Continuous NMC Secure Against Permutations and Overwrites, with Applications to CCA Secure Commitments
Non-Malleable Codes (NMC) were introduced by Dziembowski, Pietrzak and Wichs in ICS 2010 as a relaxation of error correcting codes and error detecting codes. Faust, Mukherjee, Nielsen, and Venturi in TCC 2014 introduced an even stronger notion of non-malleable codes called continuous non-malleable codes where security is achieved against continuous tampering of a single codeword without re-encoding.We construct information theoretically secure CNMC resilient to bit permutations and overwrites, this is the first Continuous NMC constructed outside of the split-state model.In this work we also study relations between the CNMC and parallel CCA commitments. We show that the CNMC can be used to bootstrap a Self-destruct parallel CCA bit commitment to a Self-destruct parallel CCA string commitment, where Self-destruct parallel CCA is a weak form of parallel CCA security. Then we can get rid of the Self-destruct limitation obtaining a parallel CCA commitment, requiring only one-way functions.