Rate one-third non-malleable codes

At ITCS 2010, Dziembowski, Pietrzak and Wichs introduced Non-malleable Codes (NMCs) which protect against tampering of a codeword of a given message into the codeword of a related message. A well-studied model of tampering is the 2-split-state model where the codeword consists of two independently tamperable states. As with standard error-correcting codes, it is of great importance to build codes with high rates.

Following a long line of work, Aggarwal and Obremski (FOCS 2020) showed the first constant rate non-malleable code in the 2-split state model; however this constant was a minuscule 10 -6 ! In this work, we build a Non-malleable Code with rate 1/3. This nearly matches the rate 1/2 lower bound for this model due to Cheraghchi and Guruswami (ITCS 2014). Our construction is simple, requiring just an inner-product extractor, a seeded extractor, and an affine-evasive function.