Combinatorial Characterizations of Algebraic Manipulation Detection Codes Involving Generalized Difference Families
Maura B. Paterson, Douglas R. Stinson
TL;DR
This paper analyzes optimal algebraic manipulation detection codes, establishing bounds on adversary success and characterizing codes that meet these bounds using generalized difference families.
Contribution
It provides new combinatorial characterizations of AMD codes involving generalized difference families, linking code optimality to combinatorial structures.
Findings
Established lower bounds on adversary success probability.
Characterized optimal AMD codes via generalized difference families.
Connected code optimality to combinatorial structures.
Abstract
This paper provides a mathematical analysis of optimal algebraic manipulation detection (AMD) codes. We prove several lower bounds on the success probability of an adversary and we then give some combinatorial characterizations of AMD codes that meet the bounds with equality. These characterizations involve various types of generalized difference families. Constructing these difference families is an interesting problem in its own right.
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