qchapp/MNLP_M3_rag_documents · Datasets at Hugging Face

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wiki_14_chunk_54	Ada (programming language)	Programming languages .NET programming languages Avionics programming languages High Integrity Programming Language Multi-paradigm programming languages Programming language standards Programming languages created in 1980 Programming languages with an ISO standard Statically typed programming languages Systems programming languages 1980 software High-level programming languages	wikipedia
wiki_15_chunk_0	Advanced Encryption Standard	The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.	wikipedia
wiki_15_chunk_1	Advanced Encryption Standard	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.	wikipedia
wiki_15_chunk_2	Advanced Encryption Standard	AES has been adopted by the U.S. government. It supersedes the Data Encryption Standard (DES), 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.	wikipedia
wiki_15_chunk_3	Advanced Encryption Standard	In the United States, AES was announced by the NIST as U.S. FIPS PUB 197 (FIPS 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 (see Advanced Encryption Standard process for more details).	wikipedia
wiki_15_chunk_4	Advanced Encryption Standard	AES is included in the ISO/IEC 18033-3 standard. AES became effective as a U.S. federal government standard on May 26, 2002, after approval by the U.S. Secretary of Commerce. AES is available in many different encryption packages, and is the first (and only) publicly accessible cipher approved by the U.S. National Security Agency (NSA) for top secret information when used in an NSA approved cryptographic module (see Security of AES, below). Definitive standards The Advanced Encryption Standard (AES) is defined in each of:	wikipedia
wiki_15_chunk_5	Advanced Encryption Standard	FIPS PUB 197: Advanced Encryption Standard (AES) ISO/IEC 18033-3: Block ciphers	wikipedia
wiki_15_chunk_6	Advanced Encryption Standard	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.	wikipedia
wiki_15_chunk_7	Advanced Encryption Standard	AES operates on a 4 × 4 column-major order array of bytes, termed the state. Most AES calculations are done in a particular finite field. For instance, 16 bytes, are represented as this two-dimensional array: 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.	wikipedia
wiki_15_chunk_8	Advanced Encryption Standard	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	wikipedia
wiki_15_chunk_9	Advanced Encryption Standard	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. Initial round key addition: each byte of the state is combined with a byte of the round key using bitwise xor. 9, 11 or 13 rounds: a non-linear substitution step where each byte is replaced with another according to a lookup table. a transposition step where the last three rows of the state are shifted cyclically a certain number of steps. a linear mixing operation which operates on the columns of the state, combining the four bytes in each column. Final round (making 10, 12 or 14 rounds in total):	wikipedia
wiki_15_chunk_10	Advanced Encryption Standard	The step	wikipedia
wiki_15_chunk_11	Advanced Encryption Standard	In the step, each byte in the state array is replaced with a using an 8-bit substitution box. Note that 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 (and so is a derangement), i.e., , and also any opposite fixed points, i.e., . While performing the decryption, the step (the inverse of ) is used, which requires first taking the inverse of the affine transformation and then finding the multiplicative inverse.	wikipedia
wiki_15_chunk_12	Advanced Encryption Standard	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	wikipedia
wiki_15_chunk_13	Advanced Encryption Standard	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 left-multiplied by column gives new value of column in the state):	wikipedia
wiki_15_chunk_14	Advanced Encryption Standard	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 (overflow must be corrected by subtraction of generating polynomial). These are special cases of the usual multiplication in .	wikipedia
wiki_15_chunk_15	Advanced Encryption Standard	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 step	wikipedia
wiki_15_chunk_16	Advanced Encryption Standard	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 each byte of the state with the corresponding byte of the subkey using bitwise XOR.	wikipedia
wiki_15_chunk_17	Advanced Encryption Standard	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 (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 step. Alternatively, the table lookup operation can be performed with a single 256-entry 32-bit table (occupying 1024 bytes) followed by circular rotation operations.	wikipedia
wiki_15_chunk_18	Advanced Encryption Standard	Using a byte-oriented approach, it is possible to combine the , , and steps into a single round operation.	wikipedia
wiki_15_chunk_19	Advanced Encryption Standard	Security 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 non-classified 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.	wikipedia
wiki_15_chunk_20	Advanced Encryption Standard	AES has 10 rounds for 128-bit keys, 12 rounds for 192-bit keys, and 14 rounds for 256-bit keys. 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.	wikipedia
wiki_15_chunk_21	Advanced Encryption Standard	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 (see Cryptanalysis). 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.	wikipedia
wiki_15_chunk_22	Advanced Encryption Standard	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. 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.	wikipedia
wiki_15_chunk_23	Advanced Encryption Standard	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.	wikipedia
