Paper 2014/316

Explicit Non-Malleable Codes Resistant to Permutations

Shashank Agrawal, Divya Gupta, Hemanta K. Maji, Omkant Pandey, and Manoj Prabhakaran


The notion of non-malleable codes was introduced as a relaxation of standard error-correction and error-detection. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a completely unrelated value. In the information theoretic setting, although existence of such codes for various rich classes of tampering functions is known, explicit constructions exist only for highly structured family of tampering functions. Prior explicit constructions of non-malleable codes rely on the ``compartmentalized'' structure of the tampering function, i.e. the codeword is partitioned into {\em a priori fixed} blocks and each block can {\em only} be tampered independently. The prominent examples of this model are the family of bit-wise independent tampering functions and the split-state model. We consider an infinitely large natural class of non-compartmentalized tampering functions. In our model, the tampering function can permute the bits of the encoding and (optionally) perturb them. In the information theoretic setting, we provide an {\em explicit} and {\em efficient}, {\em rate-1} non-malleable code for {\em multi-bit messages}. Lack of explicit constructions of non-malleable codes for non-compartmentalized tampering functions severely inhibits their utility in cryptographic protocols. As a motivation for our construction, we show an application of non-malleable codes to cryptographic protocols. In an idealized setting, we show how string commitments can be based on one-bit commitments, if non-malleable codes exist. Further, as an example of a non-trivial use of non-malleable codes in standard cryptographic protocols (not in an idealized model), we show that if explicit non-malleable codes are obtained for a slightly larger class of tampering functions than we currently handle, one can obtain a very simple non-malleable commitment scheme, under somewhat strong assumptions.

Available format(s)
Publication info
Preprint. MINOR revision.
Non-malleable CodesExplicit ConstructionInformation TheoreticNon-malleable Commitment.
Contact author(s)
hemanta maji @ gmail com
2014-05-06: received
Short URL
Creative Commons Attribution


      author = {Shashank Agrawal and Divya Gupta and Hemanta K.  Maji and Omkant Pandey and Manoj Prabhakaran},
      title = {Explicit Non-Malleable Codes Resistant to Permutations},
      howpublished = {Cryptology ePrint Archive, Paper 2014/316},
      year = {2014},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.