Distributed secret sharing scheme based on the high-dimensional rotation paraboloid

Abstract Secret sharing of ( k , n ) -threshold is naturally used to assist in security-assurance applications in smart systems. It can ensure a high level of data security and reliability. Most of existing secret sharing schemes are employing interpolating polynomial or Chinese remainder theorem, while the hyperplane geometry of Blakley’ s scheme has not been widely used. One of the reasons is that the hyperplane geometry-based scheme leaks information about the secret even via less than the threshold number of shadows. In this paper, we propose a novel secret sharing scheme based on the high-dimensional rotation paraboloid instead of the hyperplanes to overcome this weakness. The secret is corresponding to the unique focal point, and the shadows are corresponding to points on it. We prove that linearly independent k points can determine a unique ( k − 1 ) -dimensional rotation paraboloid, which is the theoretical support of secret distribution and reconstruction. Moreover, we realize verification via two well-known terms: cheater identification and cheating detection. We identify the validity of shadows submitted by participants for cheater identification and verify whether the reconstructed secret is the original one or not for cheating detection, so that dishonest behavior in the secret sharing scheme can be detected. Security analysis shows our scheme is secure against different types of attacks.