Efficient Unbounded Fault-Tolerant Aggregate Signatures Using Nested Cover-Free Families

Abstract

Aggregate signatures are used to create one short proof of authenticity and integrity from a set of digital signatures. However, one invalid signature in the set invalidates the entire aggregate, giving no information on which signatures are valid. Hartung et al. (PKC 2016) proposed a fault-tolerant aggregate signature scheme based on combinatorial group testing. Given a bound d on the number of invalid signatures, the scheme can determine which signatures are invalid, and guarantees a moderate increase on the size of the aggregate signature when there is an upper bound on the number n of signatures to be aggregated. However, for the case of unbounded n the constructions provided had constant compression ratio, i.e. the signature size grew linearly with n. In this paper we propose a solution to the unbounded scheme with increasing compression ratio for every d. In particular, for \(d=1\) the compression ratio is the best possible and meets the information theoretical bound.