title: Mitchell Robinson

text: As a junior, Robinson led the Owls to their first state playoff win in 19 years, and in the second round, helped give the first seed and eventual state champion Natchitoches Central High School all they could handle before bowing out, their closest playoff game until the state final. He averaged 20.9 points, 13.6 rebounds, 8.1 blocks, and 2 steals per game. He made the all-district, all-Metro, and all-State teams for his efforts. Robinson then joined Dallas-based Nike Pro Skills on the AAU circuit for the summer, winning individual honors in the Nike EYBL and leading Pro Skills to the season-ending Peach Jam. His recruiting ranking shot up, and he earned his fifth star. Against the top players in the country, Robinson averaged 15.5 points, 11.6 rebounds, and 4.1 blocks per game, being named to the All-EYBL second team.


title: Mitchell Robinson

text: As a senior at Chalmette, Robinson averaged 25.7 points, 12.6 rebounds, and 6 blocked shots per outing, while earning Naismith Trophy All-America honorable mention and MaxPreps All-America honorable mention status as well as "USA Today" All-USA Louisiana first team honors and being named All-District, All-Metro, All-State, and the All-Metro Player of the Year from the "New Orleans Advocate", as well as the "St. Bernard Post" Male Athlete of the Year for the parish. He led Chalmette to their first district championship in their own regular season tournament in 20 years, first district title in 21 years in the toughest basketball district in the state, and to the state semifinals for the first time in 32 years. In the Owls' 4 game state playoff run, Robinson averaged 34.5 points, 13.5 rebounds, and 7.8 blocks. Robinson became the first Chalmette basketball player to be named a McDonald's All-American, and also played in the Jordan Brand Classic and the LHSBCA All-Star game.


title: Mitchell Robinson

text: Playing in the 2017 McDonald's All-American Boys Game, Robinson tallied 14 points, three rebounds and two blocked shots. He participated in the 2017 Jordan Brand Classic, scoring 15 points in 17 minutes of play, while pulling down three rebounds.


title: Mitchell Robinson

text: Robinson originally committed to play college basketball at Texas A&M, but then de-committed to follow coach Rick Stansbury to Western Kentucky. Stansbury had recruited Robinson as the Aggies' assistant coach. Basketball writer Jason Frakes wrote in February 2017, Robinson "may go down as the biggest recruiting coup in WKU basketball history."


title: Mitchell Robinson

text: In July 2017, Robinson had enrolled at Western Kentucky University for the summer semester, and practiced with the team for about two weeks before a planned team trip to Costa Rica. Sources then indicated that he had left campus, and his room was cleaned out. He was then suspended indefinitely for violating the team rules. After speaking with head coach Rick Stansbury, he was granted a release to transfer, and barring an unexpected decision by the NCAA, would have had to sit out the 2017–18 season.


title: Mitchell Robinson

text: With the hope that a waiver would be granted by the NCAA, Robinson took visits to Louisiana State University, University of Kansas, and the University of New Orleans in August 2017. On August 27, Robinson returned to Western Kentucky a month after leaving campus.


title: Mitchell Robinson

text: On September 18, Robinson announced he would forgo college and prepare for the 2018 NBA draft on his own accord. He would be the first recruited draft pick to wind up not playing for any college, professional, or high school/postgraduate team throughout an entire year before entering an NBA draft, although he would still be credited as coming out of Western Kentucky by the NBA. Furthermore, because of his brief time going to summer classes in Western Kentucky, he was ultimately barred from participating in the NBA G League later in the season due to G League rules. The ruling also affected a few similar prospects who were stuck in difficult situations at the time as well, like Billy Preston and De'Anthony Melton. The announcement also influenced at least one person to train by themselves for a year before entering an NBA draft, as fellow five-star recruit Darius Bazley originally planned on not going to college at Syracuse University in order to try out for the NBA G League before deciding against that as well, claiming that it was the only league where winning does not matter after all.


title: Mitchell Robinson

text: Robinson was named one of 69 players who planned to participate in the NBA Draft Combine. However, on the day of the event, Robinson withdrew from all combine events.


title: Mitchell Robinson

text: On June 21, 2018, Robinson was selected with the 36th overall pick in the 2018 NBA draft by the New York Knicks. After appearing for the Knicks in the 2018 NBA Summer League, where he set summer league records for blocked shots and offensive rebounds, he signed a multi-year, rookie scale contract with the Knicks on July 8, 2018. After struggling with an ankle injury during the preseason, Robinson would make his professional debut on October 17, scoring two points in a 127–106 win against the Atlanta Hawks. Robinson made his first start on October 26, recording seven points and six rebounds in 29 minutes of action in a 128–100 loss to the Golden State Warriors. On November 2, Robinson recorded his first double-double with 13 points and 10 rebounds, alongside three assists and three steals, in a 118–106 win over the Dallas Mavericks. On November 11, Robinson set the Knicks' rookie record with nine blocks in a 115–89 loss to the Orlando Magic. On March 28, 2019, Robinson recorded season highs of 19 points and 21 rebounds in the Knicks' 117–92 loss to the Toronto Raptors, and became the first Knicks' rookie since Willis Reed in 1965 to record 19 points and 21 rebounds in a game. On April 9, he recorded eight points and 17 rebounds in a 96–86 win over the Chicago Bulls. Robinson finished the season second in the NBA in blocked shots per game, only behind Myles Turner of the Indiana Pacers, and was named to the All-Rookie Second Team.


title: Mitchell Robinson

text: On December 17, 2019, Robinson scored a career-high 22 points and recorded 13 rebounds in a 143–120 win against the Hawks. On January 1, 2020, Robinson scored 22 points on perfect 11-of-11 shooting from the field in a 117–93 win against the Portland Trail Blazers. On February 26, Robinson recorded a double-double with 12 points and a season-high 16 rebounds in a 108–101 loss to the Charlotte Hornets. When the 2019–20 regular season finished, Robinson broke Wilt Chamberlain's NBA record for highest field goal percentage in a single season.


title: Mitchell Robinson

text: On February 12, 2021, in the Knicks' game against the Washington Wizards, Robinson fractured his right hand during the second quarter and did not return after halftime.


title: Mitchell Robinson

text: Robinson was named to the preliminary roster of the United States national under-19 team in 2017, but did not make the final cut for the 12-men squad for the 2017 FIBA Under-19 Basketball World Cup.


title: Mitchell Robinson

text: Robinson has been called by some analysts "the best shot blocker in his class", with uncommon closing speed and a long reach that led to numerous highlight reel blocks. He uses that speed also to run the fast break exceptionally well for a big man of his size, being called the "most entertaining player" in the New Orleans area for his ability to convert alley-oop dunks. Robinson improved his free throw shooting over the course of his two years at Chalmette, and developed range from behind the three point line, making as many as 5 in a game. NBA draft projections have compared his game to DeAndre Jordan and Tyson Chandler.


title: Oscar Schmidt

text: Oscar Daniel Bezerra Schmidt (born February 16, 1958) is a retired Brazilian professional basketball player. He is also commonly known as Oscar Schmidt in Spain, where he played for Fórum Valladolid for the 1993–94 and 1994–95 seasons, and simply Oscar, or "Mão Santa" (Holy Hand), in his homeland. Schmidt primarily played the shooting guard and small forward position, was 2.05 m (6 ft 8 in) tall and weighed 110 kg (243 lbs). He was born in Natal, Rio Grande do Norte, Brazil.


