**Four-state Non-malleable Codes with Explicit Constant Rate**

*Bhavana Kanukurthi and Sai Lakshmi Bhavana Obbattu and Sruthi Sekar*

**Abstract: **Non-malleable codes (NMCs), introduced by Dziembowski, Pietrzak and Wichs (ITCS 2010), generalize the classical notion of error correcting codes by providing a powerful guarantee even in scenarios where error correcting codes cannot provide any guarantee: a decoded message is either the same or completely independent of the underlying message, regardless of the number of errors introduced into the codeword. Informally, NMCs are defined with respect to a family of tampering functions $F$ and guarantee that any tampered codeword either decodes to the same message or to an independent message, so long as it is tampered using a function $f \in F$.
Nearly all known constructions of NMCs are for the $t$-split-state family, where the adversary tampers each of the $t$ blocks (also known as states), of a codeword, arbitrarily but independently. Cheraghchi and Guruswami (TCC 2014) obtain a Rate-1 non-malleable code for the case where $t = O(n)$ with $n$ being the codeword length and, in (ITCS 2014), show an upper bound of $1-1/t$ on the best achievable rate for any $t-$split state NMC. For $t=10$, Chattopadhyay and Zuckerman (FOCS 2014) achieve a constant rate construction where the constant is unknown. In summary, there is no known construction
of an NMC with an explicit constant rate for any $t= o(n)$, let alone one that comes close to matching Cheraghchi and Guruswami's lowerbound!

In this work, we construct an efficient non-malleable code in the $t$-split-state model, for $t=4$, that achieves a constant rate of $\frac{1}{3+\zeta}$, for any constant $\zeta > 0$, and error $2^{-\Omega(\ell / log^{c+1} \ell)}$, where $\ell$ is the length of the message and $c > 0$ is a constant.

**Category / Keywords: **foundations / information theoretic cryptography, non-malleability

**Original Publication**** (in the same form): **IACR-TCC-2017

**Date: **received 17 Sep 2017, last revised 25 Sep 2017

**Contact author: **bhavana at iisc ac in, oslbhavana@gmail com, sruthi sekar1@gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20170925:112510 (All versions of this report)

**Short URL: **ia.cr/2017/930

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