Montgomery's method of polynomial selection for the number field sieve

Nicholas Coxon (1)

1 CARAMEL - Cryptology, Arithmetic: Hardware and Software

The number field sieve is the most efficient known algorithm for factoring large integers that are free of small prime factors. For the polynomial selection stage of the algorithm, Montgomery proposed a method of generating polynomials which relies on the construction of small modular geometric progressions. Montgomery's method is analysed in this paper and the existence of suitable geometric progressions is considered.

Mots clés: Integer factorisation; number field sieve; polynomial selection; Montgomery's method

Domaines: Cryptographie et sécurité [cs.CR]

Nicholas Coxon. Montgomery's method of polynomial selection for the number field sieve. 2014. ⟨hal-01097069⟩