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A smart grid network adjusts power allocation by collecting information about the power usage of the customers in real-time. Authentication and user privacy preservation are the two major concerns on smart grid security. Authentication schemes that preserve users' privacy from third parties, but not from the power operator, have been proposed. In this paper, we propose a scheme that preserves users' privacy information, including their daily electricity usage pattern from third parties as well as from the power operator. At the same time, the scheme ensures that authentication can be properly done. These two properties are achieved by using anonymous credential under the principle of blind signature. Basically, a customer generates a set of credentials by himself and asks the control center to blindly sign them. When the customer needs to request more power later on, he presents the signed credential to the control center as proof of his identity. Implementation and analysis show that our scheme is feasible in terms of a number of performance measures such as the signing time and the credential collision rate.