Anonymous authentication is a means of authorizing a user without revealing his/her identification. Mobile technologies such as Radio Frequency Identification (RFID) Tags, PDAs and mobile phone systems are increasingly being deployed in pervasive computing. These mobile devices have raised public concern regarding violation of privacy, anonymity and information confidentiality. Considering these concerns, there is a growing need to discover and develop techniques and methods to overcome the threats described above. In this paper we propose an architecture which enhances the privacy and anonymity of users in ubiquitous computing and yet preserves the security requirements of the system. Our proposed architecture is based on Elliptic Curve techniques, on Map-to-Curve or Map-To-Point function, on Weil Pairing techniques and finally on elliptic curve based Okamoto Identification Scheme. In addition, we present a formal validation of our protocol by using the AVISPA tool. The main comparative study of our proposed architecture is to provide privacy and Anonymity for mobile users. Our proposed architecture achieves many of desirable security requirements