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).

Features:

• Provides comprehensive treatment of authentication in information security and authentication codes
• Covers combinatorial designs and their applications to authentication codes
• Discusses the applications of finite geometry over finite fields to the theory of combinatorial designs
• Presents an in-depth analysis of unconditionally secure authentication schemes
• Covers both symmetric and asymmetric authentication codes

Contents

Authentication Schemes

• Model with Three Participants (A-Codes)
• Model with Four Participants (A2-Codes)

Authentication Schemes with Three Participants

• Entropy
• Information-Theoretic Bound
• Perfect Authentication Schemes
• Perfect Cartesian Codes
• Combinatorial Bound

Authentication Schemes with Arbitration

• Lower Bounds
• 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)

T-Designs

• 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
• Transversal Designs
• Existence of OA (n2, 4, n, 2)
• Bush's Construction
• OA and Error-Correcting Codes
• MDS Codes

A-Codes From Finite Geometries

• Symplectic Spaces over Finite Fields
• A-Codes from Symplectic Spaces
• A-Codes from Unitary Spaces

Authentication/Secrecy Schemes

• Perfect Secrecy Schemes
• Construction of Perfect Secrecy Schemes
• Authentication Schemes with Perfect Secrecy
• Construction of Perfect Authentication/Secrecy Schemes

Index

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