چكيده به لاتين
Multi-secret sharing scheme is one of the important subjects of cryptography that is widely used in
information security. In a secret sharing scheme, a dealer distributs secrets among a set of participants
according to an acces structure, so that, only authorized subsets of participants are are able to
constract the secrects. One of the biggest challenges in this branch of cryptography is existance of
fraudulent of participants; because a participant may change his private share and present it to other
shareholders from his original share.
Therefore, secret sharing schames which has the ability to verify the secret beyond the constract of
secret, are very significant. In a cryptography system, a scheme is vrifiable if participants can check
the shares they receive from the dealer.
In this thesis, we present several verifiable secret sharing scheme, by using mathematical concepts
such as lattice, nonhomogeneous linear recursions as well as using linear feedback shift register
(LFSR) public key.
Our schemes have more and new abilities in addition to the benefits of the previous schemes. For
example, these schemes have fewer public values, easier structure and more simple computing with
higher speed of executing. In summary, these schemes are easier to use and have a lot of functional
capability.
