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 ba服务器托管网sed 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 inte服务器托管网rest, 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.
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