A growing body of work addresses the security of cryptographic systems in the presence of mass surveillance, a threat made concrete by Snowden’s revelations and the widespread use of spyware against journalists and activists. In this paper, we investigate the security of symmetric encryption faced with simultaneous algorithm substitution attacks (ASAs) and key exfiltration (KE). The security of symmetric encryption in presence of ASAs or KE alone was established but no result deals with their coordinated deployment. Yet, that is a necessary step to be made if we are to achieve actual security against mass surveillance. We formalize this setting, and prove that no scheme alone stands chance against coordinated ASA and KE, by describing a realistic attack. We then describe a new kind of schemes, which make use of externally supplied randomness. We formalize their security and give a construction which provably resists simultaneous ASAs and KE when paired with a verifiable source of randomness, with security bounds in the concrete security spirit.