ASIACRYPT 2003: Advances in Cryptology - ASIACRYPT 2003 pp 302-310 | Cite as
Rotations and Translations of Number Field Sieve Polynomials
Conference paper
Abstract
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 ℤ[X]. These algorithms can be used to produce promising candidate Number Field Sieve polynomials.
Keywords
Minimal Size Error Message Chinese Remainder Theorem Distinct Root Root Property
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References
- 1.Lenstra, A.K., Lenstra Jr., H.W. (eds.): The Development of the Number Field Sieve. Lecture Notes in Mathematics, vol. 1554. Springer, Berlin (1993)MATHGoogle Scholar
- 2.Murphy, B.: Polynomial Selection for the Number Field Sieve Integer Factorisation Algorithm. PhD thesis, Australian National University (July 1999)Google Scholar
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© Springer-Verlag Berlin Heidelberg 2003