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Can the birthday bound arising from a block cipher’s block size be worked around by deriving different keys from the master key with a KBKDF using a tweak?

For example consider the following scheme, which assumes

  • K is a 256-bit key
  • tweak is an integer we can increment before 2^64 blocks have been encrypted with the current generation

and then encrypts as follows:

  • IV = random 256 bits
  • EffectiveKey = KDF(K, context=tweak)
  • ciphertext = KeyGeneration || IV || AES-CBC(IV, EffectiveKey, plain)

Would this scheme be secure for encrypting more than 2^64 blocks?

Asked in order to learn more about the birthday bound.

EDIT - this has similarities to the construction used in the Better Bounds for Block Cipher Modes of Operation via Nonce-Based Key Derivation paper (great talk too by Yehuda Lindell), which also introduces AES-GCM-SIV.

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Obviously you assume blocklength is $128$ bits. I believe the following is correct.

One might try rainbow table TMTO attacks, assuming known plaintext, and succeed with time and memory complexity somewhat better than $$ O(2^{(2/3)k}) $$ where $k$ is the effective keylenth, against such a scheme but it would be secure beyond the birthday bound.

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  • $\begingroup$ Got a link describing the TMTO attacks? Sounds really interesting. How does using the KDF figure into it? I'm assuming this isn't a valid attack when rotating to newly generated keys instead of ones generated with a KDF. $\endgroup$ – orip Jun 5 '18 at 13:20

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