Abstract
The secret sharing schemes are the important tools in cryptography that are used as building blocks in many secured protocols. It is a method used for distributing a secret among the participants in a manner that only the threshold number of participants together can recover the secret and the remaining set of participants cannot get any information about the secret. Secret sharing schemes are absolute for storing highly sensitive and important information. In a secret sharing scheme, a secret is divided into several shares. These shares are then distributed to the participants one each and thus only the threshold (t) number of participants can recover the secret. In this paper we have used Mignotte's Sequence based Secret Sharing for distribution of shares to the participants. A (k, m) Mignotte's sequence is a sequence of pair wise co-prime positive integers. We have proposed a new method for reconstruction of secret even with t-1 shares using the SMT solver.
Highlights
Secret Sharing Scheme (SSS) is a method in which a key can be divided into n pieces of information called shares such that i) key can be reconstructed from certain authorized groups of shares and ii) key cannot be reconstructed from unauthorized groups of shares[1,2,3]
Secret sharing schemes are the methods that are necessary for this purpose to keep the secret confidential
In a secret sharing scheme, a secret is divided into several shares
Summary
Secret Sharing Scheme (SSS) is a method in which a key can be divided into n pieces of information called shares such that i) key can be reconstructed from certain authorized groups of shares and ii) key cannot be reconstructed from unauthorized groups of shares[1,2,3]. There were security threats to data before the discovery of secret sharing schemes, as we needed to keep the various duplicates of information at better places. A secret sharing scheme is a method used by the dealer to distribute the shares to parties in a way that only the authorized set of parties can reconstruct the secret. In a secret sharing scheme a dealer will have a secret, there will be n parties, among them any ‘t’ participants are considered as authorized set who can reconstruct the secret. The secret cannot be reconstructed even with ‘t-1’ shares[4]
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