Rational Modular Encoding in the DCR Setting: Non-Interactive Range Proofs and Paillier-Based Naor-Yung in the Standard Model - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2022

Rational Modular Encoding in the DCR Setting: Non-Interactive Range Proofs and Paillier-Based Naor-Yung in the Standard Model

Résumé

Range proofs allow a sender to convince a verifier that committed integers belong to an interval without revealing anything else. So far, all known non-interactive range proofs in the standard model rely on groups endowed with a bilinear map. Moreover, they either require the group order to be larger than the range of any proven statement or they suffer from a wasteful rate. Recently (Eurocrypt'21), Couteau et al. introduced a new approach to efficiently prove range membership by encoding integers as a modular ratio between small integers. We show that their technique can be transposed in the standard model under the Composite Residuosity (DCR) assumption. Interestingly, with this modification, the size of ranges is not a priori restricted by the common reference string. It also gives a constant ratio between the size of ranges and proofs. Moreover, we show that their technique of encoding messages as bounded rationals provides a secure standard model instantiation of the Naor-Yung CCA2 encryption paradigm under the DCR assumption.
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Dates et versions

hal-03807457 , version 1 (09-10-2022)

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  • HAL Id : hal-03807457 , version 1

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Julien Devevey, Benoît Libert, Thomas Peters. Rational Modular Encoding in the DCR Setting: Non-Interactive Range Proofs and Paillier-Based Naor-Yung in the Standard Model. Public-Key Cryptography (PKC 2022) - 25th IACR International Conference on Practice and Theory of Public-Key Cryptography, Mar 2022, Yokohama (devenu virtuel pour cause de COVID), Japan. ⟨hal-03807457⟩
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