Non-Malleable Codes from Average-Case Hardness: AC0, Decision Trees, and Streaming Space-Bounded Tampering.

We show a general framework for constructing non-malleable codes against tampering families with average-case hardness bounds. Our framework adapts ideas from the Naor-Yung double encryption paradigm such that to protect against tampering in a class F, it suffices to have average-case hard distributions for the class, and underlying primitives (encryption and non-interactive, simulatable proof systems) satisfying certain properties with respect to the class. We instantiate our scheme in a variety of contexts, yielding efficient, non-malleable codes (NMC) against the following tampering classes: - Computational NMC against AC(0) tampering, in the CRS model, assuming a PKE scheme with decryption in AC(0) and NIZK. - Computational NMC against bounded-depth decision trees (of depth n(epsilon), where n is the number of input variables and constant 0 < epsilon < 1), in the CRS model and under the same computational assumptions as above. - Information theoretic NMC (with no CRS) against a streaming, space-bounded adversary, namely an adversary modeled as a read-once branching program with bounded width. Ours are the first constructions that achieve each of the above in an efficient way, under the standard notion of non-malleability.