Linear Multisecret-Sharing Schemes and Error-Correcting Codes
Cunsheng Ding (Dept of Information Systems & Computer Science; National University of Singapore, Singapore)
Tero Laihonen (Department of Mathematics, University of Turku, Finland)
Ari Renvall (Department of Mathematics, University of Turku, Finland)
Abstract: In this paper a characterization of the general relation between linear multisecret-sharing schemes and error-correcting codes is presented. A bridge between linear multisecret-sharing threshold schemes and maximum distance separable codes is set up. The information hierarchy of linear multisecret-sharing schemes is also established. By making use of the bridge several linear multisecret-sharing threshold schemes based on Reed-Solomon codes, generalized Reed-Solomon codes, Bossen-Yau redundant residue codes are described, which can detect and correct cheatings. The relations between linear multisecret-sharing threshold schemes and some threshold schemes for single-secret sharing are pointed out.
Keywords: Cryptosystems, error-correcting codes, information theory.