Topics in Geometry, Coding Theory and Cryptography Book

Foreword     vii
Explicit Towers of Function Fields over Finite Fields   A. Garcia   H. Stichtenoth     1
Introduction     1
Towers and Codes     5
Genus and Splitting Rate of a Tower     16
Explicit Tame Towers     24
Explicit Wild Towers     31
Miscellaneous Results     47
References     55
Function Fields over Finite Fields and Their Applications to Cryptography   H. Niederreiter   H. Wang   C. Xing     59
Introduction     59
Applications to Combinatorial Cryptography     60
Applications to Stream Ciphers and Linear Complexity     89
References     99
Artin-Schreier Extensions and Their Applications   C. Guneri   F. Ozbudak     105
Introduction     105
Artin-Schreier Extensions     107
Cyclic Codes and Their Weights     111
Trace Codes     120
Maximal Function Fields     126
References     130
Pseudorandom Sequences   A. Topuzoglu   A. Winterhof     135
Introduction     135
Linear Complexity and Linear ComplexityProfile     137
Autocorrelation and Related Distribution Measures for Binary Sequences     154
Discrepancy and Uniform Distribution     157
References     162
Group Structure of Elliptic Curves over Finite Fields and Applications   R. Murty   I. Shparlinski     167
Introduction     167
Group Structure     171
Applications to Cryptography     180
References     187
Algebraic Function Fields     195
About the Authors     199