A fair E-cash scheme based on elliptic curve cryptography

A new fair off-line electronic cash scheme on elliptic curve cryptography was presented. The new scheme is more efficient than those by extending fair off-line electronic cash scheme from finite field into elliptic curve cryptography and introducing a new elliptic curve discrete logarithm assumption. The expiry date and denomination are embedded into the blindly signed coin by integrating partially blind signature with restrictive blind signature. A 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. At the same time, the bank just needs to keep undue electronic coins for double spending check in his database, thus bank's database can be dramatically reduced.