Non-malleable Encryption: Simpler, Shorter, Stronger

Abstract

One approach toward basing public-key encryption (PKE) schemes on weak and credible assumptions is to build “stronger” or more general schemes generically from “weaker” or more restricted ones. One particular line of work in this context was initiated by Myers and Shelat (FOCS ’09) and continued by Hohenberger, Lewko, and Waters (Eurocrypt ’12), who provide constructions of multi-bit CCA-secure PKE from single-bit CCA-secure PKE. It is well known that encrypting each bit of a plaintext string independently is not CCA-secure—the resulting scheme is malleable. We therefore investigate whether this malleability can be dealt with using the conceptually simple approach of applying a suitable non-malleable code (Dziembowski et al., ICS ’10) to the plaintext and subsequently encrypting the resulting codeword bit by bit. We find that an attacker’s ability to ask multiple decryption queries requires that the underlying code be continuously non-malleable (Faust et al., TCC ’14). Since, as we show, this flavor of non-malleability can only be achieved if the code is allowed to “self-destruct,” the resulting scheme inherits this property and therefore only achieves a weaker variant of CCA security. We formalize this new notion of so-called indistinguishability under self-destruct attacks (IND-SDA) as CCA security with the restriction that the decryption oracle stops working once the attacker submits an invalid ciphertext. We first show that the above approach based on non-malleable codes yields a solution to the problem of domain extension for IND-SDA-secure PKE, provided that the underlying code is continuously non-malleable against (a reduced form of) bit-wise tampering. Then, we prove that the code of Dziembowski et al. is actually already continuously non-malleable against bit-wise tampering. We further investigate the notion of security under self-destruct attacks and combine IND-SDA security with non-malleability under chosen-ciphertext attacks (NM-CPA) to obtain the strictly stronger notion of non-malleability under self-destruct attacks (NM-SDA). We show that NM-SDA security can be obtained from basic IND-CPA security by means of a black-box construction based on the seminal work by Choi et al. (TCC ’08). Finally, we provide a domain extension technique for building a multi-bit NM-SDA scheme from a single-bit NM-SDA scheme. To achieve this goal, we define and construct a novel type of continuous non-malleable code, called secret-state NMC, since, as we show, standard continuous NMCs are insufficient for the natural “encode-then-encrypt-bit-by-bit” approach to work.