# Does security against a CCA1 attacker imply security against a CPA attacker?

I've seen it mentioned multiple times, but have not seen a formal proof of how security of an encryption scheme against a non adaptive chosen-ciphertext attacker (under non-malleability or ciphertext indistinguishability) implies security against an adaptive chosen-plaintext attacker.

Does IND-CCA1 imply IND-CPA (and NM-CCA1 imply NM-CPA)?

• The usual argument is that it's "obvious" as the attacker is given strictly more possibilities in the CCA1 scenario as opposed to the CPA one. – SEJPM May 14 '17 at 22:26