Threshold Cryptography Based on Blakley Secret Sharing Ilker˙ Nadi Bozkurt, Kamer Kaya, Ali Aydın Selc¸uk Ahmet M. Gulo¨ glu˜ Department of Computer Engineering Department of Mathematics Bilkent University Bilkent University Ankara, 06800, Turkey Ankara, 06800, Turkey Email: bozkurti,kamer,selcuk @cs.bilkent.edu.tr Email:
[email protected] f g Abstract—Function sharing deals with the problem and Asmuth-Bloom [1] based on the Chinese Remainder of distribution of the computation of a function (such Theorem. as decryption or signature) among several parties. The A shortcoming of secret sharing schemes is the need to necessary values for the computation are distributed to reveal the secret shares during the reconstruction phase. the participating parties using a secret sharing scheme The system would be more secure if the subject function (SSS). Several function sharing schemes have been pro- posed in the literature, with most of them using Shamir can be computed without revealing the secret shares or secret sharing as the underlying SSS. In this paper, we reconstructing the secret. This is known as the function investigate how threshold cryptography can be conducted sharing problem. A function sharing scheme requires with Blakley secret sharing scheme and present a novel distributing the function’s computation according to the function sharing scheme for the RSA cryptosystem. The underlying SSS such that each part of the computation challenge is that constructing the secret in Blakley’s SSS can be carried out by a different user and then the requires the solution of a linear system which normally partial results can be combined to yield the function’s involves computing inverses, while computing inverses value without disclosing the individual secrets.