Rotations and Translations of Number Field Sieve Polynomials

We present an algorithm that finds polynomials with many roots modulo many primes by rotating candidate Number Field Sieve polynomials using the Chinese Remainder Theorem. We also present an algorithm that finds a polynomial with small coefficients among all integral translations of X of a given polynomial in ZZ[X]. These algorithms can be used to produce promising candidate Number Field Sieve polynomials.

• Type: Conference
• Year: 2003
• Where: ASIACRYPT
• Authors: Jason E. Gower
• Keywords: ASIACRYPT 2003, Candidate Number Field, Cryptology, Field Sieve Polynomials, Number Field Sieve