Lattice-Based Threshold-Changeability for Standard Shamir Secret-Sharing Schemes

Abstract. We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a non-standard scheme designed specifically for this purpose, or to have communication between shareholders. In contrast, we show how to increase the threshold parameter of the standard Shamir secret-sharing scheme without communication between the shareholders. Our technique can thus be applied to existing Shamir schemes even if they were set up without consideration to future threshold increases. Our method is a new positive cryptographic application for lattice reduction algorithms, inspired by recent work on lattice-based list decoding of Reed-Solomon codes with noise bounded in the Lee norm. We use fundamental results from the theory of lattices (Geometry of Numbers) to prove quantitative statements about...

• Type: Conference
• Year: 2004
• Where: ASIACRYPT
• Authors: Ron Steinfeld, Huaxiong Wang, Josef Pieprzyk
• Keywords: ASIACRYPT 2004, Cryptology, Secret-sharing Scheme, Shamir Secret-sharing Scheme, Threshold Parameter