An efficient ID-based partially blind signature scheme and application in electronic-cash payment system

A kind of blind signature, partially blind signature, allows a user to request the signatory authority on some pre-shared information such that signatory authority only sign the message but could not able to see to message's content except the pre-shared information. In 2007, an efficient and secure ID–based partially blind signature scheme has been presented by Hu et al, but this scheme is suffer from critical forgery attack identified by Tseng et al, in 2008. In 2009, using bilinear pairing in elliptic curve, Hu et al scheme was improved by Tian et al who tackles forgery attacks. Because the computational cost of bilinear pairing on an elliptic curve is more time consuming operation than the point multiplication on an elliptic curve. Fort this reason, we present a novel efficient identity-based partially blind signature scheme (ID-PBS) based on the hardness of gap Diffie-Hellman problem and elliptic curve discrete logarithm problem. The proposed ID-PBS scheme meets the security property of partially blind signature such as untraceability, non-forgeability, completeness, and non- deniability. Finally, we proposed an electronic-payment system based on our ID-PBS scheme.