title: Oscar Schmidt

text: He is considered to be the all-time leading scorer in the history of basketball, with 49,737 career points scored (pro club league play, plus senior Brazilian national team play combined). He is the record holder for the longest career span of a professional basketball player at 29 years. He is also the top scorer in the history of the Summer Olympic Games, and the top scorer in the history of the FIBA World Cup.


title: Oscar Schmidt

text: He was named one of FIBA's 50 Greatest Players in 1991. He received the Olympic Order in 1997. On August 20, 2010, Schmidt became a FIBA Hall of Fame player, in recognition of his play in international competitions. On September 8, 2013, Schmidt was inducted into the Naismith Memorial Basketball Hall of Fame. He was inducted into the Italian Basketball Hall of Fame in 2017.


title: Oscar Schmidt

text: Schmidt played youth club basketball in the youth systems of S.E. Palmeiras and Mackenzie College. With Palmeiras' youth teams, he scored 2,114 points in 85 games, for a scoring average of 24.9 points per game. With Mackenzie's youth teams, he scored 1,332 points in 36 games, for a scoring average of 37.0 points per game.


title: Oscar Schmidt

text: Schmidt began his professional club career in 1974, at the age of 16, with the Brazilian Championship club S.E. Palmeiras. As a member of Palmeiras, he won the São Paulo State Championship in 1974, and the Brazilian Championship in 1977.


title: Oscar Schmidt

text: In 1978, he moved to the Brazilian club E.C. Sírio. As a member of Sírio, Schmidt won the São Paulo State Championship in both 1978 and 1979, and the Brazilian Championship in 1979. With Sírio, he also won the South American Club Championship, and the FIBA Intercontinental Cup title in 1979. He scored 42 points in the 1979 FIBA Intercontinental Cup's Final against the Yugoslav First Federal League club Bosna Sarajevo. Schmidt was the top scorer of the Brazilian Championship in both 1979 and 1980.


title: Oscar Schmidt

text: In 1982, Schmidt joined the Brazilian club América do Rio. However, he only stayed with the club for a brief amount of time.


title: Oscar Schmidt

text: For the 1982–83 season, Schmidt joined the Italian 2nd Division club JuveCaserta. With JuveCaserta, he played in the first division level Italian League, for the first time in the 1983–84 season. That same season, Schmidt played in a Pan-European club competition for the first time, as he also played in Europe's third-tier level FIBA Korać Cup's 1983–84 season. Schmidt played in Europe's 2nd-tier level competition, the FIBA European Cup Winners' Cup (later renamed to FIBA Saporta Cup), for the first time, in the 1984–85 season.


title: Oscar Schmidt

text: With JuveCaserta, he won the Italian Cup title in 1988. In the European-wide secondary level 1988–89 FIBA European Cup Winners' Cup's Final, Schmidt scored 44 points against the Spanish club Real Madrid. However, Real Madrid's star player Dražen Petrović, scored 62 points in the same game, and JuveCaserta lost the game, by a score of 117–113.


title: Oscar Schmidt

text: Schmidt led the Italian top division in scoring six times, while he was a member of JuveCaserta (1983–84, 1984–85, 1985–86, 1986–87, 1988–89, and 1989–90 seasons). JuveCaserta eventually retired Schmidt's #18 jersey.


title: Oscar Schmidt

text: In 1990, Schmidt joined the Italian 2nd Division club Pavia. With Pavia, Schmidt led the Italian 2nd Division in scoring, in both the 1990–91 and 1992–93 seasons. With Pavia, he also led the first division Italian League in scoring, during the 1991–92 season. He was also a member of the FIBA European Selection in 1991.


title: Oscar Schmidt

text: As a member of Pavia, Schmidt also had his highest scoring single game in the top division Italian League, as he scored 66 points in a 1991–92 season game versus Auxilium Torino, on 30 November 1991. Pavia eventually retired his #11 jersey.


title: Oscar Schmidt

text: While playing club basketball in Italy, Schmidt earned a fan in future NBA star Kobe Bryant. At that time, Bryant was a young child that was living in Italy, while his father, Joe Bryant, played professional basketball in the country. Bryant called Schmidt one of his childhood idols, and also stated that Schmidt could have been one of the greatest players in the NBA, if he had played in the league.


title: Oscar Schmidt

text: Overall during his club career in Italy, Schmidt was the Top Scorer of the Italian First Division seven times (1983–84, 1984–85, 1985–86, 1986–87, 1988–89, 1989–90, and 1991–92 seasons). In 2017, Schmidt was inducted into the Italian Basketball Hall of Fame.


title: Oscar Schmidt

text: In 1993, Schmidt joined the Spanish ACB League club Valladolid. With Valladolid, Schmidt was the Spanish league's top scorer in the 1993–94 season, with a scoring average of 33.3 points per game, in 33 games played (regular season and playoffs). On 19 March 1994, Schmidt made 11 3-point field goals, in a Spanish League game against Murcia.


title: Oscar Schmidt

text: Schmidt also spent the 1994–95 season with Valladolid. In that season, he averaged 24.0 points per game, in 38 games played. His single-game scoring high in the Spanish League, was in a game that season versus Málaga, in which he scored 47 points, and made all 8 of his 3-point field goal attempts.


title: Oscar Schmidt

text: In two seasons in the Spanish ACB, Schmidt scored a total of 2,009 points in 71 games played (regular season and playoffs), for a scoring average of 28.3 points per game.


title: Oscar Schmidt

text: Schmidt returned to his native Brazil in 1995, to once again play in the Brazilian Basketball Championship. He was a member of S.C. Corinthians Paulista, from 1995 to 1997. He then played with Grêmio Barueri Bandeirantes / Mackenzie, from 1997 to 1999, and he finished his club career with C.R. Flamengo, where he played from 1999 to 2003.


title: Oscar Schmidt

text: With Corinthians Paulista, he won the Brazilian Championship in 1996. As a member of Grêmio Barueri Bandeirantes, he won the São Paulo State Championship in 1998. With Grêmio Barueri Bandeirantes, Schmidt, at the age of 39, scored 74 points in a São Paulo State Championship game on 28 November 1997.


title: Oscar Schmidt

text: As a member of Flamengo, he won the Rio de Janeiro State Championship in 1999 and 2002. Flamengo eventually retired his #14 jersey. Schmidt was the Brazilian Championship's top scorer in each of his last eight seasons playing in the competition (1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003). That was in addition to the two times that he had previously led the same competition in scoring, in 1979 and 1980.


title: Oscar Schmidt

text: Schmidt retired from his club basketball playing career on May 26, 2003, at the age of 45. During his club playing career, he scored a total of 42,044 points, in 1,289 games played, for a career scoring average of 32.6 points per game. However, those totals do not include all of the games that he played in during his pro club career, as the data for some of the national cup games and Pan-European games that he played in Europe are not available.


