On optimal weak algebraic manipulation detection codes and weighted external difference families

Algebraic manipulation detection codes

Algebraic manipulation detection codes are a cryptographic primitive that was introduced by Cramer et al. (Eurocrypt 2008). It encompasses several methods that were previously used in cheater detection in secret sharing. Since its introduction, a number of additional applications have been found. This paper contains a detailed exposition of the known results about algebraic manipulation detecti...

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...

Jongsma Algebraic Manipulation Detection Codes

Optimal Algebraic Manipulation Detection Codes in the Constant-Error Model

Algebraic manipulation detection (AMD) codes, introduced at EUROCRYPT 2008, may, in some sense, be viewed as keyless combinatorial authentication codes that provide security in the presence of an oblivious, algebraic attacker. Its original applications included robust fuzzy extractors, secure message transmission and robust secret sharing. In recent years, however, a rather diverse array of add...

Weighted maximum matchings and optimal equi-difference conflict-avoiding codes

A conflict-avoiding code (CAC) C of length n and weight k is a collection of k-subsets of Zn such that Δ(x) ∩ Δ(y) = ∅ for any x, y ∈ C and x = y, where Δ(x) = {a − b : a, b ∈ x, a = b}. Let CAC(n, k) denote the class of all CACs of length n and weight k. A CAC C ∈ CAC(n, k) is said to be equi-difference if any codeword x ∈ C has the form {0, i, 2i, . . . , (k − 1)i}. A CAC with maximum size is...