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This diagram does not correctly depict XEX as designed by Rogaway:

  1. XEX uses a single block cipher key, not two. This was an explicit design feature, and the original security analysis even relied on it. The "Key₁" and "Key₂" in the diagram should simply be "Key".
  2. XEX requires that the tweak ( in the description) be non-zero, which means there should be a multiplication by immediately after the block cipher encryption in the topleft of the diagram. This is essential (and sufficient) for security when using a single block cipher key.

So, something like this:

   Sector number
         |
         v
      +-----+
Key-->| Enc |     α                  α                  α                  α
      +-----+     |                  |                  |                  |
         |        v                  v                  v                  v
         `------>(X)--+------------>(X)--+------------>(X)--+------------>(X)----···
                      |                  |                  |
                      |       Plaintext  |       Plaintext  |       Plaintext
                      |           |      |           |      |           |
                      |           v      |           v      |           v
                      +--------->(+)     +--------->(+)     +--------->(+)
                      |           |      |           |      |           |
                      |           v      |           v      |           v
                      |        +-----+   |        +-----+   |        +-----+
                      |  Key-->| Enc |   |  Key-->| Enc |   |  Key-->| Enc |
                      |        +-----+   |        +-----+   |        +-----+
                      |           |      |           |      |           |
                      |           v      |           v      |           v
                      `--------->(+)     `--------->(+)     `--------->(+)
                                  |                  |                  |
                                  v                  v                  v
                             Ciphertext         Ciphertext         Ciphertext

xmath (talk) 11:35, 14 August 2024 (UTC)[reply]