title: Oscar Schmidt

text: Schmidt was drafted by the New Jersey Nets in the sixth round of the 1984 NBA draft, and he played with them in their 1984 NBA training camp and preseason. However, he declined the club's offer of a fully guaranteed contract, because it was for considerably less money than he made at the time playing in Italy, and also because to accept the team's contract offer would have meant that he could no longer represent the senior Brazilian national team. That was because until 1989, NBA players were not allowed to play for national teams.


title: Oscar Schmidt

text: Schmidt played in the youth systems of Brazil's national federation program. He played in 15 games with the junior selection of São Paulo, with which he scored 393 points in 15 games, for a scoring average of 26.2 points per game. He also played in 31 games with Brazil's national junior selection, in which he scored a total of 569 points, for a scoring average of 18.4 points per game.


title: Oscar Schmidt

text: With the senior Brazil national team, Schmidt played in five Summer Olympics (he was the second player to do so after Teófilo Cruz) and was the top scorer in three of them. However, he never went past the tournament's quarterfinals. In the 1980 Summer Olympics, he played in seven games and scored 169 points, for a 24.1 average.


title: Oscar Schmidt

text: He again scored 169 points in seven games in the 1984 Summer Olympics. His best Olympic performance was the 1988 Summer Olympics. At that tournament, he scored 338 points, for an average of 42.3 points per game. In 1992, he scored 198 points in eight games, and in 1996, he scored 219 points in 8 games. In 38 career Olympic basketball games, Schmidt scored a record of 1,093 points, for an average of 28.8 points per game.


title: Oscar Schmidt

text: Schmidt is also the all-time career leader in total points scored in the FIBA World Cup, having scored a total of 843 points in 33 games, for a scoring average of 25.5 points per game. He won the bronze medal and made the All-Tournament Team at the 1978 FIBA World Cup, and he also made the All-Tournament Teams of both the 1986 FIBA World Cup and the 1990 FIBA World Cup, which he also led in scoring, with an average of 34.6 points per game.


title: Oscar Schmidt

text: Schmidt played in the gold-medal match of the 1987 Pan American Games, which was held in Indianapolis. The US national team, which was composed of NCAA Division I college basketball players at those games, featured two All-Americans in David Robinson (Hall of Fame member) and Danny Manning, two NCAA Championship Final Four MVPs, in Pervis Ellison and Keith Smart, and other future NBA players, such as Rex Chapman and Dan Majerle. Brazil faced a 68–54 halftime deficit. However, Schmidt finished the game with 46 points, in a 120–115 win for Brazil.


title: Oscar Schmidt

text: In 1996, at the age of 38, Schmidt retired from playing with the senior Brazilian national team as its all-time leading scorer. While representing Brazil, he scored a total of 7,693 points in 326 games played, for a career scoring average of 23.6 points per game. In 1997, Schmidt was given the Olympic Order award.


title: Oscar Schmidt

text: In 2004, Schmidt started his career in management. He was the CEO of "Telemar Rio de Janeiro", a Brazilian professional basketball team which won the "Campeonato Carioca" (Rio de Janeiro State Championship) in 2004, and the Brazilian Championship in 2005.


title: Oscar Schmidt

text: In 2006, Schmidt, along with other Brazilian basketball greats such as Paula and Hortência, (another Hall of Fame member), led the "NLB: Nossa Liga de Basquete" ("our basketball league"), an attempted rival to the Brazilian Basketball Championship. However, the league folded a year later.


title: Oscar Schmidt

text: On May 13, 2013, Schmidt had brain surgery to excise a malignant tumor. At first, nobody knew about it except for his family. The press found out about the disease fifteen days after the surgery, at a dinner celebrating the 50th anniversary of the two-time FIBA World Champion senior men's Brazilian National Team. Schmidt did not appear at the event, as he was recuperating from daily chemotherapy sessions. The disease was later put into remission.


title: Oscar Schmidt

text: In 2016, Schmidt was one of the guests at the opening ceremony of the 2016 Rio Summer Olympics, alongside other Brazilian celebrities, such as model Gisele Bündchen, actor Gustavo Goulart, and singer Caetano Veloso, among others.


title: Beryl Markham

text: Beryl Markham (née Clutterbuck; 26 October 1902 – 3 August 1986) was a Kenyan aviator born in England (one of the first bush pilots), adventurer, racehorse trainer and author. She was the first person to fly solo, non-stop across the Atlantic from Britain to North America. She wrote about her adventures in her memoir, "West with the Night".


title: Beryl Markham

text: Markham was born in the village of Ashwell, in the county of Rutland, England, the daughter of Charles Baldwin Clutterbuck, a horse trainer, and Clara Agnes ("née" Alexander) (1878–1952). She had an older brother, Richard Alexander "Dickie" Clutterbuck (1900–1927).


title: Beryl Markham

text: When she was four years old, she moved with her father to Kenya, which was then colonial British East Africa. He built a horse racing farm in Njoro, near the Great Rift Valley between the Mau Escarpment and the Rongai Valley. Markham spent an adventurous childhood learning, playing, and hunting with the local children. On her family's farm, she developed her knowledge of and love for horses, establishing herself as a trainer at the age of 17, after her father left for Peru.


title: Beryl Markham

text: Markham was regarded as a non-conformist. She was married three times, taking the name Markham from her second husband, the wealthy Mansfield Markham, with whom she had a son, Gervase. She had a public affair in 1929 with Prince Henry, Duke of Gloucester, the son of George V, but the Windsors allegedly cut the romance short. She also had an affair with Hubert Broad, who was later named by Mansfield Markham as a co-respondent in his 1937 divorce from Markham. After her Atlantic crossing, she returned to be with Broad, who was also an influence in her flying career.


title: Beryl Markham

text: She befriended the Danish writer Karen Blixen during the years that Blixen was managing her family's coffee farm in the Ngong hills outside Nairobi. When Blixen's romantic connection with the hunter and pilot Denys Finch Hatton was winding down, Markham started her own affair with him. He invited her to tour game lands on what turned out to be his fatal flight, but Markham supposedly declined because of a premonition of her flight instructor, British pilot Tom Campbell Black.


title: Beryl Markham

text: Inspired and coached by Tom Campbell Black, Markham learned to fly. She worked for some time as a bush pilot, spotting game animals from the air and signaling their locations to safaris on the ground.


title: Beryl Markham

text: In 1936, Markham made a solo flight across the Atlantic, from England to North America. When she decided to take on the Atlantic crossing, no pilot had yet flown non-stop from Europe to New York. On 4 September 1936, she took off from Abingdon, southern England. After a 20-hour flight, her Vega Gull, "The Messenger", suffered fuel starvation due to icing of the fuel tank vents, and she crash-landed at Baleine Cove on Cape Breton Island, Nova Scotia, Canada. She became the first person to make it from England to North America non-stop from east to west and was celebrated as an aviation pioneer.


title: Beryl Markham

text: Markham chronicled many of her adventures in her memoir, "West with the Night", published in 1942. Despite strong reviews in the press, the book sold modestly, and then quickly went out of print. After living for many years in the United States, Markham moved back to Kenya in 1952.


