Implementing the Elliptic Curve Method of Factoring in Reconfigurable Hardware Kris Gaj, Soonhak Kwon, Patrick Baier, Paul Kohlbrenner, Hoang Le, Mohammed Khaleeluddin, Ramakrishna Bachimanchi George Mason University {kg

Source URL: www.hyperelliptic.org

• Algebra
• Abstract algebra
• Mathematics
• Finite fields
• Integer factorization algorithms
• Elliptic curves
• Group theory
• Lenstra elliptic-curve factorization
• Elliptic curve
• Elliptic curve primality
• Factorization of polynomials over finite fields

Cofactorisation strategies for the number field sieve and an estimate for the sieving step for factoring 1024-bit integers Thorsten Kleinjung University of Bonn, Department of Mathematics, Beringstraße 1, DBonn,

Source URL: www.hyperelliptic.org

• Integer factorization algorithms
• Mathematics
• Quadratic sieve
• General number field sieve
• Integer factorization
• Prime number
• Factorization
• Number theory
• Factor base
• Shanks's square forms factorization

SHARK A Realizable Special Hardware Sieving Device for Factoring 1024-bit Integers Jens Franke1 , Thorsten Kleinjung1 , Christof Paar2 , Jan Pelzl2 , Christine Priplata3 , Colin Stahlke3 1

Source URL: www.hyperelliptic.org

• Integer factorization algorithms
• Mathematics
• Quadratic sieve
• Integer factorization records
• General number field sieve
• TWIRL
• Lattice sieving
• Factor base
• Prime number
• Sieve

Special-Purpose Hardware for Factoring: the NFS Sieving Step Adi Shamir Eran Tromer

Source URL: www.hyperelliptic.org

• Integer factorization algorithms
• Weizmann Institute of Science
• TWINKLE
• TWIRL
• Mathematics
• General number field sieve
• Prime number
• Sieve
• Dynamic random-access memory
• Factor base
• Computing
• Sieve of Atkin

Implementation of Mesh Routing for the Matrix Step in Number Field Sieving Factoring

Source URL: www.hyperelliptic.org

• Numerical linear algebra
• Integer factorization algorithms
• General number field sieve
• Matrix
• Sparse matrix
• LU decomposition
• Incomplete Cholesky factorization

An Efficient Hardware Architecture for Factoring Integers with the Elliptic Curve Method Jens Franke, Thorsten Kleinjung - University of Bonn Christof Paar, Jan Pelzl - University of Bochum Christine Priplata, Colin Stah

Source URL: www.hyperelliptic.org

• Cryptography
• Integer factorization algorithms
• Lenstra elliptic-curve factorization
• Quadratic sieve
• Elliptic-curve cryptography
• Elliptic curve
• Integer factorization
• General number field sieve
• RSA
• Trial division

Cofactorisation strategies for the number field sieve and an estimate for the sieving step for factoring 1024-bit integers Thorsten Kleinjung, University of Bonn

Source URL: www.hyperelliptic.org

• Mathematics
• Integer factorization algorithms
• General number field sieve
• Primality test
• Factorization
• Divisor
• Prime number
• 284
• Square root

An Efficient Hardware Architecture for Factoring Integers with the Elliptic Curve Method Jens Franke1 , Thorsten Kleinjung1 , Christof Paar2 , Jan Pelzl2 , 4 ˇ Christine Priplata3 , Martin Simka

Source URL: www.hyperelliptic.org

• Integer factorization algorithms
• Mathematics
• Abstract algebra
• Algebra
• Lenstra elliptic-curve factorization
• Quadratic sieve
• Montgomery modular multiplication
• Elliptic curve
• Exceptional case-marking
• Division algorithm
• General number field sieve

Classroom Voting Questions: Algebra Section 6.5: Factoring by Grouping and a General Strategy for Factoring Polynomials 1. Which of the following is equivalent to x2 + x + 0? (a) x(x)

Source URL: mathquest.carroll.edu

Classroom Voting Questions: Algebra Section 6.2: Factoring Trinomials of the Form x2 + bx + c 1. What two integers c1 and c2 have a product of 12 and a sum of −7? (a) c1 = −2 and c2 = −6

Source URL: mathquest.carroll.edu