wiki_15_chunk_24	Advanced Encryption Standard	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."	wikipedia
wiki_15_chunk_25	Advanced Encryption Standard	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 (i.e., implementational software) will take care not to allow related keys, essentially by constraining an attacker's means of selecting keys for relatedness.	wikipedia
wiki_15_chunk_26	Advanced Encryption Standard	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.	wikipedia
wiki_15_chunk_27	Advanced Encryption Standard	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.	wikipedia
wiki_15_chunk_28	Advanced Encryption Standard	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.	wikipedia
wiki_15_chunk_29	Advanced Encryption Standard	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, which are the current best results in key recovery attack against AES.	wikipedia
wiki_15_chunk_30	Advanced Encryption Standard	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 288 bits of data. 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, there are no practical implications on AES security. The space complexity has later been improved to 256 bits, which is 9007 terabytes.	wikipedia
wiki_15_chunk_31	Advanced Encryption Standard	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. Side-channel attacks	wikipedia
wiki_15_chunk_32	Advanced Encryption Standard	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.	wikipedia
wiki_15_chunk_33	Advanced Encryption Standard	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".	wikipedia
wiki_15_chunk_34	Advanced Encryption Standard	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.	wikipedia
wiki_15_chunk_35	Advanced Encryption Standard	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 232.	wikipedia
wiki_15_chunk_36	Advanced Encryption Standard	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.	wikipedia
wiki_15_chunk_37	Advanced Encryption Standard	In March 2016, Ashokkumar C., 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.	wikipedia
wiki_15_chunk_38	Advanced Encryption Standard	NIST/CSEC validation 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 140-2 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 140-2.”	wikipedia
wiki_15_chunk_39	Advanced Encryption Standard	The Government of Canada also recommends the use of FIPS 140 validated cryptographic modules in unclassified applications of its departments.	wikipedia
wiki_15_chunk_40	Advanced Encryption Standard	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.	wikipedia
wiki_15_chunk_41	Advanced Encryption Standard	The Cryptographic Algorithm Validation Program (CAVP) allows for independent validation of the correct implementation of the AES algorithm. Successful validation results in being listed on the NIST validations page. This testing is a pre-requisite for the FIPS 140-2 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 140-2 validation or specific approval by the NSA is not deemed secure by the US Government and cannot be used to protect government data.	wikipedia
wiki_15_chunk_42	Advanced Encryption Standard	FIPS 140-2 validation is challenging to achieve both technically and fiscally. 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) and does not include the time it takes to write, test, document and prepare a module for validation. After validation, modules must be re-submitted and re-evaluated 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 re-testing if the security functionality was impacted by the change.	wikipedia
wiki_15_chunk_43	Advanced Encryption Standard	Test vectors 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. Performance 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 8-bit smart cards to high-performance computers. On a Pentium Pro, AES encryption requires 18 clock cycles per byte, equivalent to a throughput of about 11 MB/s for a 200 MHz processor.	wikipedia
wiki_15_chunk_44	Advanced Encryption Standard	On Intel Core and AMD Ryzen CPUs supporting AES-NI instruction set extensions, throughput can be multiple GB/s (even over 10 GB/s). Implementations See also AES modes of operation Disk encryption Network encryption Whirlpool – hash function created by Vincent Rijmen and Paulo S. L. M. Barreto List of free and open-source software packages Notes References alternate link (companion web site contains online lectures on AES) External links AES algorithm archive information – (old, unmaintained)	wikipedia
wiki_15_chunk_45	Advanced Encryption Standard	Animation of Rijndael – AES deeply explained and animated using Flash (by Enrique Zabala / University ORT / Montevideo / Uruguay). This animation (in English, Spanish, and German) is also part of CrypTool 1 (menu Indiv. Procedures → Visualization of Algorithms → AES). HTML5 Animation of Rijndael – Same Animation as above made in HTML5. Advanced Encryption Standard Cryptography	wikipedia
wiki_16_chunk_0	The Apache Software Foundation	The Apache Software Foundation (ASF) is an American nonprofit corporation (classified as a 501(c)(3) organization in the United States) to support a number of open source software projects. The ASF was formed from a group of developers of the Apache HTTP Server, and incorporated on March 25, 1999. As of 2021, it includes approximately 1000 members.	wikipedia
