Secure information flow with random assignment and encryption

Type systems for secure information flow aim to prevent a program from leaking information from variables classified as $H$ to variables classified as $L$. In this work we extend such a type system to address encryption and decryption; our intuition is that encrypting a $H$ plaintext yields a $L$ ciphertext. We argue that well-typed, polynomial-time programs in our system satisfy a computational probabilistic noninterference property, provided that the encryption scheme is IND-CCA secure. As a part of our proof, we first consider secure information flow in a language with a random assignment operator (but no encryption). We establish a result that may be of independent interest, namely, that well-typed, probabilistically total programs with random assignments satisfy probabilistic noninterference. We establish this result using a weak probabilistic bisimulation.