Advanced Encryption Standard Development Description Of The

AES
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General
Designer(s)	Vincent Rijmen and Joan Daemen
First published	1998
Derived from	Square (cipher)
Cipher(s) based on this design	Crypton , Anubis (cipher) , GRAND CRU
Algorithm detail
Block size(s)	128 bits
Key size(s)	128, 192 or 256 bits
Structure	Substitution-permutation network
Number of rounds	10, 12 and 14 (for the respective key sizes)
Best cryptanalysis
A related-key attack can break up to 9 rounds of 256-bit AES. A chosen-plaintext attack can break 8 rounds of 192- and 256-bit AES, and 7 rounds of 128-bit AES. (Ferguson et al, 2000). The XSL attack is claimed to break AES faster than exhaustive search.

In cryptography, the Advanced Encryption Standard (AES), also known as Rijndael, is a block cipher adopted as an encryption standard by the US government, and is expected to be used worldwide and analysed extensively, as was the case with its predecessor, the Data Encryption Standard (DES). It was adopted by National Institute of Standards and Technology (NIST) as US FIPS PUB 197 in November 20012001 is a common year starting on Monday (see link for calendar), and also: The International Year of the Volunteer The United Nations Year of Dialogue Among Civilizations Events January January 1 A black monolith measuring approximately nine feet tall ap after a 5-year standardisation process (see Advanced Encryption Standard processOn January 2, 1997 the National Institute of Standards and Technology, or NIST, called for cryptographers to propose a new standard block cipher for United States Government use in non-classified but sensitive applications. Knowledge of what is used for c for more details).

The cipher was developed by two BelgianFor alternate meanings, see Belgium (disambiguation). Belgian redirects here. For the horse breed commonly used as a draft horse, see Belgian. The Kingdom of Belgium ( Dutch: Belgi French: Belgique German: Belgien is a country in Western Europe, bordered cryptographers, Joan Daemen and Vincent Rijmen, and submitted to the AES selection process under the name "Rijndael", a portmanteauPortmanteau has two meanings. It can refer to a travelling case or to a word formed by combining two or more words. Travelling case A portmanteau (plural portmanteaus or portmanteaux is a large travelling case made of leather. These cases consist of two h comprised of the names of the inventors. Rijndael can be pronounced "Rhine dahl", a long " iI is the 9th letter in the Latin alphabet. History The letter I derived from the Greek iota (Ι, ι). It stood for the vowel /i/, the same as in the Etruscan alphabet. In Latin (as in Modern Greek) /j/ (as English Y in YOKE) was added. In Semitic," and a silent " eThe letter E is the fifth letter in the Latin alphabet. History E is derived from the Greek letter epsilon which is much the same in appearance (Ε, ε) and function. The Semitic h probably first represented a praying or calling human figure" ( IPA: [ɹaindal] ). In the sound file linked below, it is pronounced [rʰaindau].

1 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.

2 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.

AES operates on a 4×4 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:

SubBytes — a non-linear substitution step where each byte is replaced with another according to a lookup table.
ShiftRows — a transposition step where each row of the state is shifted cyclically a certain number of steps.
MixColumns — a mixing operation which operates on the columns of the state, combining the four bytes in each column using a linear transformation.
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.

The final round omits the MixColumns stage.

