Non-disjoint strong external difference families can have any number of sets

Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the disjointness condition is replaced by non-disjointness, then abelian SEDFs can be constructed with more than 2 sets (indeed any number of sets). We demonstrate that the non-disjoint analogue has striking differences to, and connections with, the classical SEDF and arises naturally via another coding application

Non-disjoint strong external difference families can have any number of sets

Funding: Engineering and Physical Sciences Research Council (Grant number EP/X021157/1).Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the disjointness condition is replaced by non-disjointness, then abelian SEDFs can be constructed with more than 2 sets (indeed any number of sets). We demonstrate that the non-disjoint analogue has striking differences to, and connections with, the classical SEDF and arises naturally via another coding application.Peer reviewe

Comments on the security of the SPAPA strong password

The hash function based Strong Password Authentication Protocol with User Anonymity (SPAPA) was designed to protect users against monitoring by utilising temporary identities instead of true identities. In this letter we show that it is vulnerable to several attacks, including two which allow an adversary to link the activities of a user