Authentication Codes and Combinatorial Designs
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Authentication Codes and Combinatorial Designs

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Description

Researchers and practitioners of cryptography and information security are constantly challenged to respond to new attacks and threats to information systems. Authentication Codes and Combinatorial Designs presents new findings and original work on perfect authentication codes characterized in terms of combinatorial designs, namely strong partially balanced designs (SPBD). Beginning with examples illustrating the concepts of authentication schemes and combinatorial designs, the book considers the probability of successful deceptions followed by schemes involving three and four participants, respectively. From this point, the author constructs the perfect authentication schemes and explores encoding rules for such schemes in some special cases. Using rational normal curves in projective spaces over finite fields, the author constructs a new family of SPBD. He then presents some established combinatorial designs that can be used to construct perfect schemes, such as t-designs, orthogonal arrays of index unity, and designs constructed by finite geometry. The book concludes by studying definitions of perfect secrecy, properties of perfectly secure schemes, and constructions of perfect secrecy schemes with and without authentication. Supplying an appendix of construction schemes for authentication and secrecy schemes, Authentication Codes and Combinatorial Designs points to new applications of combinatorial designs in cryptography.show more

Product details

  • Hardback | 256 pages
  • 160 x 236.2 x 20.3mm | 476.28g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 50 black & white illustrations, 3 black & white tables
  • 1584884738
  • 9781584884736

Table of contents

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 INDEXshow more