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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 http://csrc.nist.gov/publications/nistpubs/800-38a/sp800-38a.pdf

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 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 at 20:46
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