Advanced Encryption Standard

The S; ij</sub>'' = ''S''(''a_ij'')"}},"i":0}}]}'/>bij = S(aij).

In the SubByte S(ai,j) ≠ ai,j, and also any opposite fixed points, i.e., 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. In this way, each column of the output state of the c(x).

In the ShiftRows, x. Addition is simply XOR. Multiplication is modulo irreducible polynomial GF(2) and is then multiplied modulo c(z)=0316⋅z3+0116⋅z2+0116⋅z+0216. The coefficients are displayed in their hexadecimal equivalent of the binary representation of bit polynomials from GF(2). This process is described further in the article Rijndael MixColumns.

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

Optimization of the cipher

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On systems with 32-bit or larger words, it is possible to speed up execution of this cipher by combining the MixColumns step by transforming them into a sequence of table lookups. This requires four 256-entry 32-bit tables (together occupying 4096 bytes). 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 ShiftRows, and (see Cryptanalysis § Computational resources required). 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 [its] 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 2. In December 2009 it was improved to 2. This is a follow-up to an attack discovered earlier in 2009 by Alex Biryukov, Dmitry Khovratovich, and Ivica Nikolić, with a complexity of 2 for one out of every 2 keys. However, related-key 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 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 2 time to recover the complete 256-bit key of a 9-round version, or 2 time for a 10-round version with a stronger type of related subkey attack, or 2 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 2, and a memory complexity of 2. 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 2 operations to recover an AES-128 key. For AES-192 and AES-256, 2 and 2 operations are needed, respectively. This result has been further improved to 2 for AES-128, 2 for AES-192, and 2 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 (instead of 128 bits) 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 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 2 bits, which is 9007 terabytes (while still keeping a time complexity of approximately 2).

According to the Snowden documents, the NSA is doing research on whether a cryptographic attack based on tau statistic may help to break AES.

As of 2026, there is no known practical attack that would allow someone without knowledge of the key to read data encrypted by AES when correctly implemented.

Side-channel attacks

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Side-channel 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 cache-timing attack that he used to break a custom server that used OpenSSL's AES encryption. The attack required over 200 million chosen plaintexts. 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 round-trip timings based on its local clock, and compensates for the increased noise by averaging over a larger number of samples."

In October 2005, Dag Arne Osvik, Adi Shamir and Eran Tromer presented a paper demonstrating several cache-timing attacks against the implementations in AES found in OpenSSL and Linux's dm-crypt partition encryption function. 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.

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 AES-128 without the need for either cipher text or plaintext. The approach also works on AES-128 implementations that use compression tables, such as OpenSSL. 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.

In March 2016, C. Ashokkumar, Ravi Prakash Giri and Bernard Menezes presented a side-channel attack on AES implementations that can recover the complete 128-bit AES key in just 6–7 blocks of plaintext/ciphertext, which is a substantial improvement over previous works that require between 100 and a million encryptions. The proposed attack requires standard user privilege and key-retrieval algorithms run under a minute.

Many modern CPUs have built-in hardware instructions for AES, which protect against timing-related side-channel attacks.

Quantum attacks

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AES-128,AES-192, and AES-256 are widely believed to be quantum resistant: that is, there are no quantum attacks that are substantially more efficient than existing classical attacks. There is a common misconception that quantum computers can recover 1.3 cpb for AES-128, and

See also

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• AES modes of operation
• Disk encryption
• Whirlpool – hash function created by Vincent Rijmen and Paulo S. L. M. Barreto
• List of free and open-source software packages

Notes

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n−1 bytes. For a 256-bit 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 256-bit block, as AES does not use 256-bit blocks.

↑ The AES Known Answer Test (KAT) Vectors are available in Zip format within the NIST site here Archived 2009-10-23 at the Wayback Machine

References

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Bruce Schneier (July 30, 2009). "Another New AES Attack". Schneier on Security, A blog covering security and security technology. Archived from the original on October 5, 2009. Retrieved March 11, 2010.

↑ "Announcing the ADVANCED ENCRYPTION STANDARD (AES)" (PDF). Federal Information Processing Standards Publication 197. United States National Institute of Standards and Technology (NIST). November 26, 2001. Archived (PDF) from the original on August 23, 2024. Retrieved August 26, 2024.

↑ Westlund, Harold B. (2002). "NIST reports measurable success of Advanced Encryption Standard". Journal of Research of the National Institute of Standards and Technology.

↑ "byte-oriented-aes – A public domain byte-oriented implementation of AES in C – Google Project Hosting". Archived from the original on July 20, 2013. Retrieved December 23, 2012.

↑ Ou, George (April 30, 2006). "Is encryption really crackable?". Ziff-Davis. Archived from the original on August 8, 2010. Retrieved August 7, 2010.

↑ Ferguson, Niels; Schroeppel, Richard; Whiting, Doug (2001). "A simple algebraic representation of Rijndael". In Vaudenay, Serge; Youssef, Amr M. (eds.). Proceedings of Selected Areas in Cryptography, 2001. Lecture Notes in Computer Science. Vol. 2259. Springer-Verlag. pp. 103–111. doi:10.1007/3-540-45537-X_8. ISBN 978-3-540-45537-0. Archived from the original on November 4, 2006.

↑ Bruce Schneier, AES Announced Archived 2009-02-01 at the Wayback Machine, October 15, 2000

↑ John Kelsey, Stefan Lucks, Bruce Schneier, Mike Stay, David Wagner, and Doug Whiting, Improved Cryptanalysis of Rijndael, Fast Software Encryption, 2000 pp213–230 Alex Biryukov; Orr Dunkelman; Nathan Keller; Dmitry Khovratovich; Adi Shamir (August 19, 2009). "Key Recovery Attacks of Practical Complexity on AES Variants With Up To 10 Rounds". Archived from the original on January 28, 2010. Retrieved March 11, 2010.

↑ Henri Gilbert; Thomas Peyrin (November 9, 2009). "Super-Sbox Cryptanalysis: Improved Attacks for AES-like permutations". IACR Cryptology ePrint Archive. Archived from the original on June 4, 2010. Retrieved March 11, 2010.

↑ Jeffrey Goldberg (August 18, 2011). "AES Encryption isn't Cracked". Archived from the original on January 8, 2015. Retrieved December 30, 2014.

↑ "Index of formal scientific papers". Cr.yp.to. Archived from the original on September 17, 2008. Retrieved November 2, 2008.

↑ "Breaking AES-128 in realtime, no ciphertext required". Hacker News. Archived from the original on October 3, 2011. Retrieved December 23, 2012.

↑ "NSTISSP No. 11, Revised Fact Sheet, National Information Assurance Acquisition Policy" (PDF). Archived from the original (PDF) on April 21, 2012. Retrieved May 29, 2012.

↑ OpenSSL, openssl@openssl.org. "OpenSSL's Notes about FIPS certification". Openssl.org. Archived from the original on January 2, 2013. Retrieved December 23, 2012.

↑ "Intel Advanced Encryption Standard (AES) New Instructions Set" (PDF). May 2010.

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