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when one increments that component of the tweak. We illustrate the use of this approach by refining the authenticated-encryption scheme OCB and the message authentication code PMAC, yielding variants of these algorithms, OCB1 and PMAC1, that are simpler and faster than the original schemes, and yet have simpler proofs. Our results bolster the thesis of Liskov, Rivest, and Wagner (12) that a desirable approach for designing modes of operation is to start from a tweakable blockcipher. We elaborate on their idea, suggesting the kind of tweak space, usage- discipline, and blockcipher-based instantiations that give rise to simple and efficien t modes of operation of a conventional blockciphers.

Efficient Instantiations of Tweakable Blockciphers and Refinements to Modes OCB and PMAC