# Chosen Plaintext Attack and Chosen Multiple-Plaintext Attack

The original CPA game:

1. The adversary gives two arbitrary messages $m_0$ and $m_1$ to a challenger;
2. The challenger encrypts an arbitrary message $m_u$, $u∈\{0,1\}$ , and sends the ciphertext to the adversary;
3. The adversary outputs the guess $u$.

Now I give a revised version of the above CPA game:

1. The adversary gives two arbitrary sets of messages $M_0$ and $M_1$ to a challenger, where $|M_0|=|M_1|$, and each pair of counterparts are of equal size;
2. The challenger encrypts an arbitrary set of message $M_u$, $u∈\{0,1\}$, and sends the ciphertexts to the adversary;
3. The adversary outputs the guess $u$.

If a public-key encryption scheme is CPA-secure is it also secure in this revised version of CPA game?

• – user991 Apr 13 '17 at 21:09
• Hi Sunny and welcome. You can it the edit line above my name to see the formatting changes that I've made so you can use them in followup posts. – Maarten Bodewes Apr 13 '17 at 21:31

If your scheme is LoR-CPA secure then you can query all message pairs from the two sets to the LoR oracle and answer any remaining queries $$x$$ by querying $$(x,x)$$.