Collaborative filtering is a popular technique for recommendation system due to its domain independence and reliance on user behavior data alone. But the possibility of identification of users based on these personal data raise privacy concerns. Differential privacy aims to minimize these identification risks by adding controlled noise with known characteristics. The addition of noise impacts the utility of the system and does not add any other value to the system other than enhanced privacy. We propose using sketching techniques to implicitly provide the differential privacy guarantees by taking advantage of the inherent randomness of the data structure. In particular, we use count sketch as a storage model for matrix factorization, one of the successful collaborative filtering techniques. Our model is also compact and scales well with data, making it well suitable for large scale applications.