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).

Block ciphers (security summary)

Common algorithms	AES Blowfish DES (Internal Mechanics, Triple DES) Serpent Twofish

Less common algorithms	Camellia CAST-128 IDEA RC2 RC5 SEED ARIA Skipjack TEA XTEA

Other algorithms	3-Way Akelarre Anubis BaseKing BassOmatic BATON BEAR and LION CAST-256 Chiasmus CIKS-1 CIPHERUNICORN-A CIPHERUNICORN-E CLEFIA CMEA Cobra COCONUT98 Crab Cryptomeria/C2 CRYPTON CS-Cipher DEAL DES-X DFC E2 FEAL FEA-M FROG G-DES GOST Grand Cru Hasty Pudding cipher Hierocrypt ICE IDEA NXT Intel Cascade Cipher Iraqi KASUMI KeeLoq KHAZAD Khufu and Khafre KN-Cipher Ladder-DES Libelle LOKI (97, 89/91) Lucifer M6 M8 MacGuffin Madryga MAGENTA MARS Mercy MESH MISTY1 MMB MULTI2 MultiSwap New Data Seal NewDES Nimbus NOEKEON NUSH PRESENT Q RC6 REDOC Red Pike S-1 SAFER SAVILLE SC2000 SHACAL SHARK Simon SMS4 Speck Spectr-H64 Square SXAL/MBAL Threefish Treyfer UES Xenon xmx XXTEA Zodiac

Design	Feistel network Key schedule Lai-Massey scheme Product cipher S-box P-box SPN Avalanche effect Block size Key size Key whitening (Whitening transformation)

Attack (cryptanalysis)	Brute-force (EFF DES cracker) MITM (Biclique attack, 3-subset MITM attack) Linear (Piling-up lemma) Differential (Impossible Truncated Higher-order) Differential-linear Distinguishing (Known-key) Integral/Square Boomerang Mod n Related-key Slide Rotational Timing XSL Interpolation Partitioning Davies' Rebound Weak key Tau Chi-square Time/memory/data tradeoff

Standardization	AES process CRYPTREC NESSIE

Utilization	Initialization vector Mode of operation Padding

Cryptography

History of cryptography Cryptanalysis Outline of cryptography

Symmetric-key algorithm Block cipher Stream cipher Public-key cryptography Cryptographic hash function Message authentication code Random numbers Steganography

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References

↑ Barış Ege, Elif Bilge Kavun, and Tolga Yalçın. "Memory Encryption for Smart Cards". 2011.
↑ Emmanuel Prouff. "Smart Card Research and Advanced Applications". 2011. p. 201.
1 2 3 Orr Dunkelman, Nathan Keller, and Adi Shamir. "Minimalism in Cryptography: The Even-Mansour Scheme Revisited".
↑ Joan Daemen , Laboratorium Esat. "Limitations of the Even-Mansour Construction". 1992. doi: 10.1007/3-540-57332-1_46
↑ Rogaway, Phillip (2004-09-24). "Efficient Instantiations of Tweakable Blockciphers and Refinements to Modes OCB and PMAC" (PDF).

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