I’ll present a study of the rate for continuously non-malleable codes. Such codes allow to encode a message in a way that continuous tampering attacks on the codeword yield a decoded value that is unrelated to the original message.

The results are: • 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).