Paper 2015/1121

On the First Fall Degree of Summation Polynomials

Stavros Kousidis and Andreas Wiemers

Abstract

We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev's summation polynomials.

Note: Timothy J. Hodges informed us about a mistake in Corollary 4.5 in the first version of the article. Our arguments do not hold in that generality. We have re-written the relevant part, the restricted statement is now Corollary 5.2 in the second version. The statement about the first fall degree of summation polynomials remains unchanged.