Short Non-Malleable Codes from Related-Key Secure Block Ciphers, Revisited

We construct non-malleable codes in the split-state model with codeword length m + 3λ or 5λ, where is message size and λ security parameter, depending on how conservative one is. Our scheme very simple involves a single call to block cipher meeting new notion which we dub entropic fixed-related-key security, essentially means that behaves like pseudorandom permutation when queried upon inputs sampled from distribution sufficient min-entropy, even under related-key attacks respect an arbitrary but fixed key relation. Importantly, indistinguishability only holds original secret (and not tampered key).In previous work, Fehr, Karpman, Mennink (ToSC 2018) used related assumption (where can be chosen by adversary, key) nonmalleable code 2λ. Unfortunately, no (even ideal one) satisfies their tampering function allowed cipher-dependent. In contrast, are able show large class of cipher-dependent (including those break Mennink).