Authenticated key distribution using given set of primes for secret sharing

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.