Tight Upper And Lower Bounds For Leakage-Resilient, Locally Decodable And Updatable Non-Malleable Codes

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 Omega(logn).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 chi is an element of poly(lambda) requires locality delta (n) is an element of omega(1), where n = poly(lambda) is the message length and lambda is security parameter. Furthermore, we present a construction of a locally decodable and updatable non-malleable code with block size chi is an element of Omega(lambda(1/mu)) (for constant 0 < mu < 1) with locality delta(n), for any delta(n) is an element of omega(1), and n = poly(lambda). (C) 2019 Published by Elsevier Inc.