Secure error correction using multiparty computation

In the last couple of decades, error correction techniques play a prominent role in various scientific and engineering fields such as information theory, communication, networking, to name a few. These techniques are mainly utilized to locate and fix corrupted data over noisy channels. The data might be corrupted due to various reasons, for instance, communication failures, noise, or adversarial activities. On the other hand, data-privacy has been in the center of attention by many researchers in recent years. As such, it's important to be able to use error correction techniques over private data. This paper therefore proposes a secure error correction method by using secure multiparty computation (MPC). To the best of our knowledge, our proposed approach is the first solution in the literature. In secure MPC protocols, parties first share their private inputs by cryptographic primitives in order to jointly compute a function without revealing those private inputs. At the end of the protocol, only the function value will be revealed to all parties. Our secure MPC protocol efficiently implements the error-locator function of Berlekamp-Welch algorithm. After locating errors, we utilize another cryptographic technique, named enrollment protocol, to fix the errors.