Combinatorial Characterizations of Algebraic Manipulation Detection Codes Involving Generalized Difference Families

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.