With the convenience of mobile network, people can do different kinds of activities, such as payments, shopping, auctions, and so on, whenever and wherever. Electronic commerce (e-commerce) has become so popular that the number of people using these online services has been increasing enormously in recent years. Hence, the security issues of e-commerce and the rights of users in transaction have raised our concerns. Electronic cash (e-cash) is definitely one of the most popular research topics among e-commerce area. It is very important that e-cash has to be able to hold the anonymity and accuracy in order to preserve the privacy and rights of customers. There are two types of e-cash in general, which are online e-cash and offline e-cash. Both systems have their own pros and cons, and they can be used to construct various applications. In this thesis, we propose a provably secure and efficient offline e-cash scheme with date attachability based on blind signature technique, where expiration date and deposit date can be embedded in an e-cash, simultaneously. With the help of expiration date, the bank can manage the huge database much more easily against unlimited growth, and the deposit date cannot be forged so that users are able to calculate the amount of interests they can receive in the future correctly. Furthermore, our scheme maintains the properties of e-cash, which are anonymity control, double-spending checking and unforgeability. We also provide security analysis and formal proofs in this thesis.