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The SubBytes step, one of four stages in a round of AES


General  

Designers  Vincent Rijmen, Joan Daemen 
First published  1998 
Derived from  Square 
Successors  Anubis, Grand Cru 
Certification  AES winner, CRYPTREC, NESSIE, NSA 
Cipher detail  
Key sizes  128, 192 or 256 bits^{[1]} 
Block sizes  128 bits^{[2]} 
Structure  Substitutionpermutation network 
Rounds  10, 12 or 14 (depending on key size) 
Best public cryptanalysis  
Attacks have been published that are computationally faster than a full brute force attack, though none as of 2013 are computationally feasible.^{[3]} For AES128, the key can be recovered with a computational complexity of 2^{126.1} using the biclique attack. For biclique attacks on AES192 and AES256, the computational complexities of 2^{189.7} and 2^{254.4} respectively apply. Relatedkey attacks can break AES192 and AES256 with complexities 2^{176} and 2^{99.5}, respectively.^{[citation needed]} 
The Advanced Encryption Standard (AES), also known by its original name Rijndael,^{[4]}^{[5]} is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.^{[6]}
AES is a subset of the Rijndael cipher^{[5]} developed by two Belgian cryptographers, Joan Daemen and Vincent Rijmen, who submitted a proposal to NIST during the AES selection process.^{[7]} Rijndael is a family of ciphers with different key and block sizes.
For AES, NIST selected three members of the Rijndael family, each with a block size of 128 bits, but three different key lengths: 128, 192 and 256 bits.
AES has been adopted by the U.S. government and is now used worldwide. It supersedes the Data Encryption Standard (DES),^{[8]} which was published in 1977. The algorithm described by AES is a symmetrickey algorithm, meaning the same key is used for both encrypting and decrypting the data.
In the United States, AES was announced by the NIST as U.S. FIPS PUB 197 (FIPS 197) on November 26, 2001.^{[6]} This announcement followed a fiveyear standardization process in which fifteen competing designs were presented and evaluated, before the Rijndael cipher was selected as the most suitable (see Advanced Encryption Standard process for more details).
AES became effective as a federal government standard on May 26, 2002 after approval by the Secretary of Commerce. AES is included in the ISO/IEC 180333 standard. AES is available in many different encryption packages, and is the first (and only) publicly accessible cipher approved by the National Security Agency (NSA) for top secret information when used in an NSA approved cryptographic module (see Security of AES, below).
The name Rijndael (Dutch pronunciation: [ˈrɛindaːl]) is a play on the names of the two inventors (Joan Daemen and Vincent Rijmen).^{[citation needed]}
The Advanced Encryption Standard (AES) is defined in each of:
AES is based on a design principle known as a substitutionpermutation network, a combination of both substitution and permutation, and is fast in both software and hardware.^{[10]} Unlike its predecessor DES, AES does not use a Feistel network. AES is a variant of Rijndael which has a fixed block size of 128 bits, and a key size of 128, 192, or 256 bits. By contrast, the Rijndael specification per se is specified with block and key sizes that may be any multiple of 32 bits, both with a minimum of 128 and a maximum of 256 bits.
AES operates on a 4 × 4 columnmajor order matrix of bytes, termed the state, although some versions of Rijndael have a larger block size and have additional columns in the state. Most AES calculations are done in a particular finite field.
For instance, if there are 16 bytes, , these bytes are represented as this matrix:
The key size used for an AES cipher specifies the number of repetitions of transformation rounds that convert the input, called the plaintext, into the final output, called the ciphertext. The number of cycles of repetition are as follows:
Each round consists of several processing steps, each containing four similar but different stages, including one that depends on the encryption key itself. A set of reverse rounds are applied to transform ciphertext back into the original plaintext using the same encryption key.
In the SubBytes step, each byte in the state matrix is replaced with a SubByte using an 8bit substitution box, the Rijndael Sbox. This operation provides the nonlinearity in the cipher. The Sbox used is derived from the multiplicative inverse 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), i.e., , and also any opposite fixed points, i.e., . While performing the decryption, the InvSubBytes step (the inverse of SubBytes) is used, which requires first taking the inverse of the affine transformation and then finding the multiplicative inverse.
