Non-Linear Polynomial Selection for the Number Field Sieve

Thomas Prest (1) , Paul Zimmermann (1)

1 CARAMEL - Cryptology, Arithmetic: Hardware and Software

We present an algorithm to find two non-linear polynomials for the Number Field Sieve integer factorization method. This algorithm extends Montgomery's "two quadratics" method; for degree 3, it gives two skewed polynomials with resultant O(N^5/4), which improves on Williams O(N^4/3) result.

Domaines: Algorithme et structure de données [cs.DS]

Thomas Prest, Paul Zimmermann. Non-Linear Polynomial Selection for the Number Field Sieve. Journal of Symbolic Computation, 2012, 47 (4), pp.401-409. ⟨inria-00540483⟩