wiki_16_chunk_1	The Apache Software Foundation	The Apache Software Foundation is a decentralized open source community of developers. The software they produce is distributed under the terms of the Apache License and is a non-copyleft form of free and open-source software (FOSS). The Apache projects are characterized by a collaborative, consensus-based development process and an open and pragmatic software license, which is to say that it allows developers who receive the software freely, to re-distribute it under nonfree terms. Each project is managed by a self-selected team of technical experts who are active contributors to the project. The ASF is a meritocracy, implying that membership of the foundation is granted only to volunteers who have actively contributed to Apache projects. The ASF is considered a second generation open-source organization, in that commercial support is provided without the risk of platform lock-in.	wikipedia
wiki_16_chunk_2	The Apache Software Foundation	Among the ASF's objectives are: to provide legal protection to volunteers working on Apache projects; to prevent the Apache brand name from being used by other organizations without permission. The ASF also holds several ApacheCon conferences each year, highlighting Apache projects and related technology.	wikipedia
wiki_16_chunk_3	The Apache Software Foundation	History The history of the Apache Software Foundation is linked to the Apache HTTP Server, development beginning in February 1993. A group of eight developers started working on enhancing the NCSA HTTPd daemon. They came to be known as the Apache Group. On March 25, 1999, the Apache Software Foundation was formed. The first official meeting of the Apache Software Foundation was held on April 13, 1999. The initial members of the Apache Software Foundation consisted of the Apache Group: Brian Behlendorf, Ken Coar, Miguel Gonzales, Mark Cox, Lars Eilebrecht, Ralf S. Engelschall, Roy T. Fielding, Dean Gaudet, Ben Hyde, Jim Jagielski, Alexei Kosut, Martin Kraemer, Ben Laurie, Doug MacEachern, Aram Mirzadeh, Sameer Parekh, Cliff Skolnick, Marc Slemko, William (Bill) Stoddard, Paul Sutton, Randy Terbush and Dirk-Willem van Gulik. After a series of additional meetings to elect board members and resolve other legal matters regarding incorporation, the effective incorporation date of the Apache Software Foundation was set to June 1, 1999.	wikipedia
wiki_16_chunk_4	The Apache Software Foundation	The foundation states that the name 'Apache' was chosen "from respect for the Native American Apache Nation, well known for their superior skills in warfare strategy and their inexhaustible endurance". Projects	wikipedia
wiki_16_chunk_5	The Apache Software Foundation	Apache divides its software development activities into separate semi-autonomous areas called "top-level projects" (formally known as a "Project Management Committee" in the bylaws), some of which have a number of sub-projects. Unlike some other organizations that host FOSS projects, before a project is hosted at Apache it has to be licensed to the ASF with a grant or contributor agreement. In this way, the ASF gains the necessary intellectual property rights for the development and distribution of all its projects.	wikipedia
wiki_16_chunk_6	The Apache Software Foundation	Board of directors The Board of Directors of The Apache Software Foundation (ASF) is responsible for management and oversight of the business and affairs of the corporation in accordance with the Bylaws. This includes management of the corporate assets (funds, intellectual property, trademarks, and support equipment), appointment of a President and corporate officers managing the core operations of the ASF, and allocation of corporate resources for the benefit of Apache projects. Technical decision-making authority for every Apache project is assigned to their independent project management committee; the participants in each project provide direction, not the board. The board is elected annually by the ASF membership.	wikipedia
wiki_16_chunk_7	The Apache Software Foundation	Since March 17, 2021, the board of directors has been: Bertrand Delacretaz Roy T. Fielding Sharan Foga Justin Mclean Sam Ruby Craig L Russell Roman Shaposhnik Sander Striker Sheng Wu See also List of Apache Software Foundation projects Apache Attic Apache Incubator Log4Shell CNCF Linux Foundation Notes Further reading Wikinomics: How Mass Collaboration Changes Everything (2006); Don Tapscott, Anthony D. Williams. External links ApacheCon website “Trillions and Trillions Served” Feature documentary by the Apache Software Foundation detailing its history and impact on the open-source software community (2020)	wikipedia
wiki_16_chunk_8	The Apache Software Foundation	1999 establishments in Maryland Free and open-source software organizations Non-profit organizations based in Maryland Software companies established in 1999 501(c)(3) organizations	wikipedia
wiki_17_chunk_0	Atanasoff–Berry computer	The Atanasoff–Berry computer (ABC) was the first automatic electronic digital computer. Limited by the technology of the day, and execution, the device has remained somewhat obscure. The ABC's priority is debated among historians of computer technology, because it was neither programmable, nor Turing-complete. Conventionally, the ABC would be considered the first electronic ALU (arithmetic logic unit) which is integrated into every modern processor's design.	wikipedia
wiki_17_chunk_1	Atanasoff–Berry computer	Its unique contribution was to make computing faster by being the first to use vacuum tubes to do the arithmetic calculations. Prior to this, slower electro-mechanical methods were used by the Harvard Mark I and Konrad Zuse's machines. The first electronic, programmable, digital machine, the Colossus computer from 1943 to 1945, used similar tube-based technology as ABC.	wikipedia
