Tight upper and lower bounds for leakage-resilient, locally decodable and updatable non-malleable codes

Abstract

Dachman-Soled et al. (TCC '15) proposed a notion called locally decodable and updatable non-malleable codes, which provide the security guarantees of a non-malleable code while allowing for efficient random access. They also considered such codes that are leakage-resilient, allowing for adversaries who continually leak information in addition to tampering. The locality of their construction was Ω(log⁡n).We prove that super-constant locality is inherent by showing tight upper and lower bounds. We show that a locally decodable and updatable non-malleable code with block size χ∈poly(λ) requires locality δ(n)∈ω(1), where n=poly(λ) is the message length and λ is security parameter. Furthermore, we present a construction of a locally decodable and updatable non-malleable code with block size χ∈Ω(λ1/μ) (for constant 0<μ<1) with locality δ(n), for any δ(n)∈ω(1), and n=poly(λ).