  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.