wiki_17_chunk_2	Atanasoff–Berry computer	Overview Conceived in 1937, the machine was built by Iowa State College mathematics and physics professor John Vincent Atanasoff with the help of graduate student Clifford Berry. It was designed only to solve systems of linear equations and was successfully tested in 1942. However, its intermediate result storage mechanism, a paper card writer/reader, was not perfected, and when John Vincent Atanasoff left Iowa State College for World War II assignments, work on the machine was discontinued. The ABC pioneered important elements of modern computing, including binary arithmetic and electronic switching elements, but its special-purpose nature and lack of a changeable, stored program distinguish it from modern computers. The computer was designated an IEEE Milestone in 1990.	wikipedia
wiki_17_chunk_3	Atanasoff–Berry computer	Atanasoff and Berry's computer work was not widely known until it was rediscovered in the 1960s, amidst patent disputes over the first instance of an electronic computer. At that time ENIAC, that had been created by John Mauchly and J. Presper Eckert, was considered to be the first computer in the modern sense, but in 1973 a U.S. District Court invalidated the ENIAC patent and concluded that the ENIAC inventors had derived the subject matter of the electronic digital computer from Atanasoff. When, in the mid-1970s, the secrecy surrounding the British World War II development of the Colossus computers that pre-dated ENIAC, was lifted and Colossus was described at a conference in Los Alamos, New Mexico, in June 1976, John Mauchly and Konrad Zuse were reported to have been astonished.	wikipedia
wiki_17_chunk_4	Atanasoff–Berry computer	Design and construction	wikipedia
wiki_17_chunk_5	Atanasoff–Berry computer	According to Atanasoff's account, several key principles of the Atanasoff–Berry computer were conceived in a sudden insight after a long nighttime drive to Rock Island, Illinois, during the winter of 1937–38. The ABC innovations included electronic computation, binary arithmetic, parallel processing, regenerative capacitor memory, and a separation of memory and computing functions. The mechanical and logic design was worked out by Atanasoff over the next year. A grant application to build a proof of concept prototype was submitted in March 1939 to the Agronomy department, which was also interested in speeding up computation for economic and research analysis. $5,000 of further funding () to complete the machine came from the nonprofit Research Corporation of New York City.	wikipedia
wiki_17_chunk_6	Atanasoff–Berry computer	The ABC was built by Atanasoff and Berry in the basement of the physics building at Iowa State College during 1939–1942. The initial funds were released in September, and the 11-tube prototype was first demonstrated in October 1939. A December demonstration prompted a grant for construction of the full-scale machine. The ABC was built and tested over the next two years. A January 15, 1941, story in the Des Moines Register announced the ABC as "an electrical computing machine" with more than 300 vacuum tubes that would "compute complicated algebraic equations" (but gave no precise technical description of the computer). The system weighed more than . It contained approximately of wire, 280 dual-triode vacuum tubes, 31 thyratrons, and was about the size of a desk.	wikipedia
wiki_17_chunk_7	Atanasoff–Berry computer	It was not programmable, which distinguishes it from more general machines of the same era, such as Konrad Zuse's 1941 Z3 and the Colossus computers of 1943–1945. Nor did it implement the stored-program architecture, first implemented in the Manchester Baby of 1948, required for fully general-purpose practical computing machines. The machine was, however, the first to implement three critical ideas that are still part of every modern computer: Using binary digits to represent all numbers and data. Performing all calculations using electronics rather than wheels, ratchets, or mechanical switches. Organizing a system in which computation and memory are separated.	wikipedia
wiki_17_chunk_8	Atanasoff–Berry computer	The memory of the Atanasoff–Berry computer was a system called regenerative capacitor memory, which consisted of a pair of drums, each containing 1600 capacitors that rotated on a common shaft once per second. The capacitors on each drum were organized into 32 "bands" of 50 (30 active bands and two spares in case a capacitor failed), giving the machine a speed of 30 additions/subtractions per second. Data was represented as 50-bit binary fixed-point numbers. The electronics of the memory and arithmetic units could store and operate on 60 such numbers at a time (3000 bits).	wikipedia
wiki_17_chunk_9	Atanasoff–Berry computer	The alternating current power-line frequency of 60 Hz was the primary clock rate for the lowest-level operations.	wikipedia
wiki_17_chunk_10	Atanasoff–Berry computer	The arithmetic logic functions were fully electronic, implemented with vacuum tubes. The family of logic gates ranged from inverters to two- and three-input gates. The input and output levels and operating voltages were compatible between the different gates. Each gate consisted of one inverting vacuum-tube amplifier, preceded by a resistor divider input network that defined the logical function. The control logic functions, which only needed to operate once per drum rotation and therefore did not require electronic speed, were electromechanical, implemented with relays.	wikipedia
wiki_17_chunk_11	Atanasoff–Berry computer	The ALU operated on only one bit of each number at a time; it kept the carry/borrow bit in a capacitor for use in the next AC cycle.	wikipedia
wiki_17_chunk_12	Atanasoff–Berry computer	Although the Atanasoff–Berry computer was an important step up from earlier calculating machines, it was not able to run entirely automatically through an entire problem. An operator was needed to operate the control switches to set up its functions, much like the electro-mechanical calculators and unit record equipment of the time. Selection of the operation to be performed, reading, writing, converting to or from binary to decimal, or reducing a set of equations was made by front-panel switches and, in some cases, jumpers.	wikipedia
