We construct efficient, unconditional non-malleable codes that are secure against tampering functions computed by decision trees of depth d = n~(1/4-o(1)). In particular, each bit of the tampered codeword is set arbitrarily after adaptively reading up to d arbitrary locations within the original codeword. Prior to this work, no efficient unconditional non-malleable codes were known for decision trees beyond depth O(log~2n). Our result also yields efficient, unconditional non-malleable codes that are exp(-n~(Ω(1)))-secure against constant-depth circuits of exp(n~(Ω(1))-size. Prior work of Chattopadhyay and Li (STOC 2017) and Ball et al. (FOCS 2018) only provide protection against exp(O(log~2 n))-size circuits with exp(-O(log~2 n))-security. We achieve our result through simple non-malleable reductions of decision tree tampering to split-state tampering. As an intermediary, we give a simple and generic reduction of leakage-resilient split-state tampering to split-state tampering with improved parameters. Prior work of Aggarwal et al. (TCC 2015) only provides a reduction to split-state non-malleable codes with decoders that exhibit particular properties.
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