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Yes, $E$ will be always be secure. This follows from a standard type of proof called a hybrid argument. Giving the full details would be tedious, so here is a sketch in case you are familiar with hybrid arguments: We define games $H_0,H_1,H_2$. We let $H_0$ be the IND-CPA game, but with the game's secret bit hardcoded to $0$. So the game always outputs ...


1

If we try to make an equivalent to these terms in intuitive cryptography (before its formalization into games became the norm) In an eavesdropper attack, the assumption is that an adversary only intercepts a single ciphertext for any given key (and, perhaps, knows the plaintext except for a small portion). In a multiple messages attack, the assumption is ...



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