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Section: New Results

A New Measure for Root Optimization

Participants : Nicolas David, Paul Zimmermann.

In the General Number Field Sieve (GNFS) for integer factorization or discrete logarithm, the first stage is polynomial selection. Polynomial selection itself consists in two steps: size-optimization and root-optimization. The classical measures used to rank polynomials during the root-optimization are the so-called $\alpha$ and Murphy-E values. During the internship of Nicolas David, it was shown that these classical measures might be off by up to 15% between two polynomial pairs, compared to a sieving test. A new measure that better corresponds to sieving tests was designed. An article describing these new results is in preparation.