Non-Malleable Codes from Two-Source Extractors

We construct an efficient information-theoretically non-malleable code in the split-state model for one-bit messages. Non-malleable codes were introduced recently by Dziembowski, Pietrzak and Wichs (ICS 2010), as a general tool for storing messages securely on hardware that can be subject to tampering attacks. Informally, a code \((\mathsf{Enc} : {\cal M} \rightarrow {\cal L} \times {\cal R}, \mathsf{Dec} : {\cal L} \times {\cal R} \rightarrow {\cal M})\) is non-malleable in the split-state model if any adversary, by manipulating independently L and R (where (L,R) is an encoding of some message M), cannot obtain an encoding of a message M′ that is not equal to M but is “related” M in some way. Until now it was unknown how to construct an information-theoretically secure code with such a property, even for \({\cal M} = \{0,1\}\). Our construction solves this problem. Additionally, it is leakage-resilient, and the amount of leakage that we can tolerate can be an arbitrary fraction ξ < 1/4 of the length of the codeword. Our code is based on the inner-product two-source extractor, but in general it can be instantiated by any two-source extractor that has large output and has the property of being flexible, which is a new notion that we define.