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 blocks of sizes 128 bits and 192 bits, the shifting pattern is the same. Row is shifted left circular by bytes. 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). For a 256bit block, the first row is unchanged and the shifting for the second, third and fourth row is 1 byte, 3 bytes and 4 bytes respectively—this change only applies for the Rijndael cipher when used with a 256bit block, as AES does not use 256bit blocks. The importance of this step is to avoid the columns being linearly independent, in which case, AES degenerates into four independent block ciphers.
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.
During this operation, each column is transformed using a fixed matrix (matrix leftmultiplied by column gives new value of column in the state):
Matrix multiplication is composed of multiplication and addition of the entries. Entries are 8 bit bytes treated as coefficients of polynomial of order . Addition is simply XOR. Multiplication is modulo irreducible polynomial . If processed bit by bit then after shifting a conditional XOR with 1B_{16} should be performed if the shifted value is larger than FF_{16} (overflow must be corrected by subtraction of generating polynomial). These are special cases of the usual multiplication in .
In more general sense, each column is treated as a polynomial over and is then multiplied modulo with a fixed polynomial . The coefficients are displayed in their hexadecimal equivalent of the binary representation of bit polynomials from . The MixColumns step can also be viewed as a multiplication by the shown particular MDS matrix in the finite field . This process is described further in the article Rijndael mix columns.
In the AddRoundKey step, the subkey is combined with the state. For each round, a subkey is derived from the main key using Rijndael's 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.
On systems with 32bit or larger words, it is possible to speed up execution of this cipher by combining the SubBytes and ShiftRows steps with the MixColumns step by transforming them into a sequence of table lookups. This requires four 256entry 32bit tables, and utilizes a total of four kilobytes (4096 bytes) of memory—one kilobyte for each table. A round can then be done with 16 table lookups and 12 32bit exclusiveor operations, followed by four 32bit exclusiveor operations in the AddRoundKey step.^{[11]}
If the resulting fourkilobyte table size is too large for a given target platform, the table lookup operation can be performed with a single 256entry 32bit (i.e. 1 kilobyte) table by the use of circular rotates.
Using a byteoriented approach, it is possible to combine the SubBytes, ShiftRows, and MixColumns steps into a single round operation.^{[12]}
Until May 2009, the only successful published attacks against the full AES were sidechannel attacks on some specific implementations. The National Security Agency (NSA) reviewed all the AES finalists, including Rijndael, and stated that all of them were secure enough for U.S. Government nonclassified data. In June 2003, the U.S. Government announced that AES could be used to protect 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.^{[13]}
AES has 10 rounds for 128bit keys, 12 rounds for 192bit keys, and 14 rounds for 256bit keys.
By 2006, the best known attacks were on 7 rounds for 128bit keys, 8 rounds for 192bit keys, and 9 rounds for 256bit keys.^{[14]}
For cryptographers, a cryptographic "break" is anything faster than a brute force attack – i.e., performing one trial decryption for each possible key in sequence (see Cryptanalysis). A break can thus include results that are infeasible with current technology; despite being impractical, theoretical breaks can illuminate vulnerability patterns in some cases. The largest successful publicly known brute force attack against any blockcipher encryption was against a 64bit RC5 key by distributed.net in 2006.^{[15]}
The key space to be searched by brute force increases by a factor of 2 for each additional bit of key length (assuming, importantly, random choice of keys) which alone increases the degree of difficulty for a brute force search very rapidly. Mere key length is not, however, regarded as sufficient for security against attack, for there are ciphers with very long keys which have been found vulnerable.
AES has a fairly simple algebraic description.^{[16]} In 2002, a theoretical attack, termed the "XSL attack", was announced by Nicolas Courtois and Josef Pieprzyk, purporting to show a weakness in the AES algorithm due to its simple description.^{[17]} Since then, other papers have shown that the attack as originally presented is unworkable; see XSL attack on block ciphers.
