# Encrypting random coins used for the encryption itself

Circular security notions for PKE schemes capture the security of (PKE) schemes when encrypting the secret decryption key.

Is there an analogous notion but for encrypting the randomness used for the encryption? i.e. what if one first fixes the random coins $$r$$ to be used for for the encryption, and then computes the ciphertext for this $$r$$: $$c := E_{pk}(m; r)$$, with $$m = r$$?

• The closest thing I'm aware of to what you seem to be looking for is this paper though that one's for symmetric encryption and the related notion of the message and the nonce having some relation.
– SEJPM
Jul 15 at 18:15
• Thanks for the link! Sep 7 at 14:18