Matching user's profile over multiple Online Social Network (OSN) brings many new insights. Considering the fact of user's disambiguation over different OSN, Existing user profile matching are highly computationally expensive. In this paper, we propose a novel e-identity Architecture using Infrastructure as a service (IaaS) of Cloud to reduce the computational cost of the profile matching algorithm. Profile equivalent through proposed architecture are based on the public attributes available in overall social network and lastly, profiles are mapped to the Aadhaar Unique Identification Number (UID).