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.
Table of Contents
Model with Three Participants (A-Codes)
Model with Four Participants (A2-Codes)
AUTHENTICATION SCHEMES WITH THREE PARTICIPANTS
Perfect Authentication Schemes
Perfect Cartesian Codes
AUTHENTICATION SCHEMES WITH ARBITRATION
Perfect Schemes with Arbitration
Perfect Cartesian A2-Codes
Combinatorial Bounds of A2-Codes
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)
2 - (v, k, 1) Designs
Steiner Triple System
3 - (v, k, 1) Designs
ORTHOGONAL ARRAYS OF INDEX UNITY
OA with Strength t = 2 and Orthogonal Latin Squares
Existence of OA (n2, 4, n, 2)
OA and Error-Correcting Codes
A-CODES FROM FINITE GEOMETRIES
Symplectic Spaces over Finite Fields
A-Codes from Symplectic Spaces
A-Codes from Unitary Spaces
Perfect Secrecy Schemes
Construction of Perfect Secrecy Schemes
Authentication Schemes with Perfect Secrecy
Construction of Perfect Authentication/Secrecy Schemes
APPENDIX A: A SURVEY OF CONSTRUCTIONS FOR A-CODES
Key Grouping Technique
Resolvable Block Design and A2-Codes
Regular Bipartite Graphs
"This monograph is devoted to the study of authentication codes and their related combinatorial designs. It is well suited for readers who want to learn how to reduce a cryptographic problem to a combinatorial problem, and how to use combinatorial design theory to solve problems in the field of authentication codes. ...one of the most interesting references for the study of authentication codes and their related combinatorial designs."
- Mathematical Reviews