Using Commutative Encryption to Share a Secret

It is shown how to use commutative encryption to share a secret. Suppose Alice wants to share a secret with Bob such that Bob cannot decrypt the secret unless a group of trustees agree. It is assumed that Alice, Bob and the trustees communicate over insecure channels. This paper presents a scheme that uses modular exponentiation and does not require key exchange. The security of the scheme rest of the difficulty of the discrete logarithm problem.