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I have written a program to run AES in CTR mode with keys of 128,192 or 256 bits and checked it gives correct results with the data given in section F.5 at

The program chooses a different nonce for each message that is enciphered. Do I need a different key for every message as well? or will a single key with a differing nonce provide all the security that is needed?

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No, you don't need a distinct key for each message in CTR mode... just make sure the same nonce/key combination never get used more than once. – hunter May 27 '14 at 15:49
@hunter ... where "used" refers to "by the block cipher" rather than "by the encryption scheme". $\hspace{.58 in}$ – Ricky Demer May 27 '14 at 20:46

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