Yao first introduced a constant-round protocol for secure two-party computation (2PC) withstanding semi-honest adversaries by using a tool called "garbled circuit". Later, many protocols based on garbled circuit approach have been presented, most of which discussed malicious adversaries and efficiency about 2PC. However, there only have a few protocols dealing with the fundamental property of fairness for Yao's garbled circuit approach, in which one involved a trusted third party and the others are very expensive. In the paper, we propose' an efficient Yao's garbled circuit protocol for fair secure 2PC based on ElGamal encryption, Pedersen commitment, Cachin et al.'s verifiable oblivious transfer and Ou-Ruan et al.'s gradual release homomorphic timed commitment. The protocol achieves two advantages: it doesn't need the third party and it is more efficient than other fair secure Yao's protocols.

In a proxy blind signature scheme, the proxy signer is allowed to generate a blind signature on behalf of the original signer. The proxy blind signature scheme is useful in several applications such as e-voting, e-payment and mobile agent environments. This paper analyzed the security shortcoming of a proxy blind signature scheme which is proposed by Tan et al. Comparing with the weakness of the previous schemes, a new proxy blind signature scheme based DLP is presented to overcome the insecurity. It is proved that this scheme is more secure and efficient than the previous schemes. As an instance, the applying of the schemes in electronic voting is describing.

A new fair e-cash payment scheme based on credit is present in this paper. In the scheme, an overdraft credit certificate is issued to user by bank. Using the overdraft credit certificate, user can produce e-cash himself to pay in exchanges. Merchant can verify the e-cash received from user. Bank can make a fair dispute resolution when there is a dissension between user and merchant. It can avoid the problem of partition e-cash for changes, prevent from reusing e-cash and faking e-cash. It fits justice, anonymity, non-deny and impartiality.