title: Beryl Markham

text: Markham's memoir lingered in obscurity until 1982, when California restaurateur George Gutekunst read a collection of Ernest Hemingway's letters, including one in which Hemingway praised Markham's writing:


title: Beryl Markham

text: Intrigued, Gutekunst read "West with the Night" and became so enamored of Markham's prose that he helped persuade a California publisher, North Point Press, to re-issue the book in 1983. The re-release of the book led to praise for the 80-year-old Markham as a great author as well as flyer.


title: Beryl Markham

text: When found in Kenya by AP East Africa correspondent Barry Shlachter, Markham was living in poverty. She had recently been badly beaten during a burglary at her house near the Nairobi racetrack, where she still trained thoroughbreds. The success of the re-issue of "West with the Night" provided enough income for Markham to finish her life in relative comfort. Earlier, she had been supported by a circle of friends and owners of race horses she trained into her 80s. The book became a best-seller, spurred by the 1986 broadcast of a public television documentary about Markham's life, "World Without Walls: Beryl Markham's African Memoir," produced by Gutekunst, Shlachter, Joan Saffa, Stephen Talbot and Judy Flannery in collaboration with KQED-TV in San Francisco. Gutekunst and Shlachter had approached the station to co-operate on the documentary, directed by Andrew Maxwell-Hyslop. British actress Diana Quick was the voice of Markham in readings from her memoir and Shlachter conducted the interviews. CNN Africa correspondent Gary Streiker did the filming for the well-reviewed, award-winning PBS program.


title: Beryl Markham

text: Markham died in Nairobi in 1986. Her short stories were posthumously collected in "The Splendid Outcast", with an introduction by Mary S. Lovell. A tale from "West with the Night" was excerpted and illustrated by Don Brown as a children's book, "The Good Lion". In 1988, CBS aired the biographical miniseries, "Beryl Markham: A Shadow on the Sun", with Stefanie Powers in the title role.


title: Beryl Markham

text: Both "West with the Night" and "Splendid Outcast" appeared on the New York Times best-seller list of hardcover fiction.


title: Beryl Markham

text: Critics raised questions as to whether Markham was the true, or sole author of "West with the Night", when her third husband Raoul C Schumacher made claims to the book. Evidence abounds that she was indeed the sole author; copies of the manuscripts sent to her editor prior to Markham meeting her ex-husband quickly silenced the critics and his claims. Schumacher was lodging with Hollywood writer Allen Vincent in California according to the 1940 census and Markham re-entered the United States via Florida in 1941. It is unlikely that Schumacher would have had time to process such a detailed biography in such a short time, but may have suggested it might make a Hollywood film to encourage Markham to marry him.


title: Beryl Markham

text: Author Mary S. Lovell visited Markham in Nairobi and interviewed her extensively shortly before Markham's death, in preparation for her biography, "Straight on Till Morning" (1987). From her research, Lovell concluded that Markham was the sole author, although Schumacher made some basic edits to the manuscript. Instead, Lovell suggests Antoine de Saint Exupéry, another of Markham's lovers, may have served as inspiration for Markham's clear, elegant language and storytelling style.


title: Beryl Markham

text: The International Astronomical Union has named the impact crater Markham, on the planet Venus, after her.


title: Block cipher

text: In cryptography, a block cipher is a deterministic algorithm operating on fixed-length groups of bits, called "blocks". Block ciphers are specified elementary components in the design of many cryptographic protocols and are widely used to encrypt large amounts of data, including in data exchange protocols. A block cipher uses blocks as an unvarying transformation.


title: Block cipher

text: Even a secure block cipher is suitable for the encryption of only a single block of data at a time, using a fixed key. A multitude of modes of operation have been designed to allow their repeated use in a secure way to achieve the security goals of confidentiality and authenticity. However, block ciphers may also feature as building blocks in other cryptographic protocols, such as universal hash functions and pseudorandom number generators.


title: Block cipher

text: A block cipher consists of two paired algorithms, one for encryption, , and the other for decryption, . Both algorithms accept two inputs: an input block of size bits and a key of size bits; and both yield an -bit output block. The decryption algorithm is defined to be the inverse function of encryption, i.e., . More formally, a block cipher is specified by an encryption function


title: Block cipher

text: which takes as input a key , of bit length (called the "key size"), and a bit string , of length (called the "block size"), and returns a string of bits. is called the plaintext, and is termed the ciphertext. For each , the function () is required to be an invertible mapping on . The inverse for is defined as a function


title: Block cipher

text: For example, a block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext. The exact transformation is controlled using a second input – the secret key. Decryption is similar: the decryption algorithm takes, in this example, a 128-bit block of ciphertext together with the secret key, and yields the original 128-bit block of plain text.


title: Block cipher

text: For each key "K", "E" is a permutation (a bijective mapping) over the set of input blocks. Each key selects one permutation from the set of formula_4 possible permutations.


title: Block cipher

text: The modern design of block ciphers is based on the concept of an iterated product cipher. In his seminal 1949 publication, "Communication Theory of Secrecy Systems", Claude Shannon analyzed product ciphers and suggested them as a means of effectively improving security by combining simple operations such as substitutions and permutations. Iterated product ciphers carry out encryption in multiple rounds, each of which uses a different subkey derived from the original key. One widespread implementation of such ciphers, named a Feistel network after Horst Feistel, is notably implemented in the DES cipher. Many other realizations of block ciphers, such as the AES, are classified as substitution–permutation networks.


title: Block cipher

text: The root of all cryptographic block formats used within the Payment Card Industry Data Security Standard (PCI DSS) and American National Standards Institute (ANSI) standards lies with the Atalla Key Block (AKB), which was a key innovation of the Atalla Box, the first hardware security module (HSM). It was developed in 1972 by Mohamed M. Atalla, founder of Atalla Corporation (now Utimaco Atalla), and released in 1973. The AKB was a key block, which is required to securely interchange symmetric keys or PINs with other actors of the banking industry. This secure interchange is performed using the AKB format. The Atalla Box protected over 90% of all ATM networks in operation as of 1998, and Atalla products still secure the majority of the world's ATM transactions as of 2014.


title: Block cipher

text: The publication of the DES cipher by the United States National Bureau of Standards (subsequently the U.S. National Institute of Standards and Technology, NIST) in 1977 was fundamental in the public understanding of modern block cipher design. It also influenced the academic development of cryptanalytic attacks. Both differential and linear cryptanalysis arose out of studies on the DES design. there is a palette of attack techniques against which a block cipher must be secure, in addition to being robust against brute-force attacks.


title: Block cipher

text: Most block cipher algorithms are classified as "iterated block ciphers" which means that they transform fixed-size blocks of plaintext into identically sized blocks of ciphertext, via the repeated application of an invertible transformation known as the "round function", with each iteration referred to as a "round".


title: Block cipher

text: Usually, the round function "R" takes different "round keys" "K" as second input, which are derived from the original key:


title: Block cipher

text: Frequently, key whitening is used in addition to this. At the beginning and the end, the data is modified with key material (often with XOR, but simple arithmetic operations like adding and subtracting are also used):


title: Block cipher

text: Given one of the standard iterated block cipher design schemes, it is fairly easy to construct a block cipher that is cryptographically secure, simply by using a large number of rounds. However, this will make the cipher inefficient. Thus, efficiency is the most important additional design criterion for professional ciphers. Further, a good block cipher is designed to avoid side-channel attacks, such as branch prediction and input-dependent memory accesses that might leak secret data via the cache state or the execution time. In addition, the cipher should be concise, for small hardware and software implementations. Finally, the cipher should be easily cryptanalyzable, such that it can be shown how many rounds the cipher needs to be reduced to, so that the existing cryptographic attacks would work – and, conversely, that it can be shown that the number of actual rounds is large enough to protect against them.


