Pairing-based Accountable Subgroup Multi-signatures with Verifiable Group Setup

Date

2025-01-01

Author

Ağırtaş, Ahmet Ramazan
Yayla, Oğuz

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An accountable subgroup multi-signature is a kind of multi-signature scheme in which any sub- group S of a group G of potential signers jointly sign a message m, ensuring that each member of S is accountable for the resulting signature. In this paper, we propose three novel pairing-based accountable subgroup multi-signature (ASM) schemes, which are secure against existential forgery under chosen-message attacks and computational co-Diffie-Hellman assumption. In the first one, we use Feldman’s verifiable secret sharing scheme as an implicit authentication and proof-of-possession for setting up group G. In the second one, the members participating in authentication are decided by the subgroup. In the third one, we consider a designated combiner managing the authentication process. All schemes we propose here require fewer computations in the signature generation, signa- ture aggregation, and verification phases than the pairing-based ASM scheme proposed by Boneh, Drijvers and Neven. Moreover, our first and third ones solve the open problem of constructing an ASM scheme in which the subgroup S of signers is unknown before the signature generation. Be- sides, we give a method of eliminating the combiner in case of knowing the subgroup of signers S in advance. Further, we extend our proposed schemes to aggregated versions. For N accountable subgroup multi-signatures, aggregated versions of our proposed schemes output an aggregated signa- ture with the size of a single group (G1) element and require N + 1 pairings in aggregated signature verification. In contrast, the partially aggregated ASM scheme of Boneh, Drijvers and Neven gives an aggregated signature with the size of N + 1 group elements and requires 2N + 1 pairings in ag- gregated signature verification.

Subject Keywords

accountable subgroup multi-signatures, BLS signature, aggregatable signatures

URI

https://eprint.iacr.org/2022/018
https://hdl.handle.net/11511/117877

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Graduate School of Applied Mathematics, Article