Paper 2023/1553

Adaptively Secure BLS Threshold Signatures from DDH and co-CDH

Abstract

Threshold signature is one of the most important cryptographic primitives in distributed systems. A popular choice of threshold signature scheme is the BLS threshold signature introduced by Boldyreva (PKC'03). Some attractive properties of Boldyreva's threshold signature are that the signatures are unique and short, the signing process is non-interactive, and the verification process is identical to that of non-threshold BLS. These properties have resulted in its practical adoption in several decentralized systems. However, despite its popularity and wide adoption, up until recently, the Boldyreva scheme has been proven secure only against a static adversary. Very recently, Bacho and Loss (CCS'22) presented the first proof of adaptive security for Boldyreva's threshold signature, but they have to rely on strong and non-standard assumptions such as the hardness of one-more discrete log (OMDL) and the Algebraic Group Model~(AGM). In this paper, we present the first adaptively secure threshold BLS signature scheme that relies on the hardness of DDH and co-CDH in asymmetric pairing group in the Random Oracle Model (ROM). Our signature scheme also has non-interactive signing, compatibility with non-threshold BLS verification, and practical efficiency like Boldyreva's scheme. Moreover, to achieve static security, our scheme only needs the hardness of CDH in the ROM, which is the same as the standard non-threshold BLS signature. These properties make our protocol a suitable candidate for practical adoption with the added benefit of provable adaptive security. We also present an efficient distributed key generation (DKG) protocol to set up the signing keys for our signature scheme. We implement our scheme in Go and evaluate its signing and aggregation costs.