We give an alternative approach and improvements on bounds developed by Hodges, Petit and Schlather [5], and Petit and Quisquater [9] concerning the first fall degree of algebraic equations. In particular, we improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials [10].

Today the computer is changing from a big, grey, and noisy thing on our desk to a small, portable, and ever-networked item most of us are carrying around. This new found mobility imposes a shift in how we view computers and the way we work with them. When interaction can occur anywhere at any time it is imperative that the system adapts to the user in whatever situation the user is in. To facil...

E Matichard, P Verpillat, R Meziani, B Gérard, V Descamps, E Legroux, M Burnouf, G Bertrand, F Bouscarat, A Archimbaud, C Picard, L Ollivaud, N Basset-Seguin, D Kerob, G Lanternier, C Lebbe, B Crickx, B Grandchamp, N Soufir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....