Explicit Rate-1 Non-malleable Codes for Local Tampering

Abstract

This paper constructs high-rate non-malleable codes in the information-theoretic plain model against tampering functions with bounded locality. We consider \(\delta \)-local tampering functions; namely, each output bit of the tampering function is a function of (at most) \(\delta \) input bits. This work presents the first explicit and efficient rate-1 non-malleable code for \(\delta \)-local tampering functions, where \(\delta =\xi \lg n\) and \(\xi <1\) is any positive constant. As a corollary, we construct the first explicit rate-1 non-malleable code against NC\(^0\) tampering functions.