
• Primality test
• Factorization
• Discrete logarithm
• Mathematics
• Cryptography
• Integer factorization algorithms

THREE NEW FACTORS OF FERMAT NUMBERS R. P. BRENT, R. E. CRANDALL, K. DILCHER, AND C. VAN HALEWYN Abstract We report the discovery of a new factor for each of the Fermat numbers F13 , F15 , F16 . These new factors have 27,

Source URL: gan.anu.edu.au

• Integer sequences
• Integer factorization algorithms
• Euclidean plane geometry
• Fermat number
• Number theory
• Pierre de Fermat
• Lenstra elliptic curve factorization
• Integer factorization
• Richard P. Brent
• Mathematics
• Abstract algebra
• Group theory

Last modified: March 20, 2005. MY MAIN WORK ON THE THREE TOPICS Zhi-Wei Sun Department of Mathematics Nanjing University

Source URL: math.nju.edu.cn

• Integer sequences
• Number theory
• Factorial
• Ring
• Binomial coefficient
• Factorization of polynomials over a finite field and irreducibility tests
• Mathematics
• Mathematical analysis
• Combinatorics

pomerance.qxp[removed]:16 AM Page[removed]A Tale of Two Sieves Carl Pomerance (This paper is dedicated to the memory of my friend and

Source URL: www.math.dartmouth.edu

• Numbers
• Quadratic sieve
• General number field sieve
• Lenstra elliptic curve factorization
• Prime number
• Integer factorization
• Factorization
• Sieve of Eratosthenes
• Factor base
• Integer factorization algorithms
• Mathematics
• Number theory

version[removed]Primality testing with Gaussian periods Primality testing with Gaussian periods H. W. Lenstra jr. and Carl Pomerance

Source URL: www.math.dartmouth.edu

• Primality tests
• Finite fields
• Polynomials
• Integer factorization algorithms
• Field theory
• Prime number
• Root of unity
• Number theory
• Miller–Rabin primality test
• Abstract algebra
• Mathematics
• Algebra

UPDATE ON PRIMALITY TESTING SERGEI V. KONYAGIN AND CARL POMERANCE Abstract. We discuss recent developments in the field of primality testing since the appearance [10] of our joint paper On primes recognizable in determi

Source URL: www.math.dartmouth.edu

• Mathematics
• AKS primality test
• Prime number
• Miller–Rabin primality test
• Integer factorization
• Randomized algorithm
• Time complexity
• Quadratic residue
• Jacobi symbol
• Theoretical computer science
• Computational complexity theory
• Primality tests