NDLI: Capacity of non-malleable codes

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Capacity of non-malleable codes

Content Provider	ACM Digital Library
Author	Cheraghchi, Mahdi Guruswami, Venkatesan
Abstract	Non-malleable codes, introduced by Dziembowski, Pietrzak and Wichs (ICS 2010), encode messages s in a manner so that tampering the codeword causes the decoder to either output s or a message that is independent of s. While this is an impossible goal to achieve against unrestricted tampering functions, rather surprisingly non-malleable coding becomes possible against every fixed family F of tampering functions that is not too large (for instance, when lF\| ≤ $2^{2^{αn}}$ for some α < 1 where n is the number of bits in a codeword). In this work, we study the "capacity of non-malleable coding", and establish optimal bounds on the achievable rate as a function of the family size, answering an open problem from Dziembowski et al. (ICS 2010). Specifically, We prove that for every family F with lF\| ≤ $2^{2^{αn}},$ there exist non-malleable codes against F with rate arbitrarily close to 1 - α (this is achieved w.h.p. by a randomized construction). We show the existence of families of size $exp(;n^{O(1)}$ $2^{αn})$ against which there is no non-malleable code of rate 1 - α (in fact this is the case w.h.p for a random family of this size). We also show that 1 - α is the best achievable rate for the family of functions which are only allowed to tamper the first αn bits of the codeword, which is of special interest. As a corollary, this implies that the capacity of non-malleable coding in the split-state model (where the tampering function acts independently but arbitrarily on the two halves of the codeword, a model which has received some attention recently) equals 1/2. We also give an efficient Monte Carlo construction of codes of rate close to 1 with polynomial time encoding and decoding that is non-malleable against any fixed c > 0 and family F of size $2^{n^{c}},$ in particular tampering functions with, say, cubic size circuits.
Starting Page	155
Ending Page	168
Page Count	14
File Format	PDF
ISBN	9781450326988
DOI	10.1145/2554797.2554814
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-01-12
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Coding theory Probabilistic method Tamper-resilient storage Error detection Cryptography Information theory
Content Type	Text
Resource Type	Article

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