wiki_17_chunk_13	Atanasoff–Berry computer	There were two forms of input and output: primary user input and output and an intermediate results output and input. The intermediate results storage allowed operation on problems too large to be handled entirely within the electronic memory. (The largest problem that could be solved without the use of the intermediate output and input was two simultaneous equations, a trivial problem.)	wikipedia
wiki_17_chunk_14	Atanasoff–Berry computer	Intermediate results were binary, written onto paper sheets by electrostatically modifying the resistance at 1500 locations to represent 30 of the 50-bit numbers (one equation). Each sheet could be written or read in one second. The reliability of the system was limited to about 1 error in 100,000 calculations by these units, primarily attributed to lack of control of the sheets' material characteristics. In retrospect, a solution could have been to add a parity bit to each number as written. This problem was not solved by the time Atanasoff left the university for war-related work.	wikipedia
wiki_17_chunk_15	Atanasoff–Berry computer	Primary user input was decimal, via standard IBM 80-column punched cards, and output was decimal, via a front-panel display.	wikipedia
wiki_17_chunk_16	Atanasoff–Berry computer	Function The ABC was designed for a specific purpose the solution of systems of simultaneous linear equations. It could handle systems with up to 29 equations, a difficult problem for the time. Problems of this scale were becoming common in physics, the department in which John Atanasoff worked. The machine could be fed two linear equations with up to 29 variables and a constant term and eliminate one of the variables. This process would be repeated manually for each of the equations, which would result in a system of equations with one fewer variable. Then the whole process would be repeated to eliminate another variable.	wikipedia
wiki_17_chunk_17	Atanasoff–Berry computer	George W. Snedecor, the head of Iowa State's Statistics Department, was very likely the first user of an electronic digital computer to solve real-world mathematics problems. He submitted many of these problems to Atanasoff.	wikipedia
wiki_17_chunk_18	Atanasoff–Berry computer	Patent dispute On June 26, 1947, J. Presper Eckert and John Mauchly were the first to file for patent on a digital computing device (ENIAC), much to the surprise of Atanasoff. The ABC had been examined by John Mauchly in June 1941, and Isaac Auerbach, a former student of Mauchly's, alleged that it influenced his later work on ENIAC, although Mauchly denied this. The ENIAC patent did not issue until 1964, and by 1967 Honeywell sued Sperry Rand in an attempt to break the ENIAC patents, arguing that the ABC constituted prior art. The United States District Court for the District of Minnesota released its judgement on October 19, 1973, finding in Honeywell v. Sperry Rand that the ENIAC patent was a derivative of John Atanasoff's invention.	wikipedia
wiki_17_chunk_19	Atanasoff–Berry computer	Campbell-Kelly and Aspray conclude: The case was legally resolved on October 19, 1973, when U.S. District Judge Earl R. Larson held the ENIAC patent invalid, ruling that the ENIAC derived many basic ideas from the Atanasoff–Berry computer. Judge Larson explicitly stated: Herman Goldstine, one of the original developers of ENIAC wrote: Replica The original ABC was eventually dismantled in 1948, when the university converted the basement to classrooms, and all of its pieces except for one memory drum were discarded.	wikipedia
wiki_17_chunk_20	Atanasoff–Berry computer	In 1997, a team of researchers led by Dr. Delwyn Bluhm and John Gustafson from Ames Laboratory (located on the Iowa State University campus) finished building a working replica of the Atanasoff–Berry computer at a cost of $350,000 (equivalent to $ in ). The replica ABC was on display in the first floor lobby of the Durham Center for Computation and Communication at Iowa State University and was subsequently exhibited at the Computer History Museum. See also History of computing hardware List of vacuum-tube computers Mikhail Kravchuk References Bibliography	wikipedia
wiki_17_chunk_21	Atanasoff–Berry computer	External links The Birth of the ABC Reconstruction of the ABC, 1994-1997 John Gustafson, Reconstruction of the Atanasoff-Berry Computer The ENIAC patent trial Honeywell v. Sperry Rand Records, 1846-1973, Charles Babbage Institute, University of Minnesota. The Atanasoff-Berry Computer In Operation (YouTube) 1940s computers One-of-a-kind computers Vacuum tube computers Computer-related introductions in 1942 History of computing hardware Iowa State University Serial computers	wikipedia
wiki_18_chunk_0	APL (programming language)	APL (named after the book A Programming Language) is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the multidimensional array. It uses a large range of special graphic symbols to represent most functions and operators, leading to very concise code. It has been an important influence on the development of concept modeling, spreadsheets, functional programming, and computer math packages. It has also inspired several other programming languages. History	wikipedia
