Truecrypt

The mode of operation used by TrueCrypt for encrypted partitions, drives, and virtual volumes is XTS.

XTS mode is in fact XEX mode [12], which was designed by Phillip Rogaway in 2003, with a minor modification (XEX mode uses a single key for two different purposes, whereas XTS mode uses two independent keys).

In 2010, XTS mode was approved by NIST for protecting the confidentiality of data on storage devices [24]. In 2007, it was also approved by the IEEE for cryptographic protection of data on block-oriented storage devices (IEEE 1619).

Description of XTS mode:

Ci = EK1 (Pi ^ (EK2 (n) ⊗ αi)) ^ (EK2 (n) ⊗ αi)

Where:

⊗ denotes multiplication of two polynomials over the binary field GF(2) modulo x128+x7+x2+x+1

K1 is the encryption key (256-bit for each supported cipher; i.e., AES, Serpent, and Twofish)

K2 is the secondary key (256-bit for each supported cipher; i.e., AES, Serpent, and Twofish)

i is the cipher block index within a data unit; for the first cipher block within a data unit, i = 0

n is the data unit index within the scope of K1; for the first data unit, n = 0

α is a primitive element of Galois Field (2128) that corresponds to polynomial x (i.e., 2)

The size of each data unit is always 512 bytes (regardless of the sector size).

For further information pertaining to XTS mode, see e.g. [12] and [24].