# A modified question of Hazay & Lindell's Efficient Secure Two-Party protocols Book

Based on the question proposed on page 27, we propose a modified question as follows:

Suppose the protocol is based on Paillier cryptosystem and $$P_2$$ has generated related public and private keys ($$P_2$$ publishes its pub key). Then, $$P_1$$ will encrypt $$x$$ using the public key and send it to $$P_2$$.

Considering this scenario, is it secure in the semi-honest model?

• Encryption hides information from someone who doesn't know the decryption key, but $P_2$ knows the key in this case. $P_2$ can obtain $x$ even when its input $y=0$, so the protocol is not semi-honest secure. – Mikero Jan 20 at 16:40
• @Mikero Isn't that an answer? – Maarten Bodewes Jan 20 at 17:09

Promoting my comment to an answer: Encryption hides information from someone who doesn't know the decryption key. In your case, $$P_2$$ knows the decryption key, and can therefore learn $$x$$. This is really no different than sending $$x$$ in the clear to $$P_2$$.
Note that this is the strange example from the book that is secure in the malicious setting but not in the semi-honest setting. Adding the encryption step doesn't change that. Your modified protocol leaks $$x$$ to a semi-honest $$P_2$$ even when its input is $$y=0$$, so the protocol is not semi-honest secure. But your modified protocol is secure against malicious $$P_2$$ since malicious $$P_2$$ always learns $$x$$ in the ideal world without loss of generality.