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State-of-art secure processors like Intel SGX remain susceptible to leaking page-level address trace of an application via the page fault channel in which a malicious OS induces spurious page faults and deduces application's secrets from it. Prior works which fix this vulnerability do not provision for OS demand paging to be oblivious. In this work, we present InvisiPage which obfuscates page fault channel while simultaneously making OS demand paging oblivious. To do so, InvisiPage first carefully distributes page management actions between the application and the OS. Second, InvisiPage secures application's page management interactions with the OS using a novel construct which is derived from Oblivious RAM (ORAM) but is customized for page management. Finally, we lower overheads of our approach by reducing page management interactions with the OS via a novel memory partition. For a suite of cloud applications which process sensitive data we show that page fault channel can be tackled while enabling oblivious demand paging at low overheads.