The Security with the Randomness Revealed for Public-Key Encryption

We consider the situation for public-key encryption that the adversary knows the randomness which was used to compute the ciphertext. In some practical scenarios, there is a possibility that the randomness is revealed. For example, the randomness used to make a ciphertext may be stored in insecure memory, or the pseudorandom generator may be corrupted. We first formalize the security notion on this situation as “the one-wayness with the randomness revealed.” In addition to the formalization, we focus on two schemes, the generic chosen-ciphertext secure encryption method (GEM) and 3-round OAEP, and prove that these two schemes satisfy our security notions