Extending the Shamir threshold secret sharing scheme for sharing simultanneously several secrets

Secret sharing schemes are very important techniques for the key management in cryptography and for the distributed computation. In 1979, Shamir [6] proposed a threshold secret sharing scheme in which one secret is divided into w pieces (shares) and are delivered to w users such that only groups of t or more users (t < w) could cooperately reconstruct the secret. In this paper, by extending the method of Shamir, we present a scheme for sharing simultaneously several secrets which is more effective in using memory space and computation time w.r.t the consecutive application of several times the Shamir’s original scheme for each secret to be shared.