[Resource Topic] 2023/1318: Two-Round Threshold Lattice Signatures from Threshold Homomorphic Encryption

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Two-Round Threshold Lattice Signatures from Threshold Homomorphic Encryption

Authors: Kamil Doruk Gur, Jonathan Katz, Tjerand Silde


Much recent work has developed efficient protocols for threshold signatures, where n parties share a signing key and some threshold t of those parties must interact to produce a signature. Yet efficient threshold signatures with post-quantum security have been elusive, with the state-of-the-art being a two-round scheme by Damgård et al. based on lattices that support only the full threshold case (i.e., t=n).

We show here a two-round threshold signature scheme based on standard lattice assumptions that support arbitrary thresholds t\leq n. Estimates of our scheme’s performance at the 128-bit security level with a trusted setup show that in the 3-out-of-5 case, we obtain signatures of size 11.5 KB and public keys of size 13.6 KB, with an execution of the signing protocol using roughly 1.5 MB of communication per party. We achieve improved parameters if only a small bounded number of signatures are ever issued with the same key.

As an essential building block and independent contribution, we construct a maliciously secure threshold (linearly) homomorphic encryption scheme that supports arbitrary thresholds t \leq n.

ePrint: https://eprint.iacr.org/2023/1318

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