Non-malleable codes from average-case hardness:, 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$${\mathcal {F}}$$, 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$${\mathsf {A}}{\mathsf {C}}^0$$ tampering, in the CRS model, assuming a PKE scheme with decryption in$${\mathsf {A}}{\mathsf {C}}^0$$ 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.