Does failure of indistinguishability of encryptions imply lack of CPA-security?

Question

Suppose we have an encryption scheme that fails the indistinguishability of encryptions test. That is, given messages $m_0, m_1$ and a ciphertext $c_b = Enc_k(m_b)$, where $b \in \{0, 1\}$, the distinguisher $D$ can extrapolate which message was encrypted. Here $D$ has the advantage of knowledge of what the messages are.

In CPA test however, after observing a set of (plaintext, ciphertext) pairs we are presented with a previously unobserved ciphertext. Our task here is not to distinguish (there is nothing to distinguish from...) but rather to decipher.

My question is, does failure of indistinguishability of encryptions imply lack of CPA-security?

Answer 1

1. Faliure of indistinguishablity of encryptions under a eavesdropper does imply faliure of indistinguishablity of encryptions under a chosen-plaintext attack. But the converse is not necessarily true (ex. OTP)

2. The aim of CPA-secure is not to decrypt previously unobserved ciphertext but to pass the distinguishability test after a set of (plaintext, ciphertext) observations.