Non-Malleable Codes for Space-Bounded Tampering

Abstract

Non-malleable codes-introduced by Dziembowski, Pietrzak and Wichs at ICS 2010are key-less coding schemes in which mauling attempts to an encoding of a given message, w.r.t. some class of tampering adversaries, result in a decoded value that is either identical or unrelated to the original message. Such codes are very useful for protecting arbitrary cryptographic primitives against tampering attacks against the memory. Clearly, non-malleability is hopeless if the class of tampering adversaries includes the decoding and encoding algorithm. To circumvent this obstacle, the majority of past research focused on designing non-malleable codes for various tampering classes, albeit assuming that the adversary is unable to decode. Nonetheless, in many concrete settings, this assumption is not realistic. In this paper, we explore one particular such scenario where the class of tampering adversaries naturally includes the decoding (but not the encoding) algorithm. In particular, we consider the class of adversaries that are restricted in terms of memory/space. Our main contributions can be summarized as follows: • We initiate a general study of non-malleable codes resisting space-bounded tampering. In our model, the encoding procedure requires large space, but decoding can be done in small space, and thus can be also performed by the adversary. Unfortunately, in such a setting it is impossible to achieve non-malleability in the standard sense, and we need to aim for slightly weaker security guarantees. In a nutshell, our main notion (dubbed leaky space-bounded non-malleability) ensures that this is the best the adversary can do, in that space-bounded tampering attacks can be simulated given a small amount of leakage on the encoded value.

Continuously non-malleable codes with split-state refresh

“…Several constructions of non-malleable codes in the split-state model appeared in the literature, both for the information-theoretic [32,31,3,20,4,2,14,5,48,49,17] and computational setting [50,36,24,1,46,52,23]. Non-malleable codes exist also for several other models besides split-state tampering, including bit-wise independent tampering and permutations [20,6,7,22,21], circuits of polynomial size [32,19,38,39], constant-state tampering [18], block-wise tampering [13], space-bounded algorithms [35,9], bounded-depth circuits [8,16], and partial functions [47].…”

Non-Malleable Codes for Small-Depth Circuits

“…Faust et al [FHMV17] gave constructions of (a weaker notion of) non-malleable codes against space-bounded tampering in the random oracle model.…”

Short Non-Malleable Codes from Related-Key Secure Block Ciphers

“…A number of constructions also aim for additional properties, such as having efficient refreshing mechanisms that allow to update an existing codeword to a new one (decoding to the same message) without the need for decoding [FN17]. Some constructions also specifically focus on computationally restricted adversaries, either in terms of time or space complexity (e.g., [FHMV17,BDSKM17]).…”