Advanced Encryption Standard
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 AES redirects here. For other meanings, see AES (disambiguation).
AES  
 
General  
Designer(s)  Vincent Rijmen and Joan Daemen  
First published  1998  
Derived from  Square (cipher)  
Cipher(s) based on this design  Crypton (cypher), Anubis (cipher), GRAND CRU  
Algorithm detail  
Block size(s)  128 bits note  
Key size(s)  128, 192 or 256 bits note  
Structure  Substitutionpermutation network  
Number of rounds  10, 12 and 14 (for the respective key sizes)  
Best cryptanalysis  
A relatedkey attack can break up to 9 rounds of 256bit AES. A chosenplaintext attack can break 8 rounds of 192 and 256bit AES, and 7 rounds of 128bit AES. (Ferguson et al, 2000). 
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 2001 after a 5year standardisation process (see Advanced Encryption Standard process for more details).
The cipher was developed by two Belgian cryptographers, Joan Daemen and Vincent Rijmen, and submitted to the AES selection process under the name "Rijndael", a portmanteau comprised of the names of the inventors. Rijndael can be pronounced "Rhine dahl", a long "i" and a silent "e" (IPA: []). In the sound file linked below, it is pronounced [].
Contents 
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 substitutionpermutation 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
Missing image AESShiftRows.png 
Missing image AESMixColumns.png 
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 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 nonlinear 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.
The SubBytes step
In the SubBytes step, each byte in the array is updated using an 8bit Sbox. This operation provides the nonlinearity in the cipher. The Sbox used is derived from the inverse function over GF(2^{8}), known to have good nonlinearity properties. To avoid attacks based on simple algebraic properties, the Sbox is constructed by combining the inverse function with an invertible affine transformation. The Sbox is also chosen to avoid any fixed points (and so is a derangement), and also any opposite fixed points.
The Sbox is more fully described in the article Rijndael Sbox.
The ShiftRows step
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).
The MixColumns step
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(2^{8}) and is then multiplied modulo <math>x^4+1<math> with a fixed polynomial <math>c(x) = 3x^3 + x^2 + x + 2<math>. The MixColumns step can also be viewed as a matrix multiply in Rijndael's finite field.
The AddRoundKey step
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.
Optimization of the cipher
On systems with 32bit 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 256entry 32bit tables, which utilizes a total of four kilobytes (4096 bytes) of memorya kilobyte for each table. A round can now be done with 16 table lookups and 16 32bit exclusive or operations, followed by four 32bit 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 256entry 32bit table by the use of circular rotates.
Security
As of 2005, 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 nonclassified 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] (http://www.cnss.gov/Assets/pdf/cnssp_15_fs.pdf)
This marks the first time that the public has had access to a cipher approved by NSA for TOP SECRET information. It is interesting to note that many public products use 128bit secret keys by default; it is possible that NSA suspects a fundamental weakness in keys this short, or they may simply prefer a safety margin for top secret documents (which may require security decades into the future).
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 128bit keys, 12 rounds for 192bit keys, and 14 rounds for 256bit keys. As of 2005, the best known attacks are on 7 rounds for 128bit keys, 8 rounds for 192bit keys, and 9 rounds for 256bit 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 128bit key AES requiring 'only' 2^{120} 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. The largest publicallyknown bruteforce attack has been against a 64 bit RC5 key by distributed.net.
Another concern is the mathematical structure of AES. Unlike most other block ciphers, AES has a very neat mathematical description [2] (http://www.macfergus.com/pub/rdalgeq.html), [3] (http://www.isg.rhul.ac.uk/~sean/). 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. Several cryptography experts have found problems in the underlying mathematics of the proposed attack, suggesting that the authors may 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, the XSL attack against AES appears speculative; it is unlikely that anyone could carry out the current attack in practice.
In April 2005, D.J. Bernstein announced a cache timing attack (http://cr.yp.to/papers.html#cachetiming) that he used to break a custom server that used OpenSSL's AES encryption. The custom server was designed to give out as much timing information as possible, and the attack required over 200 million chosen plaintexts. Some say the attack is not practical against realworld implementations [4] (http://groups.google.com/groups?selm=42620794%40news.cadence.com); Bruce Schneier called the research a "nice timing attack." [5] (http://www.schneier.com/blog/archives/2005/05/aes_timing_atta_1.html)
See also
External links
 The Rijndael Page (http://www.esat.kuleuven.ac.be/~rijmen/rijndael/)
 Literature survey on AES (http://www.iaik.tugraz.ac.at/research/krypto/AES/)
 Recordings of the pronunciation of "Rijndael" (http://rijndael.info/audio/rijndael_pronunciation.wav) (85 KB wav file)
 The archive of the old official AES website (http://csrc.nist.gov/encryption/aes/)
 FIPS PUB 197: the official AES standard (http://www.csrc.nist.gov/publications/fips/fips197/fips197.pdf) (PDF file)
 AES4 (http://www.aes4.org/english/events/aes4/index.html) — the fourth AES conference
 John Savard's description of the AES algorithm (http://www.quadibloc.com/crypto/co040401.htm)
Implementations
 A Javascript AES calculator showing intermediate values (http://www.cs.eku.edu/faculty/styer/460/Encrypt/JSAES.html)
 Brian Gladman's BSD licensed implementations of AES (http://fp.gladman.plus.com/cryptography_technology/rijndael/)
 Pablo Barreto's public domain C implementation of AES (http://www.esat.kuleuven.ac.be/~rijmen/rijndael/rijndaelfst3.0.zip)
 D.J. Bernstein's publicdomain implementation of AES (http://cr.yp.to/mac.html)
 GPLlicensed optimized Rijndael source code in C (http://www.cr0.net:8040/code/crypto/aes/)
 The GPLlicensed Nettle library also includes an AES implementation (http://www.lysator.liu.se/~nisse/nettle/)
Notes
 Block sizes of 128, 160, 192, 224, and 256 bits are supported by The Rijndael algorithm, but only the 128bit block size is specified in the AES standard.
 Key sizes of 128, 160, 192, 224, and 256 bits are supported by The Rijndael algorithm, but only the 128, 192, and 256 bit key sizes are specified in the AES standard.
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." SpringerVerlag, 2002. ISBN 3540425802.
 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 edit (https://wsw.academickids.com:443/encyclopedia/index.php?title=Template:Block_ciphers&action=edit) 
Algorithms: 3Way  AES  Akelarre  Blowfish  Camellia  CAST128  CAST256  CMEA  DEAL  DES  DESX  FEAL  FOX  FROG  GDES  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  S1  SAFER  SEED  Serpent  SHACAL  SHARK  Skipjack  Square  TEA  Triple DES  Twofish  XTEA 
Design: Feistel network  Key schedule  Product cipher  Sbox  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  Pilingup lemma  Weak key 
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