Non-Malleable Codes Against Affine Errors
This work addresses security for cryptographic applications where adversaries can apply affine errors, but it is incremental as it extends prior results without introducing new constructions.
The paper tackles the problem of constructing non-malleable codes that remain secure against an extended adversarial model where errors can be affine transformations over bits, proving that existing codes by Dziembowski et al. maintain non-malleability in this model.
Non-malleable code is a relaxed version of error-correction codes and the decoding of modified codewords results in the original message or a completely unrelated value. Thus, if an adversary corrupts a codeword then he cannot get any information from the codeword. This means that non-malleable codes are useful to provide a security guarantee in such situations that the adversary can overwrite the encoded message. In 2010, Dziembowski et al. showed a construction for non-malleable codes against the adversary who can falsify codewords bitwise independently. In this paper, we consider an extended adversarial model (affine error model) where the adversary can falsify codewords bitwise independently or replace some bit with the value obtained by applying an affine map over a limited number of bits. We prove that the non-malleable codes (for the bitwise error model) provided by Dziembowski et al. are still non-malleable against the adversary in the affine error model.