With the development of Internet technology,electronic payment system is changing our life.E-cash scheme is a research hot spot in the field of electronic payment,it has aroused widespread concern in academia and industry.However,the security of the electronic cash scheme has increasingly become the focus of attention.A secure e-cash scheme not only prevents counterfeiting of electronic cash,but also protects the privacy of consumers,prevents second spending and ensures the fairness of the transaction.Recently,Yang et al.constructed an authentication encryption scheme using ellptic curves and proposed an electronic money scheme.However,Chaudhry et al.point out that the Yang et al.'s scheme is vulnerable to counterfeit attacks and gives an improved solution.This paper finds that the Chaudhry et al.'s scheme cannot protect the privacy of consumers,and it cannot prevent the double-spending,and it cannot solve the transaction disputes.In this paper,we given the specific attack on Chaudhry et al.'s scheme,and we proposed a new scheme Our proposed scheme does not require the public key of the consumer in the payment phase,and does not require the private key of the merchant in the arbitration phase,and improved the tracking of double-spending.Finally,this paper analyzes the security and computational complexity of our scheme.Recently,Liu et al.proposed an offline electronic cash scheme for bank delegation.However,merchant cannot verify the validity of the coin,and an attacker can fake the electronic money.In this paper,given the specific attack on Liu et al's scheme,and we proposed a new scheme.During the withdrawal phase,we use Hash functions to prevent counterfeiting attacks on electronic cash,and we improve the merchant's verification algorithm.Finally,this article analyzes the security and computational complexity of our scheme. |