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.
J. Pan—Supported by the Research Council of Norway under Project No. 324235.
B. Wagner—This work was done while the second author was a student at Karlsruhe Institute of Technology (Germany) and was doing an internship with the first author at NTNU (Norway).
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Notes
- 1.
A trivial solution to argue lossiness with plain \(\mathsf {LWE}\) is to have an ID scheme with single bit challenges, but that will result in a non-compact scheme with linear-size signatures, since for such an ID scheme we need to repeat \(O(\lambda )\) times to get soundness (where \(\lambda \) is the security parameter).
- 2.
For the exact statements we use, we refer to the full version of our paper.
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Pan, J., Wagner, B. (2022). Lattice-Based Signatures with Tight Adaptive Corruptions and More. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds) Public-Key Cryptography – PKC 2022. PKC 2022. Lecture Notes in Computer Science(), vol 13178. Springer, Cham. https://doi.org/10.1007/978-3-030-97131-1_12
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