domingo, 5 de abril de 2009

The General Number Field Sieve

Actualmente, el algoritmo de factorización más rápido que existe. Dejo aquí mi colección de papers.

- The Factorization of the Ninth Fermat Number , A.K. Lenstra, H.W. Lenstra, M.S. Manasse, and J.M. Pollard (1993).
- The Number Field Sieve , A. K. Lenstra, M. S. Manasse, J. M. Pollard (1990).

Introduction to the GNFS algorithm
- An Introduction to the General Number Field Sieve , Matthew E. Briggs (1998).
- A Beginner's Guide To The General Number Field Sieve , Michael Case.
- The Number Field Sieve , Peter Stevenhagen.
- The Number Field Sieve , Steven Byrnes.

Polynomial Selection
- Polynomial Selection for the Number Field Sieve Factorisation Algorithm , Brian Murphy (1999).
- On quadratic polynomials for the number field sieve , Brian Murphy and Richard P. Brent (1998).
- Rotations and Translations of Number Field Sieve Polynomials Jason Gower (2003).
- The multiple-lattice number field sieve , Daniel J Bernstein.

- Continued Fractions and Lattice Sieving , Jens Franke, Thorsten Kleinjung.

- Strategies in filtering in the number field sieve , S. Cavallar (2000).

Linear Algebra
- Solving Large Sparse Linear Systems over Finite Fields , B. A. LaMacchia and A. M. Odlyzko (1991).
- A Block Lanczos Algorithm for Finding Dependencies over GF(2) , Peter L. Montgomery.
- Solving large sparse linear systems over finite fields , B. A. Lamacchia, A. M. Odlyzko (1991).

Square Root
- A Montgomery-like square root for the Number Field Sieve , Phong Nguyen, Ecole Normale Superieure (1998).
- Computing a Square Root for the Number Field Sieve , Jean-Marc Couveignes (1993).
- Square Roots of Products of Algebraic Numbers , Peter L. Montgomery.

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