Explicit Non-malleable Codes Against Bit-Wise Tampering and Permutations

A non-malleable code protects messages against various classes of tampering. Informally, a code is non-malleable if the message contained in a tampered codeword is either the original message, or a completely unrelated one. Although existence of such codes for various rich classes of tampering functions is known, explicit constructions exist only for “compartmentalized” tampering functions: i.e. the codeword is partitioned into a priori fixed blocks and each block can only be tampered independently. The prominent examples of this model are the family of bit-wise independent tampering functions and the split-state model. In this paper, for the first time we construct explicit non-malleable codes against a natural class of non-compartmentalized tampering functions. We allow the tampering functions to permute the bits of the codeword and (optionally) perturb them by flipping or setting them to 0 or 1. We construct an explicit, efficient non-malleable code for arbitrarily long messages in this model (unconditionally). We give an application of our construction to non-malleable commitments, as one of the first direct applications of non-malleable codes to computational cryptography. We show that non-malleable string commitments can be “entirely based on” non-malleable bit commitments. S. Agrawal, D. Gupta, O. Pandey and M. Prabhakaran—Research supported in part by NSF grant 1228856. D. Gupta, H.K. Maji and O. Pandey—Research supported in part from a DARPA/ ONR PROCEED award, NSF Frontier Award 1413955, NSF grants 1228984, 1136174, 1118096. This material is based upon work supported by the Defense Advanced Research Projects Agency through the U.S. Office of Naval Research under Contract N00014-111-0389. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense, the National Science Foundation, or the U.S. Government. c © International Association for Cryptologic Research 2015 R. Gennaro and M. Robshaw (Eds.): CRYPTO 2015, Part I, LNCS 9215, pp. 538–557, 2015. DOI: 10.1007/978-3-662-47989-6 26 Explicit Non-malleable Codes Against Bit-Wise 539