The electronic payment is an important part of E-commerce. It is such a payment means that people can pay for the goods by computer, telephone or fax. How to accomplish electronic payment securely and conveniently is a pressing problem to be solved in the development of E-commerce. This paper is to do some research into the information security problem of electronic payment, using the mathematical instrument.In the electronic payment system, there are three parties: the bank, the user and the shop. The user withdraws cash from the bank in the withdrawal agreement, the user pays for the goods in the payment agreement and the shop deposits money in the deposit agreement.There are two types of the electronic payment systems: the on-line system and the off-line system. Compared with the off-line system, the on-line system has better security and efficiency, but it also needs greater expense. Furthermore, the on-line system needs the participancy of the bank. Therefore, the on-line system has some limitations. This paper introduces the off-line system principally.This paper classifies all the existing electronic payment schemes by the different characters they have: they are the basic electronic payment scheme, the electronic payment scheme using electronic wallet, the fair electronic payment scheme and the divisible electronic payment scheme. We will give detailed introduction for these electronic payment schemes in the chapters from the second to the fifth.The most basic electronic payment systems use different public keys to represent different face values, it will bring many problems in reality. To this end, this paper puts forward a electronic payment system with variable face value, which solves the problem efficiently. This paper also puts forward a signature scheme of electronic purse, in this scheme, the electronic purse has a public key which has been signed by the bank, so the electronic purse can produce valid signatures, furthermore, anyone can not track the lawful users. There is a special kind of divisible electronic payment systems---the electronic check systems. This paper combines the electronic check system with the electronic purse, puts forward a electronic check scheme set in a electronic purse, this scheme realizes the system's fairness. The schemes are all designed for the information security of electronic payment, they safeguard the security of electronic payment systems. |