title: Block cipher

text: One important type of iterated block cipher known as a "substitution–permutation network (SPN)" takes a block of the plaintext and the key as inputs, and applies several alternating rounds consisting of a substitution stage followed by a permutation stage—to produce each block of ciphertext output. The non-linear substitution stage mixes the key bits with those of the plaintext, creating Shannon's "confusion". The linear permutation stage then dissipates redundancies, creating "diffusion".


title: Block cipher

text: A "substitution box (S-box)" substitutes a small block of input bits with another block of output bits. This substitution must be one-to-one, to ensure invertibility (hence decryption). A secure S-box will have the property that changing one input bit will change about half of the output bits on average, exhibiting what is known as the avalanche effect—i.e. it has the property that each output bit will depend on every input bit.


title: Block cipher

text: A "permutation box (P-box)" is a permutation of all the bits: it takes the outputs of all the S-boxes of one round, permutes the bits, and feeds them into the S-boxes of the next round. A good P-box has the property that the output bits of any S-box are distributed to as many S-box inputs as possible.


title: Block cipher

text: At each round, the round key (obtained from the key with some simple operations, for instance, using S-boxes and P-boxes) is combined using some group operation, typically XOR.


title: Block cipher

text: Decryption is done by simply reversing the process (using the inverses of the S-boxes and P-boxes and applying the round keys in reversed order).


title: Block cipher

text: In a "Feistel cipher", the block of plain text to be encrypted is split into two equal-sized halves. The round function is applied to one half, using a subkey, and then the output is XORed with the other half. The two halves are then swapped.


title: Block cipher

text: One advantage of the Feistel model compared to a substitution–permutation network is that the round function formula_11 does not have to be invertible.


title: Block cipher

text: The Lai–Massey scheme offers security properties similar to those of the Feistel structure. It also shares its advantage that the round function formula_26 does not have to be invertible. Another similarity is that it also splits the input block into two equal pieces. However, the round function is applied to the difference between the two, and the result is then added to both half blocks.


title: Block cipher

text: Let formula_26 be the round function and formula_28 a half-round function and let formula_29 be the sub-keys for the rounds formula_13 respectively.


title: Block cipher

text: Many modern block ciphers and hashes are ARX algorithms—their round function involves only three operations: (A) modular addition, (R) rotation with fixed rotation amounts, and (X) XOR. Examples include ChaCha20, Speck, XXTEA, and BLAKE. Many authors draw an ARX network, a kind of data flow diagram, to illustrate such a round function.


title: Block cipher

text: These ARX operations are popular because they are relatively fast and cheap in hardware and software, their implementation can be made extremely simple, and also because they run in constant time, and therefore are immune to timing attacks. The rotational cryptanalysis technique attempts to attack such round functions.


title: Block cipher

text: Other operations often used in block ciphers include data-dependent rotations as in RC5 and RC6, a substitution box implemented as a lookup table as in Data Encryption Standard and Advanced Encryption Standard, a permutation box, and multiplication as in IDEA.


title: Block cipher

text: A block cipher by itself allows encryption only of a single data block of the cipher's block length. For a variable-length message, the data must first be partitioned into separate cipher blocks. In the simplest case, known as electronic codebook (ECB) mode, a message is first split into separate blocks of the cipher's block size (possibly extending the last block with padding bits), and then each block is encrypted and decrypted independently. However, such a naive method is generally insecure because equal plaintext blocks will always generate equal ciphertext blocks (for the same key), so patterns in the plaintext message become evident in the ciphertext output.


title: Block cipher

text: To overcome this limitation, several so called block cipher modes of operation have been designed and specified in national recommendations such as NIST 800-38A and BSI TR-02102 and international standards such as ISO/IEC 10116. The general concept is to use randomization of the plaintext data based on an additional input value, frequently called an initialization vector, to create what is termed probabilistic encryption. In the popular cipher block chaining (CBC) mode, for encryption to be secure the initialization vector passed along with the plaintext message must be a random or pseudo-random value, which is added in an exclusive-or manner to the first plaintext block before it is being encrypted. The resultant ciphertext block is then used as the new initialization vector for the next plaintext block. In the cipher feedback (CFB) mode, which emulates a self-synchronizing stream cipher, the initialization vector is first encrypted and then added to the plaintext block. The output feedback (OFB) mode repeatedly encrypts the initialization vector to create a key stream for the emulation of a synchronous stream cipher. The newer counter (CTR) mode similarly creates a key stream, but has the advantage of only needing unique and not (pseudo-)random values as initialization vectors; the needed randomness is derived internally by using the initialization vector as a block counter and encrypting this counter for each block.


title: Block cipher

text: From a security-theoretic point of view, modes of operation must provide what is known as semantic security. Informally, it means that given some ciphertext under an unknown key one cannot practically derive any information from the ciphertext (other than the length of the message) over what one would have known without seeing the ciphertext. It has been shown that all of the modes discussed above, with the exception of the ECB mode, provide this property under so-called chosen plaintext attacks.


title: Block cipher

text: Some modes such as the CBC mode only operate on complete plaintext blocks. Simply extending the last block of a message with zero-bits is insufficient since it does not allow a receiver to easily distinguish messages that differ only in the amount of padding bits. More importantly, such a simple solution gives rise to very efficient padding oracle attacks. A suitable padding scheme is therefore needed to extend the last plaintext block to the cipher's block size. While many popular schemes described in standards and in the literature have been shown to be vulnerable to padding oracle attacks, a solution which adds a one-bit and then extends the last block with zero-bits, standardized as "padding method 2" in ISO/IEC 9797-1, has been proven secure against these attacks.


title: Block cipher

text: This property results in the cipher's security degrading quadratically, and needs to be taken into account when selecting a block size. There is a trade-off though as large block sizes can result in the algorithm becoming inefficient to operate. Earlier block ciphers such as the DES have typically selected a 64-bit block size, while newer designs such as the AES support block sizes of 128 bits or more, with some ciphers supporting a range of different block sizes.


title: Block cipher

text: "Linear cryptanalysis" is a form of cryptanalysis based on finding affine approximations to the action of a cipher. Linear cryptanalysis is one of the two most widely used attacks on block ciphers; the other being differential cryptanalysis.


title: Block cipher

text: The discovery is attributed to Mitsuru Matsui, who first applied the technique to the FEAL cipher (Matsui and Yamagishi, 1992).


title: Block cipher

text: "Integral cryptanalysis" is a cryptanalytic attack that is particularly applicable to block ciphers based on substitution–permutation networks. Unlike differential cryptanalysis, which uses pairs of chosen plaintexts with a fixed XOR difference, integral cryptanalysis uses sets or even multisets of chosen plaintexts of which part is held constant and another part varies through all possibilities. For example, an attack might use 256 chosen plaintexts that have all but 8 of their bits the same, but all differ in those 8 bits. Such a set necessarily has an XOR sum of 0, and the XOR sums of the corresponding sets of ciphertexts provide information about the cipher's operation. This contrast between the differences of pairs of texts and the sums of larger sets of texts inspired the name "integral cryptanalysis", borrowing the terminology of calculus.


