Explicit Rate-1 Non-malleable Codes for Local Tampering.

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 d-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 NC0 tampering functions. Before our work, no explicit construction for a constant-rate non-malleable code was known even for the simplest 1-local tampering functions. Ball et al. (EUROCRYPT-2016), and Chattopadhyay and Li (STOC-2017) provided the first explicit non-malleable codes against delta-local tampering functions. However, these constructions are rate-0 even when the tampering functions have 1-locality. In the CRS model, Faust et al. (EUROCRYPT-2014) constructed efficient rate-1 non-malleable codes for delta = O(log n) local tampering functions. Our main result is a general compiler that bootstraps a rate-0 non-malleable code against leaky input and output local tampering functions to construct a rate-1 non-malleable code against. lg n-local tampering functions, for any positive constant xi < 1. Our explicit construction instantiates this compiler using an appropriate encoding by Ball et al. (EUROCRYPT-2016).