### Lattice-based Signatures with Tight Adaptive Corruptions and More

Jiaxin Pan and Benedikt Wagner

##### Abstract

We construct the first tightly secure signature schemes in the multi-user setting with adaptive corruptions from lattices. In stark contrast to the previous tight constructions whose security is solely based on number-theoretic assumptions, our schemes are based on the Learning with Errors (LWE) assumption which is supposed to be post-quantum secure. The security of our scheme is independent of the numbers of users and signing queries, and it is in the non-programmable random oracle model. Our LWE-based scheme is compact namely, its signatures contain only a constant number of lattice vectors. At the core of our construction are a new abstraction of the existing lossy identification (ID) schemes using dual-mode commitment schemes and a refinement of the framework by Diemert et al. (PKC 2021) which transforms a lossy ID scheme to a signature using sequential OR proofs. In combination, we obtain a tight generic construction of signatures from dual-mode commitments in the multi-user setting. Improving the work of Diemert et al., our new approach can be instantiated using not only the LWE assumption, but also an isogeny-based assumption. We stress that our LWE-based lossy ID scheme in the intermediate step uses a conceptually different idea than the previous lattice-based ones. Of independent interest, we formally rule out the possibility that the aforementioned ID-to-Signature'' methodology can work tightly using parallel OR proofs. In addition to the results of Fischlin et al. (EUROCRYPT 2020), our impossibility result shows a qualitative difference between both forms of OR proofs in terms of tightness.

Available format(s)
Category
Public-key cryptography
Publication info
A minor revision of an IACR publication in PKC 2022
Keywords
Digital signaturesidentification schemesmulti-user securitytightnessOR proofscommitmentslatticeisogenyimpossibility result
Contact author(s)
Jiaxin pan @ ntnu no
Benedikt wagner @ cispa de
History
Short URL
https://ia.cr/2022/015

CC BY

BibTeX

@misc{cryptoeprint:2022/015,
author = {Jiaxin Pan and Benedikt Wagner},
title = {Lattice-based Signatures with Tight Adaptive Corruptions and More},
howpublished = {Cryptology ePrint Archive, Paper 2022/015},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/015}},
url = {https://eprint.iacr.org/2022/015}
}

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