IND-CPA We should give a slightly more rigorous definition of confidentiality than ‘attacker can’t read messages’ - it’s vague especially for partial reveals of information. Thus, confidentiality is defined as ciphertext $C$ should give attacker no new info about message $M$.
An experiment was made to describe this, which goes along these lines:
An adversary, Eve, sends two messages $M_0$ and $M_1$ to Alice. Alice flips a coin (in bits, 0 or 1) to choose which message to encrypt and send back to Eve.