Lattice-based threshold changeability for standard shamir sectret-sharing schemes

Steinfeld, Ron, Pieprzyk, Josef, & Wang, Huaxiong (2007) Lattice-based threshold changeability for standard shamir sectret-sharing schemes. IEEE Transactions on Information Theory, 53(7), pp. 2542-2559.

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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 nonstandard 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.

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7 citations in Web of Science®

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ID Code: 69382
Item Type: Journal Article
Refereed: Yes
Additional Information: This is the full version of a paper presented at Asiacrypt 2004, Dec. 5-9 2004, Jeju Island, South Korea
Keywords: Changeable threshold, Geometry of numbers, Lattice reduction, Shamir secret-sharing
DOI: 10.1109/TIT.2007.899541
ISSN: 0018-9448
Divisions: Current > Schools > School of Electrical Engineering & Computer Science
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2007 IEEE
Copyright Statement: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.
Deposited On: 27 Mar 2014 22:45
Last Modified: 22 Apr 2015 11:39

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