Advanced Encryption Standard


The Advanced Encryption Standard, also known by its original name Rijndael, is a specification for the encryption of electronic data established by the US National Institute of Standards and Technology in 2001.
AES is a variant of the Rijndael block cipher developed by two Belgian cryptographers, Joan Daemen and Vincent Rijmen, who submitted a proposal to NIST during the AES selection process. 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 US government. It supersedes the Data Encryption Standard, which was published in 1977. The algorithm described by AES is a symmetric-key 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 US FIPS PUB 197 on November 26, 2001. This announcement followed a five-year standardization process in which fifteen competing designs were presented and evaluated, before the Rijndael cipher was selected as the most suitable.
AES is included in the ISO/IEC 18033-3 standard. AES became effective as a US federal government standard on May 26, 2002, after approval by US Secretary of Commerce Donald Evans. AES is available in many different encryption packages, and is the first publicly accessible cipher approved by the US National Security Agency for top secret information when used in an NSA approved cryptographic module.

Definitive standards

The Advanced Encryption Standard is defined in each of:
  • FIPS PUB 197: Advanced Encryption Standard
  • ISO/IEC 18033-3: Block ciphers

    Description of the ciphers

AES is based on a design principle known as a substitution–permutation network, and is efficient in both software and hardware. Unlike its predecessor DES, AES does not use a Feistel network. AES is a variant of Rijndael, with a fixed block size of 128 bits, and a key size of 128, 192, or 256 bits. By contrast, Rijndael per se is specified with block and key sizes that may be any multiple of 32 bits, with a minimum of 128 and a maximum of 256 bits. Most AES calculations are done in a particular finite field.
AES operates on a 4 × 4 column-major order array of 16 bytes termed the state:
The key size used for an AES cipher specifies the number of transformation rounds that convert the input, called the plaintext, into the final output, called the ciphertext. The number of rounds are as follows:
  • 10 rounds for 128-bit keys;
  • 12 rounds for 192-bit keys;
  • 14 rounds for 256-bit keys.
Each round consists of several processing steps, 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.

High-level description of the algorithm

  1. round keys are derived from the cipher key using the AES key schedule. AES requires a separate 128-bit round key block for each round plus one more.
  2. Initial round key addition:
  3. # each byte of the state is combined with a byte of the round key using bitwise xor.
  4. 9, 11 or 13 rounds:
  5. # a non-linear substitution step where each byte is replaced with another according to a lookup table.
  6. # a transposition step where the last three rows of the state are shifted cyclically a certain number of steps.
  7. # a linear mixing operation which operates on the columns of the state, combining the four bytes in each column.
  8. #
  9. Final round :
  10. #
  11. #
  12. #

    The step

In the step, each byte in the state array is replaced with a using an 8-bit substitution box. Before round 0, the state array is simply the plaintext/input. This operation provides the non-linearity in the cipher. The S-box used is derived from the multiplicative inverse over, 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, i.e.,, and also any opposite fixed points, i.e.,.
While performing the decryption, the step is used, which requires first taking the inverse of the affine transformation and then finding the multiplicative inverse.

The step

The 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 step is composed of bytes from each column of the input state. The importance of this step is to avoid the columns being encrypted independently, in which case AES would degenerate into four independent block ciphers.

The step

In the step, the four bytes of each column of the state are combined using an invertible linear transformation. The function takes four bytes as input and outputs four bytes, where each input byte affects all four output bytes. Together with, provides diffusion in the cipher.
During this operation, each column is transformed using a fixed matrix :
Matrix multiplication is composed of multiplication and addition of the entries. Entries are 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 1B16 should be performed if the shifted value is larger than FF16. 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 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 MixColumns.

The

In the 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 of the state with the corresponding byte of the subkey using bitwise XOR.

Optimization of the cipher

On systems with 32-bit or larger words, it is possible to speed up execution of this cipher by combining the and steps with the step by transforming them into a sequence of table lookups. This requires four 256-entry 32-bit tables. A round can then be performed with 16 table lookup operations and 12 32-bit exclusive-or operations, followed by four 32-bit exclusive-or operations in the step. Alternatively, the table lookup operation can be performed with a single 256-entry 32-bit table followed by circular rotation operations.
Using a byte-oriented approach, it is possible to combine the,, and steps into a single round operation.