wiki_18_chunk_1	APL (programming language)	Mathematical notation A mathematical notation for manipulating arrays was developed by Kenneth E. Iverson, starting in 1957 at Harvard University. In 1960, he began work for IBM where he developed this notation with Adin Falkoff and published it in his book A Programming Language in 1962. The preface states its premise: This notation was used inside IBM for short research reports on computer systems, such as the Burroughs B5000 and its stack mechanism when stack machines versus register machines were being evaluated by IBM for upcoming computers.	wikipedia
wiki_18_chunk_2	APL (programming language)	Iverson also used his notation in a draft of the chapter A Programming Language, written for a book he was writing with Fred Brooks, Automatic Data Processing, which would be published in 1963. In 1979, Iverson received the Turing Award for his work on APL. Development into a computer programming language As early as 1962, the first attempt to use the notation to describe a complete computer system happened after Falkoff discussed with William C. Carter his work to standardize the instruction set for the machines that later became the IBM System/360 family.	wikipedia
wiki_18_chunk_3	APL (programming language)	In 1963, Herbert Hellerman, working at the IBM Systems Research Institute, implemented a part of the notation on an IBM 1620 computer, and it was used by students in a special high school course on calculating transcendental functions by series summation. Students tested their code in Hellerman's lab. This implementation of a part of the notation was called Personalized Array Translator (PAT).	wikipedia
wiki_18_chunk_4	APL (programming language)	In 1963, Falkoff, Iverson, and Edward H. Sussenguth Jr., all working at IBM, used the notation for a formal description of the IBM System/360 series machine architecture and functionality, which resulted in a paper published in IBM Systems Journal in 1964. After this was published, the team turned their attention to an implementation of the notation on a computer system. One of the motivations for this focus of implementation was the interest of John L. Lawrence who had new duties with Science Research Associates, an educational company bought by IBM in 1964. Lawrence asked Iverson and his group to help use the language as a tool to develop and use computers in education.	wikipedia
wiki_18_chunk_5	APL (programming language)	After Lawrence M. Breed and Philip S. Abrams of Stanford University joined the team at IBM Research, they continued their prior work on an implementation programmed in FORTRAN IV for a part of the notation which had been done for the IBM 7090 computer running on the IBSYS operating system. This work was finished in late 1965 and later named IVSYS (for Iverson system). The basis of this implementation was described in detail by Abrams in a Stanford University Technical Report, "An Interpreter for Iverson Notation" in 1966, the academic aspect of this was formally supervised by Niklaus Wirth. Like Hellerman's PAT system earlier, this implementation did not include the APL character set but used special English reserved words for functions and operators. The system was later adapted for a time-sharing system and, by November 1966, it had been reprogrammed for the IBM System/360 Model 50 computer running in a time-sharing mode and was used internally at IBM.	wikipedia
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wiki_18_chunk_7	APL (programming language)	A key development in the ability to use APL effectively, before the wide use of cathode ray tube (CRT) terminals, was the development of a special IBM Selectric typewriter interchangeable typing element with all the special APL characters on it. This was used on paper printing terminal workstations using the Selectric typewriter and typing element mechanism, such as the IBM 1050 and IBM 2741 terminal. Keycaps could be placed over the normal keys to show which APL characters would be entered and typed when that key was struck. For the first time, a programmer could type in and see proper APL characters as used in Iverson's notation and not be forced to use awkward English keyword representations of them. Falkoff and Iverson had the special APL Selectric typing elements, 987 and 988, designed in late 1964, although no APL computer system was available to use them. Iverson cited Falkoff as the inspiration for the idea of using an IBM Selectric typing element for the APL character set.	wikipedia
wiki_18_chunk_8	APL (programming language)	Many APL symbols, even with the APL characters on the Selectric typing element, still had to be typed in by over-striking two extant element characters. An example is the grade up character, which had to be made from a delta (shift-H) and a Sheffer stroke (shift-M). This was necessary because the APL character set was much larger than the 88 characters allowed on the typing element, even when letters were restricted to upper-case (capitals).	wikipedia
wiki_18_chunk_9	APL (programming language)	Commercial availability The first APL interactive login and creation of an APL workspace was in 1966 by Larry Breed using an IBM 1050 terminal at the IBM Mohansic Labs near Thomas J. Watson Research Center, the home of APL, in Yorktown Heights, New York.	wikipedia
wiki_18_chunk_10	APL (programming language)	IBM was chiefly responsible for introducing APL to the marketplace. The first publicly available version of APL was released in 1968 for the IBM 1130. IBM provided APL\1130 for free but without liability or support. It would run in as little as 8k 16-bit words of memory, and used a dedicated 1 megabyte hard disk.	wikipedia
wiki_18_chunk_11	APL (programming language)	APL gained its foothold on mainframe timesharing systems from the late 1960s through the early 1980s, in part because it would support multiple users on lower-specification systems that had no dynamic address translation hardware. Additional improvements in performance for selected IBM System/370 mainframe systems included the APL Assist Microcode in which some support for APL execution was included in the processor's firmware, as distinct from being implemented entirely by higher-level software. Somewhat later, as suitably performing hardware was finally growing available in the mid- to late-1980s, many users migrated their applications to the personal computer environment.	wikipedia