2.1 SubBytes 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. 2.2 ShiftRows 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. 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). 2.3 MixColumns In the MixColumns step, the four bytes of each column of the state are combined using an invertible linear transformation. Together with ShiftRows, MixColumns provides diffusion in the cipher. Each column is treated as a polynomial over GF(2⁸) and is then multiplied modulo with a fixed polynomial . 2.4 AddRoundKey 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. 3 Security As of 2004, no successful attacks against AES have been recognised. 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." — [1] This marks the first time that the public has had access to a cipher approved by NSA for TOP SECRET information. The most common way to attack block ciphers is to try various attacks on versions of the cipher with a reduced number of rounds. AES has 10 rounds for 128-bit keys, 12 rounds for 192-bit keys, and 14 rounds for 256-bit keys. As of 2004, the best known attacks are on 7 rounds for 128-bit keys, 8 rounds for 192-bit keys, and 9 rounds for 256-bit keys (Ferguson et al, 2000). Some cryptographers worry about the security of AES. They feel that the margin between the number of rounds specified in the cipher and the best known attacks is too small for comfort. The risk is that some way to improve these attacks might be found and that, if so, the cipher could be broken. In this meaning, a cryptographic "break" is anything faster than an exhaustive search, so an attack against 128-bit key AES requiring 'only' 2¹²⁰ operations would be considered a break even though it would be, now, quite infeasible. In practical application, any break of AES which is only this 'good' would be irrelevant. For the moment, such concerns can be ignored. Another concern is the mathematical structure of AES. Unlike most other block ciphers, AES has a very neat mathematical description [2], [3]. This has not yet led to any attacks, but some researchers are worried that future attacks may find a way to exploit this structure. In 2002, a theoretical attack, termed the " XSL attack", was announced by Nicolas Courtois and Josef Pieprzyk, showing a potential weakness in the AES algorithm. It seems that the attack, if the mathematics is correct, is not currently practical as it would have a prohibitively high "work factor". There have been claims of considerable work factor improvement, however, so the attack technique might become practical in the future. On the other hand, several cryptography experts have found problems in the underlying mathematics of the proposed attack, suggesting that the authors have made a mistake in their estimates. Whether this line of attack can be made to work against AES remains an open question. For the moment, as far as is publicly known, the XSL attack against AES is speculative; it is unlikely that anyone could carry out the current attack in practice. 4 See also Advanced Encryption Standard process 5 External links The Rijndael Page Recordings of the pronunciation of "Rijndael" (85 KB wav file) The archive of the old official AES website FIPS PUB 197: the official AES standard ( PDF file) The C.N.S.S. announcement regarding the use of AES for classified data ( PDF file) AES4 — the fourth AES conference 5.1 Implementations A Javascript AES calculator showing intermediate values Optimized Rijndael source code in C (GPL license) 6 References Nicolas Courtois, Josef Pieprzyk, "Cryptanalysis of Block Ciphers with Overdefined Systems of Equations". pp267–287, ASIACRYPT 2002. Joan Daemen and Vincent Rijmen, "The Design of Rijndael: AES - The Advanced Encryption Standard." Springer-Verlag, 2002. BooksEnthsiast.com. Niels Ferguson, John Kelsey, Stefan Lucks, Bruce Schneier, Michael Stay, David Wagner and Doug Whiting: Improved Cryptanalysis of Rijndael. FSE 2000, pp213–230 Block ciphers Type 1 encryption algorithms Block ciphers [ }|action=edit}} Edit }] Algorithms: 3-Way | AES | Akelarre | Blowfish | Camellia | CAST-128 | CAST-256 | CMEA | DEAL | DES | DES-X | FEAL | FROG | G-DES | GOST | ICE | IDEA | Iraqi | KASUMI | KHAZAD | Khufu and Khafre | LOKI89/91 | LOKI97 | Lucifer | MacGuffin | Madryga | MAGENTA | MARS | MISTY1 | MMB | NewDES | RC2 | RC5 | RC6 | REDOC | Red Pike | S-1 | SAFER | SEED | Serpent | SHACAL | SHARK | Skipjack | Square | TEA | Triple DES | Twofish | XTEA Design: Feistel network | Key schedule | Product cipher | S-box | SPN Attacks: Brute force | Linear / Differential cryptanalysis | Mod n | XSL Standardisation: AES process | CRYPTREC | NESSIE Misc: Avalanche effect | Block size | IV | Key size | Modes of operation | Piling-up lemma | Weak key <Hide>

Home > Advanced Encryption Standard

1 Development

2 Description of the cipher

2.1 `SubBytes`

2.2 `ShiftRows`

2.3 `MixColumns`

2.4 `AddRoundKey`

3 Security

4 See also

5 External links

5.1 Implementations

6 References

Topics: Advanced Encryption Standard, Development, Description Of The...