Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/116482
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Lattice-based threshold-changeability for standard Shamir secret-sharing schemes
International Conference on the Theory and Application of Cryptology and Information Security (10th : 2004) (5 - 9 December 2004 : Jeju Island, Korea)
Lee, Pil Joong. Advances in cryptology, ASIACRYPT 2004 : 10th International Conference on the Theory and Application of Cryptology and Information Security, Jeju Island, Korea, December 5-9, 2004 : proceedings, p.170-186
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 the information-theoretic security of our construction. These lattice-based security proof techniques may be of independent interest.