A block cipher is a family of permutations where the key selects a particular permutation from that family. With a tweakable blockcipher both key and tweak are used to select a permutation. So tweak and key are related.

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Adding tweak to a block cipher

I know there are XEX, XTS and other ways to add tweak to block cipher without modifying cipher itself. However they are quite slow and/or complex. If we assume we have a secure block cipher round ...