Abstract. Recently (Crypto’24), Das and Ren proposed an adaptively

secure variant of threshold BLS signatures. Unlike the initial threshold

BLS signature described by Boldyreva (PKC’03), their variant can be

proven secure in the adaptive corruption setting while preserving the

useful features of the scheme (i.e., non-interactivity, uniqueness of signatures, and optimal signature size). In this work, we present a simplification of their scheme where the sizes of partial signatures and secret key

shares are decreased by ≈ 20% and 33%, respectively. In addition, we

reduce the communication cost of the distributed key generation phase

by a factor 2. We can still prove the security of our simplified variant under adaptive corruptions in the random oracle model and under

the same assumptions (namely, the co-CDH assumption and the DDH

assumption in the first source group of the pairing) as Das and Ren.