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• W4285178307 abstract "The standard model security of the Fiat-Shamir transform has been an active research area for many years. In breakthrough results, Canetti et al. (STOC’19) and Peikert-Shiehian (Crypto’19) showed that, under the Learning-With-Errors ( $$mathsf {LWE}_{}$$ ) assumption, it provides soundness by applying correlation-intractable (CI) hash functions to so-called trapdoor $$varSigma $$ -protocols. In order to be compatible with CI hash functions based on standard $$mathsf {LWE}_{}$$ assumptions with polynomial approximation factors, all known such protocols have been obtained via parallel repetitions of a basic protocol with binary challenges. In this paper, we consider languages related to Paillier’s composite residuosity assumption ( $$mathsf {DCR}$$ ) for which we give the first trapdoor $$varSigma $$ -protocols providing soundness in one shot, via exponentially large challenge spaces. This improvement is analogous to the one enabled by Schnorr over the original Fiat-Shamir protocol in the random oracle model. Using the correlation-intractable hash function paradigm, we then obtain simulation-sound NIZK arguments showing that an element of $$mathbb {Z}_{N^2}^*$$ is a composite residue, which opens the door to space-efficient applications in the standard model. As a concrete example, we build logarithmic-size ring signatures (assuming a common reference string) with the shortest signature length among schemes based on standard assumptions in the standard model. We prove security under the $$mathsf {DCR}$$ and $$mathsf {LWE}_{}$$ assumptions, while keeping the signature size comparable with that of random-oracle-based schemes." @default.
• W4285178307 created "2022-07-14" @default.
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• W4285178307 date "2022-01-01" @default.
• W4285178307 modified "2023-10-09" @default.
• W4285178307 title "One-Shot Fiat-Shamir-Based NIZK Arguments of Composite Residuosity and Logarithmic-Size Ring Signatures in the Standard Model" @default.
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• W4285178307 doi "https://doi.org/10.1007/978-3-031-07085-3_17" @default.
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