A fair off-line electronic cash scheme based on restrictive partially blind signature

A fair off-line electronic cash scheme was presented based on a provable secure restrictive partially blind signature. The scheme is more efficient than those of previous works as the expiry date and denomination information are embedded in the electronic cash, which alleviates the storage pressure for the bank to check double spending, and the bank need not use different public keys for different coin values, shops and users need not carry a list of bank's public keys to verify in their electronic wallet. The modular exponentiations are reduced for both the user and the bank by letting the trustee publish the public values with different structure as those of previous electronic cash schemes. The scheme security is based on the random oracle model and the decision Diffie-Hellman assumption. The scheme can be easily extended to multi-trustees and multi-banks using threshold cryptography.