## Cryptology ePrint Archive: Report 2019/908

Simulation-Sound Arguments for LWE and Applications to KDM-CCA2 Security

Benoît Libert and Khoa Nguyen and Alain Passelègue and Radu Titiu

Abstract: The Naor-Yung paradigm is a well-known technique that constructs IND-CCA2-secure encryption schemes by means of non-interactive zero-knowledge proofs satisfying a notion of simulation-soundness. Until recently, it was an open problem to instantiate it under the sole Learning-With-Errors (LWE) assumption without relying on random oracles. While the recent results of Canetti {\it et al.} (STOC'19) and Peikert-Shiehian (Crypto'19) provide a solution to this problem by applying the Fiat-Shamir transform in the standard model, the resulting constructions are extremely inefficient as they proceed via a reduction to an NP-complete problem. In this paper, we give a direct, non-generic method for instantiating Naor-Yung under the LWE assumption outside the random oracle model. Specifically, we give a direct construction of an unbounded simulation-sound NIZK argument system which, for carefully chosen parameters, makes it possible to express the equality of plaintexts encrypted under different keys in Regev's cryptosystem. We also give a variant of our argument that provides tight security. As an application, we obtain an LWE-based public-key encryption scheme for which we can prove (tight) key-dependent message security under chosen-ciphertext attacks in the standard model.

Category / Keywords: cryptographic protocols / LWE, standard model, Naor-Yung, KDM-CCA2 security, NIZK arguments, simulation-soundness, tight security

Original Publication (with major differences): IACR-ASIACRYPT-2020

Date: received 6 Aug 2019, last revised 25 May 2021

Contact author: benoit libert at ens-lyon fr, khoantt at ntu edu sg, alain passelegue at inria fr, radu titiu at gmail com

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2019/908

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