Let G be an abelian group. Suppose m ≥ 2 and |G| = v. Let D1, D2, · · · , Dm be mutually disjoint k-subsets of G. {D1, D2, · · · , Dm} is called a (v, m, k, λ)-strong external difference family (SEDF) in G if

Dj(t≠jDt-1=λ(G-1G) for each 1≤j≤m.

The study of SEDFs is motivated by the so called algebraic manipulation detection (AMD) codes, which can be regarded as a variation of classical authentication codes. Moreover, further cryptographic applications of AMD codes have been discovered later.

So far, only one nontrivial example exists for m ≥ 3. In this talk, I will present some recent non-existence results on abelian SEDF for m ≥ 3. Namely, we will show that if v is a product of three (not necessarily) primes, there is no SEDF unless G is p-elementary with prime p ≥ 3 × 1012 [1]. We also consider the case λ = pq where p, q are primes. It can be shown that for any fixed q, no SEDF exists if p is sufficiently large.