In cryptography, the Advanced Encryption Standard (AES), also known as Rijndael, is a block cipher adopted as an encryption standard by the U.S. government. It is expected to be used worldwide and analysed extensively, as was the case with its predecessor, the Data Encryption Standard (DES). AES was announced by National Institute of Standards and Technology (NIST) as U.S. FIPS PUB 197 (FIPS 197) in November 26, 2001 after a 5-year standardization process. It became effective as a standard May 26, 2002. As of 2006, AES is one of the most popular algorithms used in symmetric key cryptography.

The cipher was developed by two Belgian cryptographers, Joan Daemen and Vincent Rijmen, both alumni of the Katholieke Universiteit Leuven, and submitted to the AES selection process under the name "Rijndael", a combination of the names of the inventors.

Development

Rijndael was a refinement of an earlier design by Daemen and Rijmen, Square; Square was a development from Shark.

Unlike its predecessor DES, Rijndael is a substitution-permutation network, not a Feistel network. AES is fast in both software and hardware, is relatively easy to implement, and requires little memory. As a new encryption standard, it is currently being deployed on a large scale.

Description of the cipher

Strictly speaking, AES is not precisely Rijndael (although in practice they are used interchangeably) as Rijndael supports a larger range of block and key sizes; AES has a fixed block size of 128 bits and a key size of 128, 192 or 256 bits, whereas Rijndael can be specified with key and block sizes in any multiple of 32 bits, with a minimum of 128 bits and a maximum of 256 bits.

The key is expanded using Rijndael's key schedule.

Most of AES calculations are done in a special finite field.

AES operates on an array of bytes, termed the state (versions of Rijndael with a larger block size have additional columns in the state). For encryption, each round of AES (except the last round) consists of four stages:

1. AddRoundKey each byte of the state is combined with the round key; each round key is derived from the cipher key using a key schedule.
2. SubBytes a non-linear substitution step where each byte is replaced with another according to a lookup table.
3. ShiftRows a transposition step where each row of the state is shifted cyclically a certain number of steps.
4. MixColumns a mixing operation which operates on the columns of the state, combining the four bytes in each column using a linear transformation.

The final round replaces the MixColumns stage with another instance of AddRoundKey.

The AddRoundKey step

In the AddRoundKey step, each byte of the state is combined with a byte of the round subkey using the XOR operation.

In the AddRoundKey step, the subkey is combined with the state. For each round, a subkey is derived from the main key using the key schedule; each subkey is the same size as the state. The subkey is added by combining each byte of the state with the corresponding byte of the subkey using bitwise XOR.

The SubBytes step

In the SubBytes step, each byte in the state is replaced with its entry in a fixed 8-bit lookup table, S; b_ij = S(a_ij).

In the SubBytes step, each byte in the array is updated using an 8-bit S-box. This operation provides the non-linearity in the cipher. The S-box used is derived from the inverse function over GF(2⁸), known to have good non-linearity properties. To avoid attacks based on simple algebraic properties, the S-box is constructed by combining the inverse function with an invertible affine transformation. The S-box is also chosen to avoid any fixed points (and so is a derangement), and also any opposite fixed points.

The S-box is more fully described in the article Rijndael S-box.

The ShiftRows step

In the ShiftRows step, bytes in each row of the state are shifted cyclically to the left. The number of places each byte is shifted differs for each row.

The ShiftRows step operates on the rows of the state; it cyclically shifts the bytes in each row by a certain offset. For AES, the first row is left unchanged. Each byte of the second row is shifted one to the left. Similarly, the third and fourth rows are shifted by offsets of two and three respectively. For the block of size 128 bits and 192 bits the shifting pattern is same. In this way, each column of the output state of the ShiftRows step is composed of bytes from each column of the input state. (Rijndael variants with a larger block size have slightly different offsets). In case of 256 bit block first row is unchanged and the shifting for second, third and fourth row is 1 byte, 2 byte and 4 byte respectively - although this change only applies for the Rijndael cipher when used with a 256-bit block, which is not used for AES.

The MixColumns step

In the MixColumns step, each column of the state is multiplied with a fixed polynomial c(x).

In the MixColumns step, the four bytes of each column of the state are combined using an invertible linear transformation. The MixColumns function takes four bytes as input and outputs four bytes, where each input byte affects all four output bytes. Together with ShiftRows, MixColumns provides diffusion in the cipher. Each column is treated as a polynomial over GF(2⁸) and is then multiplied modulo x⁴ + 1 with a fixed polynomial c(x) = 3x³ + x² + x + 2. The MixColumns step can also be viewed as a matrix multiply in Rijndael's finite field.

This process is described further in the article Rijndael mix columns.

Optimization of the cipher

On systems with 32-bit or larger words, it is possible to speed up execution of this cipher by converting the SubBytes, ShiftRows and MixColumns transformations into tables. One then has four 256-entry 32-bit tables, which utilizes a total of four kilobytes (4096 bytes) of memory--a kilobyte for each table. A round can now be done with 16 table lookups and 12 32-bit exclusive-or operations, followed by four 32-bit exclusive-or operations in the AddRoundKey step.

If the resulting four kilobyte table size is too large for a given target platform, the table lookup operation can be performed with a single 256-entry 32-bit table by the use of circular rotates.

Security

As of 2006, the only successful attacks against AES have been side channel attacks. The National Security Agency (NSA) reviewed all the AES finalists, including Rijndael, and stated that all of them were secure enough for US Government non-classified data. In June 2003, the US Government announced that AES may be used for classified information:

"The design and strength of all key lengths of the AES algorithm (i.e., 128, 192 and 256) are sufficient to protect classified information up to the SECRET level. TOP SECRET information will require use of either the 192 or 256 key lengths. The implementation of AES in products intended to protect national security systems and/or information must be reviewed and certified by NSA prior to their acquisition and use."

This marks the first time that the public has had access to a cipher approved by NSA for TOP SECRET information.