During the AES selection process, developers of competing algorithms wrote of Rijndael, "... we are concerned about [its] use ... in securitycritical applications."^{[18]} However, in October 2000 at the end of the AES selection process, Bruce Schneier, a developer of the competing algorithm Twofish, wrote that while he thought successful academic attacks on Rijndael would be developed someday, he does not "believe that anyone will ever discover an attack that will allow someone to read Rijndael traffic."^{[19]}
On 2009, a new attack was discovered which exploits AES's somewhat simple key schedule and has a complexity of 2^{119}. In December 2009 it was improved to 2^{99.5}. This is a followup to an attack discovered earlier in 2009 by Alex Biryukov, Dmitry Khovratovich, and Ivica Nikolić, with a complexity of 2^{96} for one out of every 2^{35} keys.^{[20]} However, relatedkey attacks are not of concern in any properly designed cryptographic protocol, as a properly designed protocol (i.e., implementational software) will take care not to allow relatedkeys, forcing key choice to be as random as possible.^{[citation needed]}
Another attack was blogged by Bruce Schneier^{[21]} on July 30, 2009 and released as a preprint^{[22]} on August 3, 2009. This new attack, by Alex Biryukov, Orr Dunkelman, Nathan Keller, Dmitry Khovratovich, and Adi Shamir, is against AES256 that uses only two related keys and 2^{39} time to recover the complete 256bit key of a 9round version, or 2^{45} time for a 10round version with a stronger type of related subkey attack, or 2^{70} time for an 11round version. 256bit AES uses 14 rounds, so these attacks aren't effective against full AES.
The practicality of these attacks with stronger related keys has been criticized,^{[23]} for instance, by the paper on "chosenkeyrelationsinthemiddle" attacks on AES128 authored by Vincent Rijmen in 2010.^{[24]}
In November 2009, the first knownkey distinguishing attack against a reduced 8round version of AES128 was released as a preprint.^{[25]} This knownkey distinguishing attack is an improvement of the rebound, or the startfromthemiddle attack, against AESlike permutations, which view two consecutive rounds of permutation as the application of a socalled SuperSbox. It works on the 8round version of AES128, with a time complexity of 2^{48}, and a memory complexity of 2^{32}. 128bit AES uses 10 rounds, so this attack isn't effective against full AES128.
The first keyrecovery attacks on full AES were due to Andrey Bogdanov, Dmitry Khovratovich, and Christian Rechberger, and were published in 2011.^{[26]} The attack is a biclique attack and is faster than brute force by a factor of about four. It requires 2^{126.2} operations to recover an AES128 key. For AES192 and AES256, 2^{190.2} and 2^{254.6} operations are needed, respectively. This result has been further improved to 2^{126.0} for AES128, 2^{189.9} for AES192 and 2^{254.3} for AES256,^{[27]} which are the current best results in key recovery attack against AES.
This is a very small gain, as a 126bit key (instead of 128bits) would still take billions of years to brute force on current and foreseeable hardware. Also, the authors calculate the best attack using their technique on AES with a 128 bit key requires storing 2^{88} bits of data (though this has later been improved to 2^{56},^{[27]} which is 9 petabytes). That works out to about 38 trillion terabytes of data, which is more than all the data stored on all the computers on the planet in 2016. As such this is a seriously impractical attack which has no practical implication on AES security.^{[28]}
According to the Snowden documents, the NSA is doing research on whether a cryptographic attack based on tau statistic may help to break AES.^{[29]}
At present, there are no known practical attacks that would allow anyone to read correctly implemented AES encrypted data.
Sidechannel attacks do not attack the cipher as a black box, and thus are not related to cipher security as defined in the classical context, but are important in practice. They attack implementations of the cipher on hardware or software systems that inadvertently leak data. There are several such known attacks on various implementations of AES.
In April 2005, D.J. Bernstein announced a cachetiming attack that he used to break a custom server that used OpenSSL's AES encryption.^{[30]} The attack required over 200 million chosen plaintexts.^{[31]} The custom server was designed to give out as much timing information as possible (the server reports back the number of machine cycles taken by the encryption operation); however, as Bernstein pointed out, "reducing the precision of the server's timestamps, or eliminating them from the server's responses, does not stop the attack: the client simply uses roundtrip timings based on its local clock, and compensates for the increased noise by averaging over a larger number of samples."^{[30]}
In October 2005, Dag Arne Osvik, Adi Shamir and Eran Tromer presented a paper demonstrating several cachetiming attacks against AES.^{[32]} One attack was able to obtain an entire AES key after only 800 operations triggering encryptions, in a total of 65 milliseconds. This attack requires the attacker to be able to run programs on the same system or platform that is performing AES.
