Spring 2017

Non-Malleable Codes for Small-Depth Circuits

Wednesday, Jun. 20, 2018 3:45 pm4:15 pm

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We construct efficient, unconditional non-malleable codes that are secure against tampering functions computed by small-depth circuits. For constant-depth circuits of polynomial size (i.e. AC^0 tampering functions), our codes have codeword length n = k^{1+o(1)} for a k-bit message. This is an exponential improvement of the previous best construction due to Chattopadhyay and Li (STOC 2017), which had codeword length 2^{O(k^{1/2})}. Our construction remains efficient for circuit depths as large as \Theta(log(n)/loglog(n)) (indeed, our codeword length remains n \leq k^{1+\eps}), and extending our result beyond this would require separating P from NC^1.

We obtain our codes via a new efficient non-malleable reduction from small-depth tampering to split-state tampering. A novel aspect of our work is the incorporation of techniques from unconditional derandomization into the framework of non-malleable reductions. In particular, a key ingredient in our analysis is a recent pseudorandom switching lemma of Trevisan and Xue (CCC 2013), a derandomization of the influential switching lemma from circuit complexity; the randomness-efficiency of this switching lemma translates into the rate-efficiency of our codes via our non-malleable reduction. Joint work with Marshall Ball, Dana Dachman-Soled, Tal Malkin and Li-Yang Tan.