**Towards Practical and Round-Optimal Lattice-Based Threshold and Blind Signatures**

*Shweta Agrawal and Damien Stehle and Anshu Yadav*

**Abstract: **Threshold and blind signature schemes have found numerous applications in cryptocurrencies, e-cash, e-voting and other privacy-preserving technologies. In this work, we make advances in bringing lattice-based constructions for these primitives closer to practice.

1. Threshold Signatures. For round optimal threshold signatures, we improve the only known construction by Boneh et al. [CRYPTO'18] as follows:

a. Efficiency. We reduce the amount of noise flooding from $2^{\Omega(\lambda)}$ down to $\sqrt{Q_S}$, where $Q_S$ is the bound on the number of generated signatures and $\lambda$ is the security parameter. By using lattice hardness assumptions over polynomial rings, this allows to decrease signature bit-lengths from $\widetilde{O}(\lambda^3)$ to $\widetilde{O}(\lambda)$.

b. Towards Adaptive Security. The construction of Boneh et al. satisfies only selective security, where all the corrupted parties must be announced before any signing queries are made. We improve this in two ways: in the ROM, we obtain partial adaptivity where signing queries can be made before the corrupted parties are announced but the set of corrupted parties must be announced all at once. In the standard model, we obtain full adaptivity, where parties can be corrupted at any time but this construction is in a weaker pre-processing model where signers must be provided correlated randomness of length proportional to the number of signatures, in an offline pre-processing phase.

2. Blind Signatures. For blind signatures, we improve the state of art lattice-based construction by Hauck et al.[CRYPTO'20] as follows:

a. Round Complexity. We improve the round complexity from three to two -- this is optimal.

b. Efficiency. Again, we reduce the amount of noise flooding from $2^{\Omega(\lambda)}$ down to $\sqrt{Q_S}$, where $Q_S$ is the bound on the number of signatures and $\lambda$ is the security parameter.

c. Number of Signing Queries. Unlike the scheme from Hauck et al., our construction enjoys a proof that is not restricted to a polylogarithmic number of signatures. Using lattice hardness assumptions over rings, we obtain signatures of bit-lengths bounded as $\widetilde{O}(\lambda)$. In contrast, the signature bit-length in the scheme from Hauck et al. is $\Omega(\lambda^3 + Q_S \cdot \lambda)$.

Concretely, we can obtain blind/threshold signatures of size $\approx 3$ KB using a variant of Dilithium-G with $\approx 128$ bit-security, for adversaries limited to getting $256$ signatures. In contrast, parameters provided by Hauck et al. lead to blind signatures of $\approx 7.73$ MB, for adversaries limited to getting 7 signatures, while concrete parameters are not provided for the construction of threshold signatures by Boneh et al.

**Category / Keywords: **cryptographic protocols / blind signatures, threshold signatures, lattices, practical

**Date: **received 22 Mar 2021

**Contact author: **shweta a at gmail com, anshu yadav06 at gmail com, damien stehle at ens-lyon fr

**Available format(s): **PDF | BibTeX Citation

**Version: **20210322:194200 (All versions of this report)

**Short URL: **ia.cr/2021/381

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