Constant-rate Three-state Non-malleable Code

Dziembowski, Pietrzak, and Wichs (ICS–2010) introduced the notion of non-malleable codes as a relaxation of the error-correcting codes. Intuitively, a non-malleable code ensures that the tampered codeword encodes the original message or a message that is entirely independent of the original message. One of the fundamental research directions in the field of non-malleable code construction considers encoding the message into k separates states, where k > 2, such that each state can be tampered separately by an arbitrary function. The goal of this research effort is to reduce the number of states k, while achieving high encoding rate, i.e., the ratio of the message length to the cumulative size of all the k encoded states. The current state-of-the-art provides non-malleable code constructions for 2-states at 1/ log ` rate (Li, STOC–2017), where ` is the length of the encoded message, and, very recently, for 4-states at ≈ 1/3 rate (Kanukurthi, Obbattu, and Sekar, TCC–2017). However, there are no known non-malleable code constructions for k = 2 or k = 3 with a constant rate. This work contributes to this research endeavor by providing a rate ≈ 1/3 non-malleable code for k = 3. Reducing the number of states k in a non-malleable code is notoriously hard. However, our work succeeds in reducing the number of states required by the construction of Kanukurthi et al. by leveraging a unique characteristic of the non-malleable code for 2-states provided by Aggarwal, Dodis, and Lovett (STOC, 2014). ∗Microsoft Research, Bangalore, India. [email protected] †Department of Computer Science, Purdue University. [email protected]. ‡The research effort is supported in part by a Purdue Research Foundation grant. §Department of Computer Science, Purdue University. [email protected].