This paper constructs high-rate non-malleable codes in the information-theoretic plain model against tampering functions with bounded locality. We consider\u00a0\\(\\delta\\)-local tampering functions; namely, each output bit of the tampering function is a function of (at most)\u00a0\\(\\delta\\) input bits. This work presents the first explicit and efficient rate-1 non-malleable code for \\(\\delta\\)\\(\\delta\\)-local tampering functions, where\u00a0\\(\\delta =\\xi lg\u2061n\\)and\u00a0\\(\\xi <1\\)<\/p>\n\n\n\n
\\(\\xi <1\\)<\/p>\n\n\n\n
is any positive constant. As a corollary, we construct the first explicit rate-1 non-malleable code against NC\\(0^{}\\)<\/p>\n\n\n\n
\\(0^{}\\)<\/p>\n\n\n\n
tampering functions.<\/p>\n\n\n\n
Before our work, no explicit construction for a constant-rate non-malleable code was known even for the simplest 1-local tampering functions. Ball\u00a0et al. (EUROCRYPT\u20132016), and Chattopadhyay and Li (STOC\u20132017) provided the first explicit non-malleable codes against\u00a0\\(\\delta\\)<\/p>\n\n\n\n
\\(\\delta\\)<\/p>\n\n\n\n
-local tampering functions. However, these constructions are rate-0 even when the tampering functions have 1-locality. In the CRS model, Faust\u00a0et al. (EUROCRYPT\u20132014) constructed efficient rate-1 non-malleable codes for\u00a0\\(\\delta =O(log\u2061n)\\)<\/p>\n\n\n\n
\\(\\delta =O(log\u2061n)\\)<\/p>\n\n\n\n
local tampering functions.<\/p>\n\n\n\n
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\u00a0\\(\\xi lg\u2061n\\)<\/p>\n\n\n\n
\\(\\xi lg\u2061n\\)<\/p>\n\n\n\n
-local tampering functions, for any positive constant\u00a0\\(\\xi <1\\)<\/p>\n\n\n\n
\\(\\xi <1\\)<\/p>\n\n\n\n
. Our explicit construction instantiates this compiler using an appropriate encoding by Ball\u00a0et al. (EUROCRYPT\u20132016).<\/p>\n","protected":false},"excerpt":{"rendered":"
This paper constructs high-rate non-malleable codes in the information-theoretic plain model against tampering functions with bounded locality. We consider\u00a0-local tampering functions; namely, each output bit of the tampering function is a function of (at most)\u00a0 input bits. This work presents the first explicit and efficient rate-1 non-malleable code for -local tampering functions, where\u00a0and\u00a0 tampering functions. 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