title: Block cipher

text: In addition to linear and differential cryptanalysis, there is a growing catalog of attacks: truncated differential cryptanalysis, partial differential cryptanalysis, integral cryptanalysis, which encompasses square and integral attacks, slide attacks, boomerang attacks, the XSL attack, impossible differential cryptanalysis and algebraic attacks. For a new block cipher design to have any credibility, it must demonstrate evidence of security against known attacks.


title: Block cipher

text: When a block cipher is used in a given mode of operation, the resulting algorithm should ideally be about as secure as the block cipher itself. ECB (discussed above) emphatically lacks this property: regardless of how secure the underlying block cipher is, ECB mode can easily be attacked. On the other hand, CBC mode can be proven to be secure under the assumption that the underlying block cipher is likewise secure. Note, however, that making statements like this requires formal mathematical definitions for what it means for an encryption algorithm or a block cipher to "be secure". This section describes two common notions for what properties a block cipher should have. Each corresponds to a mathematical model that can be used to prove properties of higher level algorithms, such as CBC.


title: Block cipher

text: This general approach to cryptography – proving higher-level algorithms (such as CBC) are secure under explicitly stated assumptions regarding their components (such as a block cipher) – is known as "provable security".


title: Block cipher

text: Informally, a block cipher is secure in the standard model if an attacker cannot tell the difference between the block cipher (equipped with a random key) and a random permutation.


title: Block cipher

text: The attacker, which we can model as an algorithm, is called an "adversary". The function "f" (which the adversary was able to query) is called an "oracle".


title: Block cipher

text: Note that an adversary can trivially ensure a 50% chance of winning simply by guessing at random (or even by, for example, always guessing "heads"). Therefore, let "P"("A") denote the probability that the adversary "A" wins this game against "E", and define the "advantage" of "A" as 2("P"("A") − 1/2). It follows that if "A" guesses randomly, its advantage will be 0; on the other hand, if "A" always wins, then its advantage is 1. The block cipher "E" is a "pseudo-random permutation" (PRP) if no adversary has an advantage significantly greater than 0, given specified restrictions on "q" and the adversary's running time. If in Step 2 above adversaries have the option of learning "f"("X") instead of "f"("X") (but still have only small advantages) then "E" is a "strong" PRP (SPRP). An adversary is "non-adaptive" if it chooses all "q" values for "X" before the game begins (that is, it does not use any information gleaned from previous queries to choose each "X" as it goes).


title: Block cipher

text: These definitions have proven useful for analyzing various modes of operation. For example, one can define a similar game for measuring the security of a block cipher-based encryption algorithm, and then try to show (through a reduction argument) that the probability of an adversary winning this new game is not much more than "P"("A") for some "A". (The reduction typically provides limits on "q" and the running time of "A".) Equivalently, if "P"("A") is small for all relevant "A", then no attacker has a significant probability of winning the new game. This formalizes the idea that the higher-level algorithm inherits the block cipher's security.


title: Block cipher

text: Lucifer is generally considered to be the first civilian block cipher, developed at IBM in the 1970s based on work done by Horst Feistel. A revised version of the algorithm was adopted as a U.S. government Federal Information Processing Standard: FIPS PUB 46 Data Encryption Standard (DES). It was chosen by the U.S. National Bureau of Standards (NBS) after a public invitation for submissions and some internal changes by NBS (and, potentially, the NSA). DES was publicly released in 1976 and has been widely used.


title: Block cipher

text: DES was designed to, among other things, resist a certain cryptanalytic attack known to the NSA and rediscovered by IBM, though unknown publicly until rediscovered again and published by Eli Biham and Adi Shamir in the late 1980s. The technique is called differential cryptanalysis and remains one of the few general attacks against block ciphers; linear cryptanalysis is another, but may have been unknown even to the NSA, prior to its publication by Mitsuru Matsui. DES prompted a large amount of other work and publications in cryptography and cryptanalysis in the open community and it inspired many new cipher designs.


title: Block cipher

text: DES has a block size of 64 bits and a key size of 56 bits. 64-bit blocks became common in block cipher designs after DES. Key length depended on several factors, including government regulation. Many observers in the 1970s commented that the 56-bit key length used for DES was too short. As time went on, its inadequacy became apparent, especially after a special purpose machine designed to break DES was demonstrated in 1998 by the Electronic Frontier Foundation. An extension to DES, Triple DES, triple-encrypts each block with either two independent keys (112-bit key and 80-bit security) or three independent keys (168-bit key and 112-bit security). It was widely adopted as a replacement. As of 2011, the three-key version is still considered secure, though the National Institute of Standards and Technology (NIST) standards no longer permit the use of the two-key version in new applications, due to its 80-bit security level.


title: Block cipher

text: The "International Data Encryption Algorithm" ("IDEA") is a block cipher designed by James Massey of ETH Zurich and Xuejia Lai; it was first described in 1991, as an intended replacement for DES.


title: Block cipher

text: IDEA operates on 64-bit blocks using a 128-bit key, and consists of a series of eight identical transformations (a "round") and an output transformation (the "half-round"). The processes for encryption and decryption are similar. IDEA derives much of its security by interleaving operations from different groups – modular addition and multiplication, and bitwise "exclusive or (XOR)" – which are algebraically "incompatible" in some sense.


title: Block cipher

text: The designers analysed IDEA to measure its strength against differential cryptanalysis and concluded that it is immune under certain assumptions. No successful linear or algebraic weaknesses have been reported. , the best attack which applies to all keys can break full 8.5-round IDEA using a narrow-bicliques attack about four times faster than brute force.


title: Block cipher

text: RC5 is a block cipher designed by Ronald Rivest in 1994 which, unlike many other ciphers, has a variable block size (32, 64 or 128 bits), key size (0 to 2040 bits) and number of rounds (0 to 255). The original suggested choice of parameters were a block size of 64 bits, a 128-bit key and 12 rounds.


title: Block cipher

text: A key feature of RC5 is the use of data-dependent rotations; one of the goals of RC5 was to prompt the study and evaluation of such operations as a cryptographic primitive. RC5 also consists of a number of modular additions and XORs. The general structure of the algorithm is a Feistel-like network. The encryption and decryption routines can be specified in a few lines of code. The key schedule, however, is more complex, expanding the key using an essentially one-way function with the binary expansions of both e and the golden ratio as sources of "nothing up my sleeve numbers". The tantalizing simplicity of the algorithm together with the novelty of the data-dependent rotations has made RC5 an attractive object of study for cryptanalysts.


title: Block cipher

text: 12-round RC5 (with 64-bit blocks) is susceptible to a differential attack using 2 chosen plaintexts. 18–20 rounds are suggested as sufficient protection.


title: Block cipher

text: The "Rijndael" cipher developed by Belgian cryptographers, Joan Daemen and Vincent Rijmen was one of the competing designs to replace DES. It won the 5-year public competition to become the AES, (Advanced Encryption Standard).


