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Arithmetic, geometry, cryptography and coding theory : [electronic resource] 13th Conference on Arithmetic, Geometry, Cryptography and Coding Theory, March 14-18, 2011, CIRM, Marseille, France : Geocrypt 2011, June 19-24, 2011, Bastia, France / Yves Aubry, Christophe Ritzenthaler, Alexey Zykin, editors.

By: (13th : International Conference "Arithmetic, Geometry, Cryptography and Coding Theory" (13th : 2011 : Marseille, France)Contributor(s): Aubry, Yves, 1965- | Ritzenthaler, Christophe, 1976- | Zykin, Alexey, 1984- | Geocrypt Conference (2011 : Bastia, France)Material type: Text

TextSeries: Contemporary mathematics ; v. 574Publication details: Providence, R.I. : American Mathematical Society, c2012Description: 1 online resource (183 p.)ISBN: 9780821890271 (online)Subject(s): Abelian varieties -- Congresses | Dimension theory (Algebra) -- Congresses | Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Abelian varieties of dimension $> 1$ | Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Curves over finite and local fields | Number theory -- Zeta and $L$-functions: analytic theory -- Zeta and $L$-functions in characteristic $p$ | Number theory -- Algebraic number theory: global fields -- Zeta functions and $L$-functions of number fields | Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Polynomials | Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Algebraic coding theory; cryptography | Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Zeta-functions and related questions | Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Finite ground fields | Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Applications to coding theory and cryptography | Algebraic geometry -- Computational aspects in algebraic geometry -- CurvesAdditional physical formats: Arithmetic, geometry, cryptography and coding theory :DDC classification: 510 LOC classification: QA564 | .I576 2011Other classification: 11G10 | 11G20 | 11M38 | 11R42 | 11T06 | 11T71 | 14G10 | 14G15 | 14G50 | 14Q05 Online resources: Contents | Contents

Contents:

Construction of a $\Bbbk $-complete addition law on Jacobians of hyperelliptic curves of genus two / Christophe Ar�ene and Romain Cosset -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11429 Number of points in an Artin-Schreier covering / R�egis Blache -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11427 Some more functions that are not APN infinitely often. The case of Gold and Kasami exponents / Eric F�erard, Roger Oyono and Fran�cois Rodier -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11423 Rational curves with many rational points over a finite field / Satoru Fukasawa, Masaaki Homma and Seon Jeong Kim -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11420 Enumeration of Splitting Subspaces over Finite Fields / Sudhir R. Ghorpade and Samrith Ram -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11430 The characteristic polynomials of abelian varieties of dimension 4 over finite fields / Safia Haloui and Vijaykumar Singh -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11446 New bounds on the maximum number of points on genus-$4$ curves over small finite fields / Everett W. Howe -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11431 Some planar maps and related function fields / Gohar M. Kyureghyan, Ferruh �Ozbudak and Alexander Pott -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11425 New families of APN functions in characteristic 3 or 5 / Elodie Leducq -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11419 Identities for Kloosterman sums and modular curves / Petr Lison�ek -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11421 Degree growth, linear independence and periods of a class of rational dynamical systems / Alina Ostafe and Igor Shparlinski -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11426 Computer search for curves with many points among abelian covers of genus 2 curves / Karl R�okaeus -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11422 The groups of points on abelian surfaces over finite fields / Sergey Rybakov -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11424 Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method / Benjamin Smith -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11418 Hodge classes on certain hyperelliptic prymians / Yuri G. Zarhin -- http://www.ams.org/conm/574/ http://dx.doi.org/10.1090/conm/574/11432

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Includes bibliographical references.

Construction of a $\Bbbk $-complete addition law on Jacobians of hyperelliptic curves of genus two / Christophe Ar�ene and Romain Cosset -- Number of points in an Artin-Schreier covering / R�egis Blache -- Some more functions that are not APN infinitely often. The case of Gold and Kasami exponents / Eric F�erard, Roger Oyono and Fran�cois Rodier -- Rational curves with many rational points over a finite field / Satoru Fukasawa, Masaaki Homma and Seon Jeong Kim -- Enumeration of Splitting Subspaces over Finite Fields / Sudhir R. Ghorpade and Samrith Ram -- The characteristic polynomials of abelian varieties of dimension 4 over finite fields / Safia Haloui and Vijaykumar Singh -- New bounds on the maximum number of points on genus-$4$ curves over small finite fields / Everett W. Howe -- Some planar maps and related function fields / Gohar M. Kyureghyan, Ferruh �Ozbudak and Alexander Pott -- New families of APN functions in characteristic 3 or 5 / Elodie Leducq -- Identities for Kloosterman sums and modular curves / Petr Lison�ek -- Degree growth, linear independence and periods of a class of rational dynamical systems / Alina Ostafe and Igor Shparlinski -- Computer search for curves with many points among abelian covers of genus 2 curves / Karl R�okaeus -- The groups of points on abelian surfaces over finite fields / Sergey Rybakov -- Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method / Benjamin Smith -- Hodge classes on certain hyperelliptic prymians / Yuri G. Zarhin --