Cryptology ePrint Archive: Report 2014/564

A Security Definition for Multi Secret Sharing and a Scheme Based on LWE

Massoud Hadian Dehkordi and Reza Ghasemi

Abstract: Since the advent of secret sharing scheme many researches have been allocated to study on this topic because it has a lot of application. For the first time Shamir and Blakley introduced the concepts of secret sharing. In their scheme, just one secret is shared. After a while, Harn present a scheme in which many secrets can be shared, but the secrets have to recover in predetermined order. In addition, in his scheme just one share is assigned to each participant. After a while, many scheme introduced such that they have not any constraint on the order of recovering secrets. These kind of scheme is called Multi Secret Sharing Scheme and it abbreviated by MSS. To the best of our knowledge, up until now, no exact definition for the security of MSS scheme has been presented. In this paper, a definition for secrecy of MSS scheme is introduced and a MSS scheme is presented based on Learning With Error (LWE). LWE is a one of lattice concepts which nowadays constitutes the core of many cryptographic constructions because the hardness of lattice problems is well studied and the hardness of these constructions can be reduced to NP-Hard problems. The advantage of using LWE is twofold, first is that the hardness of LWE is well understood, second working with it is very simple because just simple operations are used. At the end of the paper a verifiable version of presented MSS scheme is given. Verifiability is an important feature which has defined. In this kind of schemes, dishonest dealer or participants can be identified.

Category / Keywords: ‎Secret sharing

Date: received 19 Jul 2014

Contact author: rezaghasemi_67 at iust ac ir

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Version: 20140719:164642 (All versions of this report)

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