Threshold cryptosystem with multiple secret sharing policies

In a group-oriented threshold cryptosystem, each group, instead of each individual member within the group, publishes a single group public key. An outsider can use this group public key to send encrypted messages to the group. However, the received encrypted messages can only be decrypted properly when the number of participating members is larger than or equal to the threshold value. All earlier solutions assume that there is only one secret sharing policy. We propose the first threshold cryptosystem with multiple secret sharing policies. In other words, a group can set up multiple secret sharing policies and a trusted key centre is responsible for selecting three publicly-known moduli, secret keys for group members, and publishing a corresponding public key for each policy during the initiation time. Moreover, there is only one single secret key kept by each group member. Whenever an outsider wants to send a message to the group, he needs to determine how the message should be revealed to the group members, and therefore selects a proper public key to encrypt messages. Once the encrypted message is received by the group, according to the specified information, a predetermined number of group members is required to decipher the cipher-text