title: Block cipher

text: Adopted by NIST in 2001, AES has a fixed block size of 128 bits and a key size of 128, 192, or 256 bits, whereas Rijndael can be specified with block and key sizes in any multiple of 32 bits, with a minimum of 128 bits. The block size has a maximum of 256 bits, but the keysize has no theoretical maximum. AES operates on a 4×4 column-major order matrix of bytes, termed the "state" (versions of Rijndael with a larger block size have additional columns in the state).


title: Block cipher

text: "Blowfish" is a block cipher, designed in 1993 by Bruce Schneier and included in a large number of cipher suites and encryption products. Blowfish has a 64-bit block size and a variable key length from 1 bit up to 448 bits. It is a 16-round Feistel cipher and uses large key-dependent S-boxes. Notable features of the design include the key-dependent S-boxes and a highly complex key schedule.


title: Block cipher

text: It was designed as a general-purpose algorithm, intended as an alternative to the ageing DES and free of the problems and constraints associated with other algorithms. At the time Blowfish was released, many other designs were proprietary, encumbered by patents or were commercial/government secrets. Schneier has stated that, "Blowfish is unpatented, and will remain so in all countries. The algorithm is hereby placed in the public domain, and can be freely used by anyone." The same applies to Twofish, a successor algorithm from Schneier.


title: Block cipher

text: M. Liskov, R. Rivest, and D. Wagner have described a generalized version of block ciphers called "tweakable" block ciphers. A tweakable block cipher accepts a second input called the "tweak" along with its usual plaintext or ciphertext input. The tweak, along with the key, selects the permutation computed by the cipher. If changing tweaks is sufficiently lightweight (compared with a usually fairly expensive key setup operation), then some interesting new operation modes become possible. The disk encryption theory article describes some of these modes.


title: Block cipher

text: Block ciphers traditionally work over a binary alphabet. That is, both the input and the output are binary strings, consisting of "n" zeroes and ones. In some situations, however, one may wish to have a block cipher that works over some other alphabet; for example, encrypting 16-digit credit card numbers in such a way that the ciphertext is also a 16-digit number might facilitate adding an encryption layer to legacy software. This is an example of "format-preserving encryption". More generally, format-preserving encryption requires a keyed permutation on some finite language. This makes format-preserving encryption schemes a natural generalization of (tweakable) block ciphers. In contrast, traditional encryption schemes, such as CBC, are not permutations because the same plaintext can encrypt to multiple different ciphertexts, even when using a fixed key.


title: Block cipher

text: Block ciphers can be used to build other cryptographic primitives, such as those below. For these other primitives to be cryptographically secure, care has to be taken to build them the right way.


title: Block cipher

text: Just as block ciphers can be used to build hash functions, like SHA-1 and SHA-2 are based on block ciphers which are also used independently as SHACAL, hash functions can be used to build block ciphers. Examples of such block ciphers are BEAR and LION.


title: Eeramana Rojave 2 (TV series)

text: Eeramana Rojave 2 () is a 2022 Indian-Tamil Love drama airing on Star Vijay. The series starrs Gabriella Charlton, Dhiraviam Rajakumaran,Siddharth Kumaran and Swathi Konde. The series serves a Sequel to the 2018 series of the same name. The show premiered on 17 January 2022, is also telecasted on the digital platform Disney+ Hotstar.


title: Eeramana Rojave 2 (TV series)

text: The following story is about Jeeva and Kavya, who are lovers. Jeeva's brother and Kavya's sister were going to get married, but there happens to be a mix up. This results in Kavya marrying Jeeva's brother and Jeeva marrying Kavya's sister.


title: Eeramana Rojave 2 (TV series)

text: The second season stars Dhiraviam Rajakumaran, who played Vetrivel Naatarasan in the first season, was also play in the second season of this series. Gabriella Charlton was cast as Kavya, Thaenmozhi B.A fame Siddharth Kumaran was cast as Parthiban and Kannada television actress Swathi Konde was cast as Priya, were selected for leads.


title: Eeramana Rojave 2 (TV series)

text: The first promo was unveiled on December-end 2021, featuring the cast members. The second promo was unveiled in January 2022, featuring the protagonists and revealing the release date. The first episode aired on 17 January 2022 replacing Bigg Boss Tamil 5.


title: Buddhist meditation

text: Buddhist meditation is the practice of meditation in Buddhism. The closest words for meditation in the classical languages of Buddhism are "bhāvanā" ("mental development") and "jhāna/dhyāna" (mental training resulting in a calm and luminous mind).


title: Buddhist meditation

text: Buddhists pursue meditation as part of the path toward liberation from defilements ("kleshas") and clinging and craving ("upādāna"), also called awakening, which results in the attainment of Nirvana, and includes a variety of meditation techniques, most notably "anapanasati" (mindfulness of breathing). Other techniques include "asubha bhavana" ("reflections on repulsiveness"); reflection on "pratityasamutpada" (dependent origination); "anussati" (recollections, including "anapanasati") and "sati" (mindfulness), culminating in "dhyana" (developing an alert and luminous mind); and the Brahma-viharas (loving-kindness and compassion). These techniques aim to develop equanimity and sati (mindfulness); samadhi (unification of mind) c.q. samatha (tranquility) and vipassanā (insight); and are also said to lead to abhijñā (supramundane powers). These meditation techniques are preceded by and combined with practices which aid this development, such as moral restraint and right effort to develop wholesome states of mind.


title: Buddhist meditation

text: While these techniques are used across Buddhist schools, there is also significant diversity. A basic classification of meditation techniques is "samatha" (calming the mind) and "vipassana" (gaining insight). In the Theravada tradition, emphasizing "vipassana", these are seen as opposing techniques, while Mahayana Buddhism stresses the interplay between "samatha" and "vipassana". In both traditions, breath meditation is a central practice. Chinese and Japanese Buddhism also preserved a wide range of meditation techniques, which go back to early Buddhism, and were transmitted via Sarvastivada Buddhism. In Tibetan Buddhism, deity yoga includes visualisations, which precede the realization of "sunyata" ("emptiness").


title: Buddhist meditation

text: The closest words for meditation in the classical languages of Buddhism are "bhāvanā" (mental development) and "jhāna/dhyāna".


title: Buddhist meditation

text: Modern Buddhist studies have attempted to reconstruct the meditation practices of early Buddhism, mainly through philological and text critical methods using the early canonical texts.


title: Buddhist meditation

text: According to Indologist Johannes Bronkhorst, "the teaching of the Buddha as presented in the early canon contains a number of contradictions," presenting "a variety of methods that do not always agree with each other," containing "views and practices that are sometimes accepted and sometimes rejected." These contradictions are due to the influence of non-Buddhist traditions on early Buddhism. One example of these non-Buddhist meditative methods found in the early sources is outlined by Bronkhorst:


title: Buddhist meditation

text: According to Bronkhorst, such practices which are based on a "suppression of activity" are not authentically Buddhist, but were later adopted from the Jains by the Buddhist community.


