VERIFIABLE ACCOUNTABLE SUBGROUP MULTI-SIGNATURES

Date

2024-1-22

Author

Ağırtaş, Ahmet Ramazan

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In this thesis, we introduce an accountable subgroup multi-signature (ASM) framework. The framework comprises three novel pairing-based ASM schemes, i.e., vASM, ASMwSA and ASMwCA, each designed to be secure against chosen-message attacks and based on the computational co-Diffie-Hellman/ψ-co-Diffie-Hellman assumption. We address an open problem by proposing novel ASM schemes where the subgroup of signers is unknown before signature generation. Our schemes outperform existing methods in terms of computational efficiency in signature generation, aggregation, and verification. Additionally, we propose novel methods for compartment-based and hierarchical threshold delegation of signing power of the verifiable accountable subgroup multi-signature scheme. We demonstrate that the scheme can function as a proxy signature, allowing an authorized user to delegate signing rights to an unauthorized user or group. We present four constructions, employing the recursive application of vASM, Shamir’s secret sharing scheme, nested secret sharing, and hierarchical threshold secret sharing, comparing their efficiency and security. Moreover, we propose a novel lattice-based ASM scheme (vMS2) by combining the group setup method of vASM with Damgård et al.’s lattice-based MS2 multi-signature scheme. We showcase the equivalence of key generation, signature generation, and verification phases with the MS2 scheme. Our vMS2 scheme achieves accountability through a joint verifiable secret sharing scheme during group setup, with a cost of slightly higher than the underlying MS2 scheme.

Subject Keywords

multi-signatures, accountable subgroup multi-signatures, pairing-based cryptography, lattice-based cryptography

URI

https://hdl.handle.net/11511/108469

Collections

Graduate School of Applied Mathematics, Thesis