First fall degree and Weil descent

Timothy J. Hodges, Christophe Petit, Jacob Schlather

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
180 Downloads (Pure)


Polynomial systems arising from a Weil descent have many applications in cryptography, including the HFE cryptosystem and the elliptic curve discrete logarithm problem over small characteristic fields. Understanding the exact complexity of solving these systems is essential for the applications. A first step in that direction is to study the first fall degree of the systems. In this paper, we establish a rigorous general bound on the first fall degree of polynomial systems arising from a Weil descent. We also provide experimental data to study the tightness of our bound in general and its plausible consequences on the complexity of polynomial systems arising from a Weil descent.
Original languageEnglish
Pages (from-to)155-177
Number of pages22
JournalFinite Fields and Their Applications
Early online date26 Jul 2014
Publication statusPublished - Nov 2014


  • First fall degree
  • Weil descent
  • Finite field
  • Degree of regularity


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