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 \(\delta\)\(\delta\)-local tampering functions, where \(\delta =\xi lg⁡n\)and \(\xi <1\)

\(\xi <1\)

is any positive constant. As a corollary, we construct the first explicit rate-1 non-malleable code against NC\(0^{}\)

\(0^{}\)

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 \(\delta\)

\(\delta\)

-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 \(\delta =O(log⁡n)\)

\(\delta =O(log⁡n)\)

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 \(\xi lg⁡n\)

\(\xi lg⁡n\)

-local tampering functions, for any positive constant \(\xi <1\)

\(\xi <1\)

. Our explicit construction instantiates this compiler using an appropriate encoding by Ball et al. (EUROCRYPT–2016).

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