Contents Preface vii Differentially 4-uniform functions Yves Aubry and Franc ¸ois Rodier 1 Computing Hironaka’s invariants: Ridge and directrix J´ ´ emy Berthomieu, Pascal Hivert and Hussein Mourtada 9 Nondegenerate curves of low genus over small finite fields Wouter Castryck and John Voight 21 Faster side-channel resistant elliptic curve scalar multiplication Alexandre Venelli and Franc ¸ois Dassance 29 Non lin´earit´ e des fonctions bool´ eennes donn´ ees par des polynˆ omes de degr´e binaire 3 d´ efinies sur F2m avec m pair Eric Ferard ´ and Franc ¸ois Rodier 41 A note on a maximal curve Arnaldo Garcia and Henning Stichtenoth 55 Computing Humbert surfaces and applications David Gruenewald 59 Genus 3 curves with many involutions and application to maximal curves in characteristic 2 Enric Nart and Christophe Ritzenthaler 71 Uniqueness of low genus optimal curves over F2 Alessandra Rigato 87 Group order formulas for reductions of CM elliptic curves Alice Silverberg 107 Families of explicit isogenies of hyperelliptic Jacobians Benjamin Smith 121 Computing congruences of modular forms and Galois representations modulo prime powers Xavier Taix´ i Ventosa and Gabor Wiese 145 v
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