Includes bibliographical references and index.

Fast addition on non-hyperelliptic genus 3 curves / S. Flon, R. Oyono, C. Ritzenthaler -- Computing endomorphism rings of Jacobians of genus 2 curves over finite fields / D. Freeman, K. Lauter -- Complex multiplication and canonical lifts / D. Kohel -- Two letters to Jaap Top / J.-P. Serre -- On some questions of Serre on abelian threefolds / G. Lachaud, C. Ritzenthaler -- Pseudorandom points on elliptic curves over finite fields / I. Shparlinski -- Symmetric cryptography and algebraic curves / F. Voloch -- Galois invariant smoothness basis / J.-M. Couveignes, R.Lercier -- Fuzzy pairings-based CL-PKC / M. Kiviharju -- Trace zero varieties over fields of characteristic 2 for cryptographic applications / R. Avanzi, E. Cesena -- Group law algorithms for Jacobian varieties of curves over finite fields / R. Cohen -- Discrete logarithms, duality, and arithmetic in Brauer groups / G. Frey -- On generators of the group Ĥ[symbol](Gal(L/K),E[symbol]) in some abelian p-extension L/K / E. Hallouin, M. Perret -- On the semiprimitivity of cyclic codes / Y. Aubry, P. Langevin -- Decoding of scroll codes / G. H. Hitching, T. Johnsen -- List decoding using syndromes / P. Beelem, T. Høholdt -- A note on the tensor rank of the multiplication in certain finite fields / S. Ballet -- Multiplication in small finite fields using elliptic curves / J. Chaumine -- An optimal unramified tower of function fields / K. Brander -- Partial covering sequences: a method for designing classes of cryptographic functions / C. Carlet -- Non linéarité des fonctions booléennes données par des tracesde polynômes de degré binaire 3 / E. Férard, F. Rodier -- On exponents with highly divisible Fourier coefficients and conjectures of Niho and Dobbertin / G. Leander, P. Langevin -- On the number of resilient boolean functions / S. Mesnager -- On quadratic extensions of cyclic projective planes / H. F. Law, P. P. W. Wong -- Some integral representations of finite groups and their arithmetic applications / D. A. Malinin -- Number of points of non-absolutely irreducible hypersurfaces / R. Rolland -- Neuberg cubics over finite fields / N. J. Wildberger -- Partitions of vector spaces over finite fields / Y. Zelenyuk.

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.

Electronic reproduction. Singapore : World Scientific Publishing Co., 2008. System requirements: Adobe Acrobat Reader. Mode of access: World Wide Web. Available to subscribing institutions.