wiki_18_chunk_12	APL (programming language)	Early IBM APL interpreters for IBM 360 and IBM 370 hardware implemented their own multi-user management instead of relying on the host services, thus they were their own timesharing systems. First introduced for use at IBM in 1966, the APL\360 system was a multi-user interpreter. The ability to programmatically communicate with the operating system for information and setting interpreter system variables was done through special privileged "I-beam" functions, using both monadic and dyadic operations.	wikipedia
wiki_18_chunk_13	APL (programming language)	In 1973, IBM released APL.SV, which was a continuation of the same product, but which offered shared variables as a means to access facilities outside of the APL system, such as operating system files. In the mid-1970s, the IBM mainframe interpreter was even adapted for use on the IBM 5100 desktop computer, which had a small CRT and an APL keyboard, when most other small computers of the time only offered BASIC. In the 1980s, the VSAPL program product enjoyed wide use with Conversational Monitor System (CMS), Time Sharing Option (TSO), VSPC, MUSIC/SP, and CICS users.	wikipedia
wiki_18_chunk_14	APL (programming language)	In 1973–1974, Patrick E. Hagerty directed the implementation of the University of Maryland APL interpreter for the 1100 line of the Sperry UNIVAC 1100/2200 series mainframe computers. At the time, Sperry had nothing. In 1974, student Alan Stebbens was assigned the task of implementing an internal function. Xerox APL was available from June 1975 for Xerox 560 and Sigma 6, 7, and 9 mainframes running CP-V and for Honeywell CP-6.	wikipedia
wiki_18_chunk_15	APL (programming language)	In the 1960s and 1970s, several timesharing firms arose that sold APL services using modified versions of the IBM APL\360 interpreter. In North America, the better-known ones were IP Sharp Associates, Scientific Time Sharing Corporation (STSC), Time Sharing Resources (TSR), and The Computer Company (TCC). CompuServe also entered the market in 1978 with an APL Interpreter based on a modified version of Digital Equipment Corp and Carnegie Mellon's, which ran on DEC's KI and KL 36-bit machines. CompuServe's APL was available both to its commercial market and the consumer information service. With the advent first of less expensive mainframes such as the IBM 4300, and later the personal computer, by the mid-1980s, the timesharing industry was all but gone.	wikipedia
wiki_18_chunk_16	APL (programming language)	Sharp APL was available from IP Sharp Associates, first as a timesharing service in the 1960s, and later as a program product starting around 1979. Sharp APL was an advanced APL implementation with many language extensions, such as packages (the ability to put one or more objects into a single variable), file system, nested arrays, and shared variables.	wikipedia
wiki_18_chunk_17	APL (programming language)	APL interpreters were available from other mainframe and mini-computer manufacturers also, notably Burroughs, Control Data Corporation (CDC), Data General, Digital Equipment Corporation (DEC), Harris, Hewlett-Packard (HP), Siemens, Xerox and others.	wikipedia
wiki_18_chunk_18	APL (programming language)	Garth Foster of Syracuse University sponsored regular meetings of the APL implementers' community at Syracuse's Minnowbrook Conference Center in Blue Mountain Lake, New York. In later years, Eugene McDonnell organized similar meetings at the Asilomar Conference Grounds near Monterey, California, and at Pajaro Dunes near Watsonville, California. The SIGAPL special interest group of the Association for Computing Machinery continues to support the APL community.	wikipedia
wiki_18_chunk_19	APL (programming language)	Microcomputers On microcomputers, which became available from the mid 1970s onwards, BASIC became the dominant programming language. Nevertheless, some microcomputers provided APL instead - the first being the Intel 8008-based MCM/70 which was released in 1974 and which was primarily used in education. Another machine of this time was the VideoBrain Family Computer, released in 1977, which was supplied with its dialect of APL called APL/S. The Commodore SuperPET, introduced in 1981, included an APL interpreter developed by the University of Waterloo.	wikipedia
wiki_18_chunk_20	APL (programming language)	In 1976, Bill Gates claimed in his Open Letter to Hobbyists that Microsoft Corporation was implementing APL for the Intel 8080 and Motorola 6800 but had "very little incentive to make [it] available to hobbyists" because of software piracy. It was never released.	wikipedia
wiki_18_chunk_21	APL (programming language)	APL2 Starting in the early 1980s, IBM APL development, under the leadership of Jim Brown, implemented a new version of the APL language that contained as its primary enhancement the concept of nested arrays, where an array can contain other arrays, and new language features which facilitated integrating nested arrays into program workflow. Ken Iverson, no longer in control of the development of the APL language, left IBM and joined I. P. Sharp Associates, where one of his major contributions was directing the evolution of Sharp APL to be more in accord with his vision. APL2 was first released for CMS and TSO in 1984. The APL2 Workstation edition (Windows, OS/2, AIX, Linux, and Solaris) followed later.	wikipedia

