Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

TheAAECCsymposiumwasstartedinJune1983byAlainPoli(Toulouse),who, together with Roger Desq, Daniel Lazard, and Paul Camion, organized the ?rst conference. The meaning of the acronym AAECC changed from Applied - gebra and Error Correcting Codes to Applied Algebra, Algebraic Algorithms, and Error Correcting Codes. One reason for this was the increasing importance of complexity, particularly for decoding algorithms. During the AAECC-12 s- posium the conference committee decided to enforce the theory and practice of the coding side as well as the cryptographic aspects. Algebra was conserved, as in the past, but was slightly more oriented to algebraic geometry codes, ?nite ?elds, complexity, polynomials, and graphs. For AAECC-15 the main subjects covered were: Block codes. Algebra and codes: rings, ?elds, AG codes. Cryptography. Sequences. Algorithms, decoding algorithms. Algebra: constructions in algebra, Galois groups, di?erential algebra, po- nomials. The talks of the six invited speakers characterized the aims of AAECC-15: P. Sole ( Public Key Cryptosystems Based on Rings ). S. Lin ( Combinatorics Low Density Parity Check Codes ). J. Stern ( Cryptography and the Methodology of Provable Security ). D. Costello ( Graph-Based Convolutional LDPC Codes ). I. Shparlinsky ( Dynamical Systems Generated by Rational Functions ). A. Lauder ( Algorithms for Multivariate Polynomials over Finite Fields ).

Includes supplementary material: sn.pub/extras

Inhalt
Cryptography and the Methodology of Provable Security.- Dynamical Systems Generated by Rational Functions.- Homotopy Methods for Equations over Finite Fields.- Three Constructions of Authentication/Secrecy Codes.- The Jacobi Model of an Elliptic Curve and Side-Channel Analysis.- Fast Point Multiplication on Elliptic Curves through Isogenies.- Interpolation of the Elliptic Curve Diffie-Hellman Mapping.- An Optimized Algebraic Method for Higher Order Differential Attack.- Fighting Two Pirates.- Copyright Control and Separating Systems.- Unconditionally Secure Homomorphic Pre-distributed Commitments.- A Class of Low-Density Parity-Check Codes Constructed Based on Reed-Solomon Codes with Two Information Symbols.- Relative Duality in MacWilliams Identity.- Good Expander Graphs and Expander Codes: Parameters and Decoding.- On the Covering Radius of Certain Cyclic Codes.- Unitary Error Bases: Constructions, Equivalence, and Applications.- Differentially 2-Uniform Cocycles The Binary Case.- The Second and Third Generalized Hamming Weights of Algebraic Geometry Codes.- Error Correcting Codes over Algebraic Surfaces.- A Geometric View of Decoding AG Codes.- Performance Analysis of M-PSK Signal Constellations in Riemannian Varieties.- Improvements to Evaluation Codes and New Characterizations of Arf Semigroups.- Optimal 2-Dimensional 3-Dispersion Lattices.- On g-th MDS Codes and Matroids.- On the Minimum Distance of Some Families of ?2 k-Linear Codes.- Quasicyclic Codes of Index ? over F q Viewed as F q-Submodules of F q ?/?x m?1?.- Fast Decomposition of Polynomials with Known Galois Group.