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Given a key $K$ (the key is fixed) and a nonce $N$ (changes from one message to another)

Using a secure Key derivation function (KDF) such as the ANSI-X9.63-KDF with SHA-1 option to derive a key for encryption

Can we reach the IND-CPA security level for our encryption ?

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I assume you mean obtaining an ephemeral key $k_N=$KDF($K | N$)? –  rath Feb 28 '14 at 21:52
@rath Yes...... –  zof Feb 28 '14 at 21:53
What kind of encryption would you use? If you have a key and a nonce, you shouldn't really need a KDF as well. You could use one in various ways, but ... –  K.G. Feb 28 '14 at 22:35
@K.G: Symmetric encryption. –  zof Feb 28 '14 at 22:45
If you have a key and a nonce, you are done (use AES-GCM or even AES-CBC reach IND-CPA). Why ask about KDFs? –  K.G. Mar 1 '14 at 18:00

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