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

• Main Authors: Serge Fehr, Pierre Karpman, Bart Mennink
• Format: Article
• Language: English
• Published: Ruhr-Universität Bochum 2018-03-01
• Series: IACR Transactions on Symmetric Cryptology
• Subjects: Non-malleable code; split-state tampering model; related-key security; block cipher
• Online Access: https://tosc.iacr.org/index.php/ToSC/article/view/854

A non-malleable code is an unkeyed randomized encoding scheme that offers the strong guarantee that decoding a tampered codeword either results in the original message, or in an unrelated message. We consider the simplest possible construction in the computational split-state model, which simply encodes a message m as k||Ek(m) for a uniformly random key k, where E is a block cipher. This construction is comparable to, but greatly simplifies over, the one of Kiayias et al. (ACM CCS 2016), who eschewed this simple scheme in fear of related-key attacks on E. In this work, we prove this construction to be a strong non-malleable code as long as E is (i) a pseudorandom permutation under leakage and (ii) related-key secure with respect to an arbitrary but fixed key relation. Both properties are believed to hold for “good” block ciphers, such as AES-128, making this non-malleable code very efficient with short codewords of length |m|+2τ (where τ is the security parameter, e.g., 128 bits), without significant security penalty.