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Rijndael supports block lengths of 128, 192 and 256. AES does not but Rijndael does.

What other algorithms support variable block lengths? Or is Rijndael unique in that regard?

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Rijndael-128, Rijndael-192 and Rijndael-256 are actually 3 different variants of block cipher that are very similar.

Simon, Speck, Threefish and RC5 also define different block size variants in similar way. Rijndael is not unique in this regard.

Block cipher that really has variable block length is XXTEA as its block length is not limited.

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