In recent years, Chinese remainder theorem (CRT)-based function sharing schemes are proposed in the literature. In this paper, we study systems of two or more linear congruences. When the moduli are pairwise coprime, the main theorem is known as the CRT, because special cases of the theorem were known to the ancient Chinese. In modern algebra the CRT is a powerful tool in a variety of applications, such as cryptography, error control coding, fault-tolerant systems and certain aspects of signal processing. Threshold schemes enable a group of users to share a secret by providing each user with a share. The scheme has a threshold t + 1 if any subset with cardinality t + 1 of the shares enables the secret to be recovered. In this paper, we are considering 2t prime numbers to construct t share holders. Using the t share holders, we split the secret S into t parts and all the t shares are needed to reconstruct the secret using CRT.

A key distribution scheme for dynamic conferences is a method by which initially an trusted server distributes private individual pieces of information to a set of users. Later each member of any group of users of given size can compute a common secure group key. In this setting any group of t users can compute a common key by each user computing using only his private initial piece of information and the identities of the other t − 1 users in the group. Keys are secure against coalition of to k users, that is, even if k users pool together their pieces they cannot compute anything about a key of any t-size conference comprised of other users. In this paper, we introduce an algorithm for such perfectly secure scheme by using Pell's equation. IntroductionKey distribution is a central problem in cryptographic systems, and major component of the security subsystem of distributed systems, communication systems, and data networks. Secret sharing was invented independently by Adi Shamir [3] and George Blakley [1] in 1979. Secret sharing schemes are ideal for storing information that is highly sensitive and highly important. If

In resent years the security of operations taking place over a computer network become very important. It is necessary to protect such actions against bad users who may try to misuse the system (e.g. steal credit card numbers, read personal mail, or impersonate other users.) Many protocols and schemes were designed to solve problem of this type. Threshold cryptography is a novel cryptographic technique sharing secret among members. It divides a secret key into multiple shares by a cryptographic operation. In this paper, we proposed a key distribution algorithm based on Simple Continued Fraction. The goal of our algorithm is to divide a secret S into ℓ pieces s 1 + s 2 + • • • + s ℓ such that, ℓ pieces are necessary to reconstruct S, but any m < ℓ pieces give no information about S.