To tackle with physical attacks to real world cryptosystems,leakage resilient cryptography was developed.In this setting, the adversary is allowed to have access to the internal state of a cryptographic system, thus violates the black-box reduction used in cryptography.Especially when considering continual memory leakage (CML), i.e., there is no predetermined bound on the leakage of the internal information, the task is extremely tough.In this paper, we solve this problem by introducing a new primitive called updatable hash proof system (UHPS).A UHPS can be viewed as a special Hash proof system (HPS), which served as a fundamental tool in constructing public key encryption (PKE) schemes in both leakage-free and leaky settings.A remarkable property of UHPS is that by simply substituting the HPS component with a UHPS component in a PKE scheme, one obtains a new PKE scheme secure in the CML setting.Moreover, the resulting PKE scheme enjoys the same advantage of the original HPS-based PKE, for instance, still "compatible" with known transforms [8, 24, 20, 32].We then give instantiations of UHPS from widely-accepted assumptions, including the symmetric external Diffie-Hellman assumption and the d-linear assumption.Interestingly, we notice that when instantiated with concrete assumptions, the resulting chosenciphertext secure PKE scheme is by far the most efficient.