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Programming languages .NET programming languages Avionics programming languages High Integrity Programming Language Multi-paradigm programming languages Programming language standards Programming languages created in 1980 Programming languages with an ISO standard Statically typed programming languages Systems programming languages 1980 software High-level programming languages

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The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.

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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.

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AES has been adopted by the U.S. government. It supersedes the Data Encryption Standard (DES), 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.

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In the United States, AES was announced by the NIST as U.S. FIPS PUB 197 (FIPS 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 (see Advanced Encryption Standard process for more details).

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AES is included in the ISO/IEC 18033-3 standard. AES became effective as a U.S. federal government standard on May 26, 2002, after approval by the U.S. Secretary of Commerce. AES is available in many different encryption packages, and is the first (and only) publicly accessible cipher approved by the U.S. National Security Agency (NSA) for top secret information when used in an NSA approved cryptographic module (see Security of AES, below). Definitive standards The Advanced Encryption Standard (AES) is defined in each of:

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FIPS PUB 197: Advanced Encryption Standard (AES) ISO/IEC 18033-3: Block ciphers

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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.

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AES operates on a 4 × 4 column-major order array of bytes, termed the state. Most AES calculations are done in a particular finite field. For instance, 16 bytes, are represented as this two-dimensional array: 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.

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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

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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. Initial round key addition: each byte of the state is combined with a byte of the round key using bitwise xor. 9, 11 or 13 rounds: a non-linear substitution step where each byte is replaced with another according to a lookup table. a transposition step where the last three rows of the state are shifted cyclically a certain number of steps. a linear mixing operation which operates on the columns of the state, combining the four bytes in each column. Final round (making 10, 12 or 14 rounds in total):

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The step

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In the step, each byte in the state array is replaced with a using an 8-bit substitution box. Note that 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 (and so is a derangement), i.e., , and also any opposite fixed points, i.e., . While performing the decryption, the step (the inverse of ) is used, which requires first taking the inverse of the affine transformation and then finding the multiplicative inverse.

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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

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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 left-multiplied by column gives new value of column in the state):

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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 (overflow must be corrected by subtraction of generating polynomial). These are special cases of the usual multiplication in .

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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 step

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

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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 (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 step. Alternatively, the table lookup operation can be performed with a single 256-entry 32-bit table (occupying 1024 bytes) followed by circular rotation operations.

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Using a byte-oriented approach, it is possible to combine the , , and steps into a single round operation.

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Security 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 non-classified 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.

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AES has 10 rounds for 128-bit keys, 12 rounds for 192-bit keys, and 14 rounds for 256-bit keys. 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.

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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 (see Cryptanalysis). 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.

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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. 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.

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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.

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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."

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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 (i.e., implementational software) will take care not to allow related keys, essentially by constraining an attacker's means of selecting keys for relatedness.

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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.

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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.

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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.

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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, which are the current best results in key recovery attack against AES.

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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 288 bits of data. 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, there are no practical implications on AES security. The space complexity has later been improved to 256 bits, which is 9007 terabytes.

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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. 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.

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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".

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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.

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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 232.

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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.

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In March 2016, Ashokkumar C., 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.

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NIST/CSEC validation 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 140-2 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 140-2.”

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The Government of Canada also recommends the use of FIPS 140 validated cryptographic modules in unclassified applications of its departments.

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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.

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The Cryptographic Algorithm Validation Program (CAVP) allows for independent validation of the correct implementation of the AES algorithm. Successful validation results in being listed on the NIST validations page. This testing is a pre-requisite for the FIPS 140-2 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 140-2 validation or specific approval by the NSA is not deemed secure by the US Government and cannot be used to protect government data.

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FIPS 140-2 validation is challenging to achieve both technically and fiscally. 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) and does not include the time it takes to write, test, document and prepare a module for validation. After validation, modules must be re-submitted and re-evaluated 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 re-testing if the security functionality was impacted by the change.

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Test vectors 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. Performance 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 8-bit smart cards to high-performance computers. On a Pentium Pro, AES encryption requires 18 clock cycles per byte, equivalent to a throughput of about 11 MB/s for a 200 MHz processor.

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On Intel Core and AMD Ryzen CPUs supporting AES-NI instruction set extensions, throughput can be multiple GB/s (even over 10 GB/s). Implementations See also AES modes of operation Disk encryption Network encryption Whirlpool – hash function created by Vincent Rijmen and Paulo S. L. M. Barreto List of free and open-source software packages Notes References alternate link (companion web site contains online lectures on AES) External links AES algorithm archive information – (old, unmaintained)

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Animation of Rijndael – AES deeply explained and animated using Flash (by Enrique Zabala / University ORT / Montevideo / Uruguay). This animation (in English, Spanish, and German) is also part of CrypTool 1 (menu Indiv. Procedures → Visualization of Algorithms → AES). HTML5 Animation of Rijndael – Same Animation as above made in HTML5. Advanced Encryption Standard Cryptography

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