Traditionally, the theory of cryptography community proved security of cryptographic primitives under the assumption that no information about the secret key is leaked. However, there is a growing realization that in reality information about the secret key may be leaked via various so called "side channel" attacks. Thus, the problem of designing cryptographic primitives that are provably secure even with keys which may be partly compromised has recently gained much popularity. In this talk, I will survey some of these recent results, while focusing on one result: The robustness of the learning with error (LWE) assumption, which is joint work with Shafi Goldwasser, Chris Peikert and Vinod Vaikuntanathan.