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.