A Thesis for the Degree of Master A Study on Fair Electronic Cash System with and without TTP

The research on off-line electronic cash(e-cash) schemes has drawn much attention since Chaum etc [8] presented the first off-line anonymous electronic cash scheme in 1988. However, anonymous electronic cash schemes also facilitate fraud and criminal activities [32], such as money laundering, blackmailing and illegal purchases. Frankel etc [13]. first introduces the concept of fair electronic cash scheme in 1996, fair off-line e-cash (FOLC) schemes extend off-line anonymous electronic cash scheme to allow a qualified trust third party(TTP) to revoke the anonymity of the user under a warrant. The research on FOLC scheme has been one of the hottest topics on electronic cash since then. In this thesis, we propose two off-line fair E-cash schemes: a fair e-cash protocol with the limited power of TTP and a fair e-cash system without TTP. We first present a fair e-cash scheme with the limited power of TTP, which is normally used in several fair e-cash systems in order to conduct tracing mechanism. Generally user should send his withdrawal information to TTP before he withdraws the money from bank. In our protocol, bank first gives the signature on user’s coin by using the blind