BROADCASTING CRYPTOSYSTEM IN COMPUTER-NETWORKS USING INTERPOLATING POLYNOMIALS

Abstract

Based on the characteristics of the interpolating polynomials and some properties of the Euclidean geometry, a cryptosystem for broadcasting secrets in computer networks is presented. It is assumed that there is a central authority server (CAS) in a network system. Each principal of the network owns a secret point, known only to the principal and the CAS. When a secure broadcasting request is initiated, the CAS computes an interpolating polynomial P(x) on the secret points owned by the originator and the legal recipient(s). The CAS then cleverly reveals some public points to let the originator and legal recipient(s) reconstruct P(x), whereas illegal recipients are unable to do so. With these public points and a value c, the originator has P(c) as the encryption/decryption key, and can broadcast c and the message encrypted by P(c) in the network. For the legal recipients, P(x) can be reconstructed, and thus P(c) obtained. Since the legal recipients cannot obtain the exact P(x), they have no way of finding the decryption key.