Continuous Non-malleable Codes

Abstract

Abstract. Non-malleable codes are a natural relaxation of error correcting/detecting codes that have useful applications in the context of tamper resilient cryptography. Informally, a code is non-malleable if an adversary trying to tamper with an encoding of a given message can only leave it unchanged or modify it to the encoding of a completely unrelated value. This paper introduces an extension of the standard non-malleability security notion -so-called continuous non-malleability -where we allow the adversary to tamper continuously with an encoding. This is in contrast to the standard notion of non-malleable codes where the adversary only is allowed to tamper a single time with an encoding. We show how to construct continuous non-malleable codes in the common split-state model where an encoding consist of two parts and the tampering can be arbitrary but has to be independent with both parts. Our main contributions are outlined below:1. We propose a new uniqueness requirement of split-state codes which states that it is computationally hard to find two codewords X = (X0, X1) and X = (X0, X 1 ) such that both codewords are valid, but X0 is the same in both X and X . A simple attack shows that uniqueness is necessary to achieve continuous non-malleability in the split-state model. Moreover, we illustrate that none of the existing constructions satisfies our uniqueness property and hence is not secure in the continuous setting. 2. We construct a split-state code satisfying continuous non-malleability.Our scheme is based on the inner product function, collision-resistant hashing and non-interactive zero-knowledge proofs of knowledge and requires an untamperable common reference string. 3. We apply continuous non-malleable codes to protect arbitrary cryptographic primitives against tampering attacks. Previous applications of non-malleable codes in this setting required to perfectly erase the entire memory after each execution and required the adversary to be restricted in memory. We show that continuous non-malleable codes avoid these restrictions.

Locally Decodable and Updatable Non-malleable Codes and Their Applications

“…To our knowledge, we can use the explicit constructions (of the non-malleable codes) in the work [23,11,44,24,26,1,3]. First we overview different classes of tampering/leakage function allowed for these results: the constructions of [23] work for bit-wise tampering functions, and split-state functions in the random oracle model.…”

Affine-evasive sets modulo a prime

“…In particular, it does not include functions of the form f (c) := Enc(h(Dec(c))), since Dec(f (Enc(m))) = h(m) is clearly related to m. One of the largest and practically relevant tampering families for which we can construct NMCs is the so-called split-state tampering family where the codeword is split into two parts c 1 c 2 , and the adversary is only allowed to tamper with c 1 , c 2 independently to get f 1 (c 1 ) f 2 (c 2 ). A lot of the aforementioned results [LL12,DKO13,ADL14,CG14b,FMNV14] have studied NMCs against split-state tampering. [ADL14] gave the first (and the only one so far) information-theoretically secure construction in the split-state model from n-bit messages to n 7 log 7 n-bit codewords (i.e., code rate n 6 log 7 n).…”

Non-Malleable Encryption: Simpler, Shorter, Stronger

“…Unfortunately, we show that no standard non-malleable code (as originally defined by Dziembowski et al [17] and Faust et al [18]) can achieve this notion (see Section B). Fortunately, we observe that the NMC concept can be extended to allow the decoder to make use of (an initially generated) secret state, which simply becomes part of the secret key in the combined scheme.…”