Threshold decryption scheme with multiple policies

Abstract

Based on the difficulty in computing discrete logarithm and square root on some special conditions, we propose a basic threshold secret sharing scheme for multiple secrets with multiple policies, which allows a group of users to share multiple secret keys and only one secret shadow to be kept by each user. An efficient threshold decryption scheme with multiple policies is designed on the basis of the basic threshold scheme. This decryption scheme allows multiple secret keys to be shared among a group of users, and each user to keep only one secret shadow. Different public keys can be used to encrypt documents. If and only if the number of cooperated users who keep the secret shadows is greater than or equal to the threshold value of the corresponding secret key, they can cooperate to decrypt the documents. It is proved that the proposed scheme has very strong security, unless the attackers can solve the discrete logarithm problem and the square root problem.