Blakley ve Asmuth-Bloom anahtar paylaştırma yöntemleri için fonksiyon ve anahtar paylaştırma eklentileri

Threshold cryptography deals with situations where the authority to initiate orperform cryptographic operations is distributed amongst a group of individuals.Usually in these situations a secret sharing scheme is used to distribute sharesof a highly sensitive secret, such as the private key of a bank, to the involvedindividuals so that only when a su ? cient number of them can reconstruct thesecret but smaller coalitions cannot. The secret sharing problem was introducedindependently by Blakley and Shamir in 1979. They proposed two di ? erent so-lutions. Both secret sharing schemes (SSS) are examples of linear secret sharing.Many extensions and solutions based on these secret sharing schemes have ap-peared in the literature, most of them using Shamir SSS. In this thesis, we applythese ideas to Blakley secret sharing scheme.Many of the standard operations of single-user cryptography have counter-parts in threshold cryptography. Function sharing deals with the problem ofdistribution of the computation of a function (such as decryption or signature)among several parties. The necessary values for the computation are distributedto the participants using a secret sharing scheme. Several function sharingschemes have been proposed in the literature with most of them using Shamirsecret sharing as the underlying SSS. In this work, we investigate how functionsharing can be achieved using linear secret sharing schemes in general and givesolutions of threshold RSA signature, threshold Paillier decryption and thresholdDSS signature operations. The threshold RSA scheme we propose is a generaliza-tion of Shoup?s Shamir-based scheme. It is similarly robust and provably secureunder the static adversary model.In threshold cryptography the authorization of groups of people are decided simply according to their size. There are also general access structures in whichany group can be designed as authorized. Multipartite access structures consti-tute an example of general access structures in which members of a subset areequivalent to each other and can be interchanged. Multipartite access structurescan be used to represent any access structure since all access structures are mul-tipartite. To investigate secret sharing schemes using these access structures,we used Mignotte and Asmuth-Bloom secret sharing schemes which are basedon the Chinese remainder theorem (CRT). The question we tried to asnwer waswhether one can ? nd a Mignotte or Asmuth-Bloom sequence for an arbitraryaccess structure. For this purpose, we adapted an algorithm that appeared in theliterature to generate these sequences. We also proposed a new SSS which solvesthe mentioned problem by generating more than one sequence.