Anonymous data sharing has been becoming more challenging in today's interconnected digital world, especially for individuals that have both anonymous and identified online activities. The most prominent example of such data sharing platforms today are online social networks (OSNs). Many individuals have multiple profiles in different OSNs, including anonymous and identified ones (depending on the nature of the OSN). Here, the privacy threat is profile matching: if an attacker links anonymous profiles of individuals to their real identities, it can obtain privacy-sensitive information which may have serious consequences, such as discrimination or blackmailing. Therefore, it is very important to quantify and show to the OSN users the extent of this privacy risk. Existing attempts to model profile matching in OSNs are inadequate and computationally inefficient for real-time risk quantification. Thus, in this work, we develop algorithms to efficiently model and quantify profile matching attacks in OSNs as a step towards real-time privacy risk quantification. For this, we model the profile matching problem using a graph and develop a belief propagation (BP)-based algorithm to solve this problem in a significantly more efficient and accurate way compared to the state-of-the-art. We evaluate the proposed framework on three real-life datasets (including data from four different social networks) and show how users' profiles in different OSNs can be matched efficiently and with high probability. We show that the proposed model generation has linear complexity in terms of number of user pairs, which is significantly more efficient than the state-of-the-art (which has cubic complexity). Furthermore, it provides comparable accuracy, precision, and recall compared to state-of-the-art.