Non-Malleable Codes Against Affine Errors

Abstract

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.