In December 2009 an attack on some hardware implementations was published that used differential fault analysis and allows recovery of a key with a complexity of 2^{32}.^{[33]}
In November 2010 Endre Bangerter, David Gullasch and Stephan Krenn published a paper which described a practical approach to a "near real time" recovery of secret keys from AES128 without the need for either cipher text or plaintext. The approach also works on AES128 implementations that use compression tables, such as OpenSSL.^{[34]} Like some earlier attacks this one requires the ability to run unprivileged code on the system performing the AES encryption, which may be achieved by malware infection far more easily than commandeering the root account.^{[35]}
In March 2016, Ashokkumar C., Ravi Prakash Giri and Bernard Menezes presented a very efficient sidechannel attack on AES that can recover the complete 128bit AES key in just 67 blocks of plaintext/ciphertext which is a substantial improvement over previous works that require between 100 and a million encryptions.^{[36]} The proposed attack require standard user privilege as previous attacks and keyretrieval algorithms run under a minute.
Many modern CPUs have builtin hardware instructions for AES, which would protect against timingrelated sidechannel attacks.^{[37]}^{[38]}
The Cryptographic Module Validation Program (CMVP) is operated jointly by the United States Government's National Institute of Standards and Technology (NIST) Computer Security Division and the Communications Security Establishment (CSE) of the Government of Canada. The use of cryptographic modules validated to NIST FIPS 1402 is required by the United States Government for encryption of all data that has a classification of Sensitive but Unclassified (SBU) or above. From NSTISSP #11, National Policy Governing the Acquisition of Information Assurance: "Encryption products for protecting classified information will be certified by NSA, and encryption products intended for protecting sensitive information will be certified in accordance with NIST FIPS 1402."^{[39]}
The Government of Canada also recommends the use of FIPS 140 validated cryptographic modules in unclassified applications of its departments.
Although NIST publication 197 ("FIPS 197") is the unique document that covers the AES algorithm, vendors typically approach the CMVP under FIPS 140 and ask to have several algorithms (such as Triple DES or SHA1) validated at the same time. Therefore, it is rare to find cryptographic modules that are uniquely FIPS 197 validated and NIST itself does not generally take the time to list FIPS 197 validated modules separately on its public web site. Instead, FIPS 197 validation is typically just listed as an "FIPS approved: AES" notation (with a specific FIPS 197 certificate number) in the current list of FIPS 140 validated cryptographic modules.
The Cryptographic Algorithm Validation Program (CAVP)^{[40]} allows for independent validation of the correct implementation of the AES algorithm at a reasonable cost^{[citation needed]}. Successful validation results in being listed on the NIST validations page.^{[41]} This testing is a prerequisite for the FIPS 1402 module validation described below. However, successful CAVP validation in no way implies that the cryptographic module implementing the algorithm is secure. A cryptographic module lacking FIPS 1402 validation or specific approval by the NSA is not deemed secure by the US Government and cannot be used to protect government data.^{[39]}
FIPS 1402 validation is challenging to achieve both technically and fiscally.^{[42]} There is a standardized battery of tests as well as an element of source code review that must be passed over a period of a few weeks. The cost to perform these tests through an approved laboratory can be significant (e.g., well over $30,000 US)^{[42]} and does not include the time it takes to write, test, document and prepare a module for validation. After validation, modules must be resubmitted and reevaluated if they are changed in any way. This can vary from simple paperwork updates if the security functionality did not change to a more substantial set of retesting if the security functionality was impacted by the change.
Test vectors are a set of known ciphers for a given input and key. NIST distributes the reference of AES test vectors as AES Known Answer Test (KAT) Vectors (in ZIP format).
High speed and low RAM requirements were criteria of the AES selection process. As the chosen algorithm, AES performed well on a wide variety of hardware, from 8bit smart cards to highperformance computers.
On a Pentium Pro, AES encryption requires 18 clock cycles per byte,^{[43]} equivalent to a throughput of about 11 MB/s for a 200 MHz processor. On a 1.7 GHz Pentium M throughput is about 60 MB/s.
On Intel Core i3/i5/i7 and AMD APU and FX CPUs supporting AESNI instruction set extensions, throughput can be over 700 MB/s per thread.^{[44]}