Abstract
Non-malleable codes, defined by Dziembowski, Pietrzak and Wichs (ICS ’10), provide roughly the following guarantee: if a codeword c encoding some message x is tampered to c′ = f(c) such that c′ ≠ c, then the tampered message x′ contained in c′ reveals no information about x. Non-malleable codes have applications to immunizing cryptosystems against tampering attacks and related-key attacks.
One cannot have an efficient non-malleable code that protects against all efficient tampering functions f. However, in this work we show “the next best thing”: for any polynomial bound s given a-priori, there is an efficient non-malleable code that protects against all tampering functions f computable by a circuit of size s. More generally, for any family of tampering functions \(\mathcal{F}\) of size \(|\mathcal{F}| \leq 2^{s}\), there is an efficient non-malleable code that protects against all \(f \in \mathcal{F}\). The rate of our codes, defined as the ratio of message to codeword size, approaches 1. Our results are information-theoretic and our main proof technique relies on a careful probabilistic method argument using limited independence. As a result, we get an efficiently samplable family of efficient codes, such that a random member of the family is non-malleable with overwhelming probability. Alternatively, we can view the result as providing an efficient non-malleable code in the “common reference string” (CRS) model.
We also introduce a new notion of non-malleable key derivation, which uses randomness x to derive a secret key y = h(x) in such a way that, even if x is tampered to a different value x′ = f(x), the derived key y′ = h(x′) does not reveal any information about y. Our results for non-malleable key derivation are analogous to those for non-malleable codes.
As a useful tool in our analysis, we rely on the notion of “leakage-resilient storage” of Davì, Dziembowski and Venturi (SCN ’10) and, as a result of independent interest, we also significantly improve on the parameters of such schemes.
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Faust, S., Mukherjee, P., Venturi, D., Wichs, D. (2014). Efficient Non-malleable Codes and Key-Derivation for Poly-size Tampering Circuits. In: Nguyen, P.Q., Oswald, E. (eds) Advances in Cryptology – EUROCRYPT 2014. EUROCRYPT 2014. Lecture Notes in Computer Science, vol 8441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55220-5_7
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