Invited Talks -- Gauss Composition and Generalizations -- Elliptic Curves - The Crossroads of Theory and Computation -- The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems -- Using Elliptic Curves of Rank One towards the Undecidability of Hilbert's Tenth Problem over Rings of Algebraic Integers -- On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields -- Number Theory -- On Arithmetically Equivalent Number Fields of Small Degree -- A Survey of Discriminant Counting -- A Higher-Rank Mersenne Problem -- An Application of Siegel Modular Functions to Kronecker's Limit Formula -- Computational Aspects of NUCOMP -- Efficient Computation of Class Numbers of Real Abelian Number Fields -- An Accelerated Buchmann Algorithm for Regulator Computation in Real Quadratic Fields -- Arithmetic Geometry -- Some Genus 3 Curves with Many Points -- Trinomials ax 7 + bx + c and ax 8 + bx + c with Galois Groups of Order 168 and 8 · 168 -- Computations on Modular Jacobian Surfaces -- Integral Points on Punctured Abelian Surfaces -- Genus 2 Curves with (3, 3)-Split Jacobian and Large Automorphism Group -- Transportable Modular Symbols and the Intersection Pairing -- Elliptic Curves and CM -- Action of Modular Correspondences around CM Points -- Curves Dy 2 = x 3 - x of Odd Analytic Rank -- Comparing Invariants for Class Fields of Imaginary Quadratic Fields -- A Database of Elliptic Curves - First Report -- Point Counting -- Isogeny Volcanoes and the SEA Algorithm -- Fast Elliptic Curve Point Counting Using Gaussian Normal Basis -- An Extension of Kedlaya's Algorithm to Artin-Schreier Curves in Characteristic 2 -- Cryptography -- Implementing the Tate Pairing -- Smooth Orders and Cryptographic Applications -- Chinese Remaindering for Algebraic Numbers in a Hidden Field -- Function Fields -- An Algorithm for Computing Weierstrass Points -- New Optimal Tame Towers of Function Fields over Small Finite Fields -- Periodic Continued Fractions in Elliptic Function Fields -- Discrete Logarithms and Factoring -- Fixed Points and Two-Cycles of the Discrete Logarithm -- Random Cayley Digraphs and the Discrete Logarithm -- The Function Field Sieve Is Quite Special -- MPQS with Three Large Primes -- An Improved Baby Step Giant Step Algorithm for Point Counting of Hyperelliptic Curves over Finite Fields -- Factoring N = pq 2 with the Elliptic Curve Method -- Gröbner Bases -- A New Scheme for Computing with Algebraically Closed Fields -- Complexity -- Additive Complexity and Roots of Polynomials over Number Fields and -adic Fields.