Security

The National Security Agency 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 could be used to protect classified information:
AES has 10 rounds for 128-bit keys, 12 rounds for 192-bit keys, and 14 rounds for 256-bit keys.

Known attacks

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. A break can thus include results that are infeasible with current technology. Despite being impractical, theoretical breaks can sometimes provide insight into vulnerability patterns. The largest successful publicly known brute-force attack against a widely implemented block-cipher encryption algorithm was against a 64-bit RC5 key by distributed.net in 2006.
The key space increases by a factor of 2 for each additional bit of key length, and if every possible value of the key is equiprobable; this translates into a doubling of the average brute-force key search time with every additional bit of key length. This implies that the effort of a brute-force search increases exponentially with key length. Key length in itself does not imply security against attacks, since there are ciphers with very long keys that have been found to be vulnerable.
AES has a fairly simple algebraic framework. In 2002, a theoretical attack, named the "XSL attack", was announced by Nicolas Courtois and Josef Pieprzyk, purporting to show a weakness in the AES algorithm, partially due to the low complexity of its nonlinear components. 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's algorithm "we are concerned about use ... in security-critical applications." In October 2000, however, 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 "did not believe that anyone will ever discover an attack that will allow someone to read Rijndael traffic."
By 2006, the best known attacks were on 7 rounds for 128-bit keys, 8 rounds for 192-bit keys, and 9 rounds for 256-bit keys.
Until May 2009, the only successful published attacks against the full AES were side-channel attacks on some specific implementations. In 2009, a new related-key attack was discovered that exploits the simplicity of AES's key schedule and has a complexity of 2119. In December 2009 it was improved to 299.5. This is a follow-up to an attack discovered earlier in 2009 by Alex Biryukov, Dmitry Khovratovich, and Ivica Nikolić, with a complexity of 296 for one out of every 235 keys. However, related-key attacks are not of concern in any properly designed cryptographic protocol, as a properly designed protocol will take care not to allow related keys, essentially by constraining an attacker's means of selecting keys for relatedness.
Another attack was blogged by Bruce Schneier
on July 30, 2009, and released as a preprint
on August 3, 2009. This new attack, by Alex Biryukov, Orr Dunkelman, Nathan Keller, Dmitry Khovratovich, and Adi Shamir, is against AES-256 that uses only two related keys and 239 time to recover the complete 256-bit key of a 9-round version, or 245 time for a 10-round version with a stronger type of related subkey attack, or 270 time for an 11-round version. 256-bit AES uses 14 rounds, so these attacks are not effective against full AES.
The practicality of these attacks with stronger related keys has been criticized, for instance, by the paper on chosen-key-relations-in-the-middle attacks on AES-128 authored by Vincent Rijmen in 2010.
In November 2009, the first known-key distinguishing attack against a reduced 8-round version of AES-128 was released as a preprint.
This known-key distinguishing attack is an improvement of the rebound, or the start-from-the-middle attack, against AES-like permutations, which view two consecutive rounds of permutation as the application of a so-called Super-S-box. It works on the 8-round version of AES-128, with a time complexity of 248, and a memory complexity of 232. 128-bit AES uses 10 rounds, so this attack is not effective against full AES-128.
The first key-recovery attacks on full AES were by Andrey Bogdanov, Dmitry Khovratovich, and Christian Rechberger, and were published in 2011. The attack is a biclique attack and is faster than brute force by a factor of about four. It requires 2126.2 operations to recover an AES-128 key. For AES-192 and AES-256, 2190.2 and 2254.6 operations are needed, respectively. This result has been further improved to 2126.0 for AES-128, 2189.9 for AES-192, and 2254.3 for AES-256 by Biaoshuai Tao and Hongjun Wu in a 2015 paper, which are the current best results in key recovery attack against AES.
This is a very small gain, as a 126-bit key 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 288 bits of data. That works out to about 38 trillion terabytes of data, which was more than all the data stored on all the computers on the planet in 2016. A paper in 2015 later improved the space complexity to 256 bits, which is 9007 terabytes.
According to the Snowden documents, the NSA is doing research on whether a cryptographic attack based on tau statistic may help to break AES.
At present, there is no known practical attack that would allow someone without knowledge of the key to read data encrypted by AES when correctly implemented.