Rate-optimizing compilers for continuously non-malleable codes

We study the rate of so-called continuously non-malleable codes, which allow to encode a message in such a way that (possibly adaptive) continuous tampering attacks on the codeword yield a decoded value that is unrelated to the original message. Our results are as follows: For the case of bit-wise independent tampering, we establish the existence of rate-one continuously non-malleable codes with information-theoretic security, in the plain model.For the case of split-state tampering, we establish the existence of rate-one continuously non-malleable codes with computational security, in the (non-programmable) random oracle model. We further exhibit a rate-1/2 code and a rate-one code in the common reference string model, but the latter only withstands non-adaptive tampering. It is well known that computational security is inherent for achieving continuous non-malleability in the split-state model (even in the presence of non-adaptive tampering). Continuously non-malleable codes are useful for protecting arbitrary cryptographic primitives against related-key attacks, as well as for constructing non-malleable public-key encryption schemes. Our results directly improve the efficiency of these applications.