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Non-malleable codes were introduced by Dziembowski, Pietrzak, and Wichs (JACM2018) as a generalization of standard error correcting codes to handle severeforms of tampering on codewords. This notion has attracted a lot of recentresearch, resulting in various explicit constructions, which have foundapplications in tamper-resilient cryptography and connections to otherpseudorandom objects in theoretical computer science.  We continue the line of investigation on explicit constructions ofnon-malleable codes in the information theoretic setting, and give explicitconstructions for several new classes of tampering functions.  (1) Interleaved split-state tampering: Here the codeword is partitioned in anunknown way by an adversary, and then tampered with by a split-state tamperingfunction. (2) Linear function composed with split-state tampering: In thismodel, the codeword is first tampered with by a split-state adversary, and thenthe whole tampered codeword is further tampered with by a linear function. Infact our results are stronger, and we can handle linear function composed withinterleaved split-state tampering. (3) Bounded communication split-statetampering: In this model, the two split-state tampering adversaries are allowedto participate in a communication protocol with a bounded communication budget.  Our results are the first explicit constructions of non-malleable codes inany of these tampering models. We derive all these results from explicitconstructions of seedless non-malleable extractors, which we believe are ofindependent interest.  Using our techniques, we also give an improved seedless extractor for anunknown interleaving of two independent sources.

Non-Malleable Extractors and Codes for Composition of Tampering, Interleaved Tampering and More