Xor-encrypt-xor

The xor-encrypt-xor (XEX) is a (tweakable) mode of operation of a block cipher. XEX-based tweaked-codebook mode with ciphertext stealing (XTS mode) is one of the more popular modes of operation for whole-disk encryption.

XEX is a common form of key whitening.

XEX is part of some smart card proposals.^[1][2]

History

In 1984, to protect DES against exhaustive search attacks, Ron Rivest proposed DESX: XOR a prewhitening 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.^[3][4]

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.^[3]

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.^[5]

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).

References