چكيده به لاتين
In modern cryptography, a secret sharing (SS) scheme is a method by which a dealer distributes shares to parties such that only predifiend authorized subsets of parties can reconstruct the secret. SS sheme was introduce firstly by Shamir[57]. Shamir’ SS sheme is based on polynomial interpolation; This SS sheme is completely explained in this Theis. Although its efficiency, Shamir’s SS sheme still present some problems. In SS sheme it is assumed that the dealer and shareholders are honest as it is usually not in the real problem. Verifiable Secret Sharing (VSS) scheme has been proposed to achieve security against cheating participants (dealer and/or shareholders). First VSS schem was proposed in [15]. Afterward, Felman[19] present a new VSS scheme that this one was an interactive VSS shceme (Feldman’s VSS sheme is completely explained in this Theis). A case of VSS schemes (such as first VSS scheme [15]) had the special property that everybody, not only the participants, can verify that the shares are correctly distributed. This VSS schemes was named as Publicly Verifiable Secret Sharing (PVSS) scheme by Stadler[62]. The PVSS scheme can be applied in many real applications such as Electronic Voting, Electronic Cash, and Key Escrow.
In this thesis, PVSS schemes are discussed. For this purpose, we first deal with preliminaries of cryptography (using references [44, 48, 55] ), and then we review some SS schemes. Shamir’ thresould SS scheme[57] and its details is dealt with exactly. Befor PVSS shemes, Feldman’ VSS scheme [19] is completely explained. Cham-Pedersen protocol [13] is briefly reviewed, and then, Schomakers’ simple and efficient PVSS scheme and its application to Electronic Voting is present completely. Finally, pairing-based PVSS scheme are explaind which are used references
[27, 31, 32, 40, 49, 50, 64, 67, 68, 71] for this purpose. And a bilinear pairing-baes PVSS scheme [64] and a multilinear pairing-based scheme [49] are completely discussed and analyzed.
