Xor–encrypt–xor explained

The xor–encrypt–xor (XEX) is a (tweakable) mode of operation of a block cipher. In tweaked-codebook mode with ciphertext stealing (XTS mode), it is one of the more popular modes of operation for whole-disk encryption. XEX is also a common form of key whitening, and part of some smart card proposals.^{[1] [2]}

History

In 1984, to protect DES against exhaustive search attacks, Ron Rivest proposed DESX: XOR a pre-whitening key to the plaintext, encrypt the result with DES using a secret key, and then XOR a postwhitening key to the encrypted result to produce the final ciphertext.^[3]

In 1991, motivated by Rivest's DESX construction, Even and Mansour proposed a much simpler scheme (the "two-key Even–Mansour scheme"), which they suggested was perhaps the simplest possible block cipher: XOR the plaintext with a prewhitening key, apply a publicly known unkeyed permutation (in practice, a pseudorandom permutation) to the result, and then XOR a postwhitening key to the permuted result to produce the final ciphertext.^[4]

Studying simple Even–Mansour style block ciphers gives insight into the security of Feistel ciphers (DES-like ciphers) and helps understand block cipher design in general.^[5]

Orr Dunkelman, Nathan Keller, and Adi Shamir later proved it was possible to simplify the Even–Mansour scheme even further and still retain the same provable security, producing the "single-key Even–Mansour scheme": XOR the plaintext with the key, apply a publicly known unkeyed permutation to the result, and then XOR the same key to the permuted result to produce the final ciphertext.^[6]

In 2004, Rogaway presented the XEX scheme with key and location-dependent "tweaks":

Rogaway used XEX to allow efficient processing of consecutive blocks (with respect to the cipher used) within one data unit (e.g., a disk sector) for whole-disk encryption.^[7]

Many whole-disk encryption systems – BestCrypt, dm-crypt, FreeOTFE, TrueCrypt, DiskCryptor, FreeBSD's geli, OpenBSD softraid disk encryption software, and Mac OS X Lion's FileVault 2 – support XEX-based tweaked-codebook mode with ciphertext stealing (XTS mode).

Notes and References

1. Barış Ege, Elif Bilge Kavun, and Tolga Yalçın. "Memory Encryption for Smart Cards" . 2011.
2. Emmanuel Prouff. "Smart Card Research and Advanced Applications". 2011, p. 201.
3. [Orr Dunkelman]
4. Joan Daemen, Laboratorium Esat. "Limitations of the Even–Mansour Construction". 1992.
5. Craig Gentry and Zulfikar Ramzan. "Eliminating Random Permutation Oracles in the Even–Mansour Cipher". 2004.
6. Orr Dunkelman; Nathan Keller; and Adi Shamir."Eurocrypt 2012: Minimalism in Cryptography: The Even-Mansour Scheme Revisited".
7. Web site: Rogaway . Phillip . 2004-09-24 . Efficient Instantiations of Tweakable Blockciphers and Refinements to Modes OCB and PMAC.