Algebraic geometry and its applications: dedicated to Gilles Lachaud on his 60th birthday : proceedings of the First SAGA Conference, Papeete, France, 7-11 May 2007

This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields.

It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas.

New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.Sample Chapter(s)Chapter 1: Fast addition on non-hyperelliptic genus 3 curves (424 KB)Contents: Symmetric Cryptography and Algebraic Curves (F Voloch)Galois Invariant Smoothness Basis (J-M Couveignes & R Lercier)Fuzzy Pairing-Based CL-PKC (M Kiviharju)On the Semiprimitivity of Cyclic Codes (Y Aubry & P Langevin)Decoding of Scroll Codes (G H Hitching & T Johnsen)An Optimal Unramified Tower of Function Fields (K Brander)On the Number of Resilient Boolean Functions (S Mesnager)On Quadratic Extensions of Cyclic Projective Planes (H F Law & P P W Wong)Partitions of Vector Spaces over Finite Fields (Y Zelenyuk)and other papersReadership: Mathematicians, researchers in mathematics (academic and industry R&D).