Authentication codes and combinatorial designs
Ting-i Pʿei · Chapman & Hall/CRC eBooks · 2006
INTRODUCTION Authentication Problems Authentication Schemes Combinatorial Designs AUTHENTICATION SCHEMES Model with Three Participants (A-Codes) Model with Four Participants (A2-Codes) Comments AUTHENTICATION SCHEMES WITH THREE PARTICIPANTS Entropy Information-Theoretic Bound Perfect Authentication Schemes Perfect Cartesian Codes Combinatorial Bound Comments Exercises AUTHENTICATION SCHEMES WITH ARBITRATION Lower Bounds Perfect Schemes with Arbitration Perfect Cartesian A2-Codes Combinatorial Bounds of A2-Codes Comments Exercises A-CODES BASED ON RATIONAL NORMAL CURVES SPBD Based on RNC A Family of Non-Cartesian Perfect A-Codes Encoding Rules (n = 2, q Odd) Encoding Rules (n = 2, q Even) Comments Exercises t-DEISGNS 2 - (v, k, 1) Designs Steiner Triple System 3 - (v, k, 1) Designs Comments Exercises ORTHOGONAL ARRAYS OF INDEX UNITY OA with Strength t = 2 and Orthogonal Latin Squares Transversal Designs Existence of OA (n2, 4, n, 2) Bush's Construction OA and Error-Correcting Codes MDS Codes Comments Exercises A-CODES FROM FINITE GEOMETRIES Symplectic Spaces over Finite Fields A-Codes from Symplectic Spaces A-Codes from Unitary Spaces Comments Exercises AUTHENTICATION/SECRECY SCHEMES Perfect Secrecy Schemes Construction of Perfect Secrecy Schemes Authentication Schemes with Perfect Secrecy Construction of Perfect Authentication/Secrecy Schemes Comments Exercises APPENDIX A: A SURVEY OF CONSTRUCTIONS FOR A-CODES Key Grouping Technique Perpendicular Arrays Generalized Quadrangles Resolvable Block Design and A2-Codes Regular Bipartite Graphs REFERENCES NOTATIONS INDEX