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.
CITATION STYLE
Agrawal, S., Gupta, D., Maji, H. K., Pandey, O., & Prabhakaran, M. (2015). Explicit non-malleable codes against bit-wise tampering and permutations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9215, pp. 538–557). Springer Verlag. https://doi.org/10.1007/978-3-662-47989-6_26
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