# Beginners question about revealing randomness in probabilistic asymmetric encryption

I am encrypting "1" with probabilistic encryption with a foreign public key (I don't have the private key for it) which results in an encrypted file e.

Can I prove to a third party, that e contains the plain text "1" if I reveal the randomness that I used to encrypt it?

If yes, is there any way to prevent that?

• Hints for the question in the second paragraph: if you reveal to W the randomness R that you used during your encryption, what could prevent W from making the encryption again assuming the encrypted string is "1", using the same method and R, and comparing to the actual result of your encryption? Assume that it would be possible that you could also reveal to W a randomness R' that pass this test with the encrypted string "0" and the same actual result of your encryption; what would that mean for decryption? Beyond trusted implementation I pass at the last question. – fgrieu Oct 7 '17 at 16:22
• ok. i see what you mean. if this assumption would be true there would be no way to decrypt it and knowing whether the plaintext was 1 or 0 because there would be no way to tell them apart – solaire Oct 7 '17 at 17:01
• If the encrypter can't get anything from the third party beforehand, $\hspace{2.02 in}$ then deniable PKE would prevent that. ​ ​ – user991 Oct 8 '17 at 4:59