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 δ">δ-local tampering functions; namely, each output bit of the tampering function is a function of (at most) δ">δ input bits. This work presents the first explicit and efficient rate-1 non-malleable code for δ">$\delta$-local tampering functions, where δ=ξlg⁡n">δ=ξ lgn and ξ<1">ξ<1

$\xi <1$

is any positive constant. As a corollary, we construct the first explicit rate-1 non-malleable code against NC0">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 δ">δ

$\delta$

-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 δ=O(log⁡n)">δ=O(logn)

$\delta =O(\log n)$

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 ξlg⁡n">ξlgn

$\xi \lg n$

-local tampering functions, for any positive constant ξ<1">ξ<1

$\xi <1$

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