Adaptively Secure BLS Threshold Signatures from DDH and co-CDH
Sourav Das
Abstract:
Threshold signatures are 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 the Boldyreva scheme, 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 groups 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. These properties make our protocol a suitable candidate for practical adoption with the added benefit of provable adaptive security. This is a joint work with Ling Ren.
Bio:
Sourav Das is a Ph.D. candidate at UIUC working with Prof. Ling Ren on applied cryptography and consensus algorithms. He is a recipient of the Chainlink Ph.D. Fellowship, a best paper runner's up at ACM CCS 2021, and the Mavis Future Faculty fellow at UIUC. He received his Bachelor's degree from IIT Delhi, where his thesis “Scaling smart contracts in Proof-of-work Blockchains" won the best undergraduate thesis award in the department.