Non-Linear Polynomial Selection for the Number Field Sieve

Thomas Prest 1 Paul Zimmermann 1
1 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : 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(N5/4), which improves on Williams O(N4/3) result.
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Thomas Prest, Paul Zimmermann. Non-Linear Polynomial Selection for the Number Field Sieve. Journal of Symbolic Computation, Elsevier, 2012, 47 (4), pp.401-409. ⟨inria-00540483⟩

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