On optimal weak algebraic manipulation detection codes and weighted external difference families
This work addresses security in coding theory for applications like data integrity, but it is incremental as it builds on existing combinatorial frameworks.
The paper tackles the problem of characterizing and constructing weak algebraic manipulation detection (AMD) codes, improving a lower bound on the maximum tampering probability for adversaries and providing explicit constructions that yield new optimal codes.
This paper provides a combinatorial characterization of weak algebraic manipulation detection (AMD) codes via a kind of generalized external difference families called bounded standard weighted external difference families (BSWEDFs). By means of this characterization, we improve a known lower bound on the maximum probability of successful tampering for the adversary's all possible strategies in weak AMD codes. We clarify the relationship between weak AMD codes and BSWEDFs with various properties. We also propose several explicit constructions for BSWEDFs, some of which can generate new optimal weak AMD codes.