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 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 for the LWE relation. For a carefully chosen modulus, this relation makes it possible to express the equality of plaintexts encrypted under different keys in the dual Regev cryptosystem. As an application, we obtain an LWE-based public-key encryption scheme for which we can prove key-dependent message (KDM-CCA2) security under chosen-ciphertext attacks in the standard model.

Category / Keywords: cryptographic protocols / LWE, standard model, Naor-Yung, KDM-CCA security, NIZK proofs, simulation-soundness

Date: received 6 Aug 2019, last revised 22 Nov 2019

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

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Version: 20191122:125831 (All versions of this report)

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