Noise-Tolerant Threshold Cryptography

Threshold Cryptography conventionally requires that all the received shares are valid - that is, free of errors arising from lossy transmission or faulty devices. In this paper, we propose a threshold cryptography scheme wherein the secret may be retrieved as long as a specified threshold of valid shares is met, even in the presence of other invalid shares. The proposed scheme is based on a mathematical formulation where the shares are modelled as the constraints of a linear programming problem, the solution of which produces the secret. The fact that modern hardware is capable of efficiently solving fairly large linear programming problems makes the proposal practical. This can aid in the use of threshold cryptography in environments like IoT systems, where there is a possibility of receiving erroneous shares.