Non-Malleable Codes with Leakage and Applications to Secure Communication

Abstract: Non-malleable codes are randomized codes that protect coded messages against modification by functions in a tampering function class. These codes are motivated by providing tamper resilience in applications where a cryptographic secret is stored in a tamperable storage device and the protection goal is to ensure that the adversary cannot benefit from their tamperings with the device. In this paper we consider non-malleable codes for protection of secure communication against active physical layer adversaries. We define a class of functions that closely model tampering of communication by adversaries who can eavesdrop on a constant fraction of the transmitted codeword, and use this information to select a vector of tampering functions that will be applied to a second constant fraction of codeword components (possibly overlapping with the first set). We derive rate bounds for non-malleable codes for this function class and give two modular constructions. The first construction adapts and provides new analysis for an existing construction in the new setting. The second construction uses a new approach that results in an explicit construction of non-malleable codes. We show applications of our results in securing message communication against active physical layer adversaries in two settings: wiretap II with active adversaries and Secure Message Transmission (SMT) in networks. We discuss our results and directions for future work.