title: Buddhist meditation

text: The two major traditions of meditative practice in pre-Buddhist India were the Jain ascetic practices and the various Vedic Brahmanical practices. There is still much debate in Buddhist studies regarding how much influence these two traditions had on the development of early Buddhist meditation. The early Buddhist texts mention that Gautama trained under two teachers known as Āḷāra Kālāma and Uddaka Rāmaputta, both of them taught formless jhanas or mental absorptions, a key practice of Theravada Buddhist meditation. Alexander Wynne considers these figures historical persons associated with the doctrines of the early Upanishads. Other practices which the Buddha undertook have been associated with the Jain ascetic tradition by the Indologist Johannes Bronkhorst including extreme fasting and a forceful "meditation without breathing". According to the early texts, the Buddha rejected the more extreme Jain ascetic practices in favor of the middle way.


title: Buddhist meditation

text: Early Buddhism, as it existed before the development of various schools, is called pre-sectarian Buddhism. Its meditation-techniques are described in the Pali Canon and the Chinese Agamas.


title: Buddhist meditation

text: Meditation and contemplation are preceded by preparatory practices. As described in the Noble Eightfold Path, right view leads to leaving the household life and becoming a wandering monk. "Sila", morality, comprises the rules for right conduct. Sense restraint and right effort, c.q. the four right efforts, are important preparatory practices. Sense restraint means controlling the response to sensual perceptions, not giving in to lust and aversion but simply noticing the objects of perception as they appear. Right effort aims to prevent the arising of unwholesome states, and to generate wholesome states. By following these preparatory steps and practices, the mind becomes set, almost naturally, for the onset of "dhyana".


title: Buddhist meditation

text: An important quality to be cultivated by a Buddhist meditator is mindfulness (sati). Mindfulness is a polyvalent term which refers to remembering, recollecting and "bearing in mind". It also relates to remembering the teachings of the Buddha and knowing how these teachings relate to one's experiences. The Buddhist texts mention different kinds of mindfulness practice.


title: Buddhist meditation

text: The Pali "Satipatthana Sutta" and its parallels as well as numerous other early Buddhist texts enumerates four subjects ("satipaṭṭhānas") on which mindfulness is established: the body (including the four elements, the parts of the body, and death); feelings ("vedana"); mind ("citta"); and phenomena or principles ("dhammas"), such as the five hindrances and the seven factors of enlightenment. Different early texts give different enumerations of these four mindfulness practices. Meditation on these subjects is said to develop insight.


title: Buddhist meditation

text: According to Bronkhorst, there were originally two kinds of mindfulness, "observations of the positions of the body" and the four "satipaṭṭhānas", the "establishment of mindfulness," which constituted formal meditation. Bhikkhu Sujato and Bronkhorst both argue that the mindfulness of the positions of the body (which is actually "clear comprehension") wasn't originally part of the four satipatthana formula, but was later added to it in some texts.


title: Buddhist meditation

text: Bronkhorst (1985) also argues that the earliest form of the satipaṭṭhāna sutta only contained the observation of the impure body parts under mindfulness of the body, and that mindfulness of dhammas was originally just the observation of the seven awakening factors. Sujato's reconstruction similarly only retains the contemplation of the impure under mindfulness of the body, while including only the five hindrances and the seven awakening factors under mindfulness of dhammas. According to Analayo, mindfulness of breathing was probably absent from the original scheme, noting that one can easily contemplate the body's decay taking an external object, that is, someone else's body, but not be externally mindfull of the breath, thst is, someone else's breath.


title: Buddhist meditation

text: According to Grzegorz Polak, the four "upassanā" have been misunderstood by the developing Buddhist tradition, including Theravada, to refer to four different foundations. According to Polak, the four "upassanā" do not refer to four different foundations of which one should be aware, but are an alternate description of the "jhanas", describing how the "samskharas" are tranquilized:


title: Buddhist meditation

text: "Anussati" (Pāli; Sanskrit: "Anusmriti") means "recollection," "contemplation," "remembrance," "meditation" and "mindfulness." It refers to specific meditative or devotional practices, such as recollecting the sublime qualities of the Buddha or "anapanasati" (mindfulness of breathing), which lead to mental tranquillity and abiding joy. In various contexts, the Pali literature and Sanskrit Mahayana sutras emphasize and identify different enumerations of recollections.


title: Buddhist meditation

text: "Asubha bhavana" is reflection on "the foul"/unattractiveness (Pāli: "asubha"). It includes two practices, namely cemetery contemplations, and "Paikkūlamanasikāra", "reflections on repulsiveness". "Patikulamanasikara" is a Buddhist meditation whereby thirty-one parts of the body are contemplated in a variety of ways. In addition to developing sati (mindfulness) and samādhi (concentration, "dhyana"), this form of meditation is considered to be conducive to overcoming desire and lust.


title: Buddhist meditation

text: "Anapanasati", mindfulness of breathing, is a core meditation practice in Theravada, Tiantai and Chan traditions of Buddhism as well as a part of many mindfulness programs. In both ancient and modern times, anapanasati by itself is likely the most widely used Buddhist method for contemplating bodily phenomena.


title: Buddhist meditation

text: The "Ānāpānasati Sutta" specifically concerns mindfulness of inhalation and exhalation, as a part of paying attention to one's body in quietude, and recommends the practice of anapanasati meditation as a means of cultivating the Seven Factors of Enlightenment: sati (mindfulness), dhamma vicaya (analysis), viriya (persistence), which leads to pīti (rapture), then to passaddhi (serenity), which in turn leads to samadhi (concentration) and then to upekkhā (equanimity). Finally, the Buddha taught that, with these factors developed in this progression, the practice of anapanasati would lead to release (Pali: "vimutti"; Sanskrit "mokṣa") from dukkha (suffering), in which one realizes nibbana.


title: Buddhist meditation

text: Many scholars of early Buddhism, such as Vetter, Bronkhorst and Anālayo, see the practice of "jhāna" (Sanskrit: dhyāna) as central to the meditation of Early Buddhism. According to Bronkhorst, the oldest Buddhist meditation practice are the four dhyanas, which lead to the destruction of the asavas as well as the practice of mindfulness ("sati"). According to Vetter, the practice of dhyana may have constituted the core liberating practice of early Buddhism, since in this state all "pleasure and pain" had waned. According to Vetter,


title: Buddhist meditation

text: Alexander Wynne agrees that the Buddha taught a kind of meditation exemplified by the four dhyanas, but argues that the Buddha adopted these from the Brahmin teachers Āḷāra Kālāma and Uddaka Rāmaputta, though he did not interpret them in the same Vedic cosmological way and rejected their Vedic goal (union with Brahman). The Buddha, according to Wynne, radically transformed the practice of dhyana which he learned from these Brahmins which "consisted of the adaptation of the old yogic techniques to the practice of mindfulness and attainment of insight". For Wynne, this idea that liberation required not just meditation but an act of insight, was radically different from the Brahminic meditation, "where it was thought that the yogin must be without any mental activity at all, ‘like a log of wood’."


title: Buddhist meditation

text: According to Richard Gombrich, the sequence of the four "rupa-jhanas" describes two different cognitive states. Alexander Wynne further explains that the "dhyana"-scheme is poorly understood. According to Wynne, words expressing the inculcation of awareness, such as "sati", "sampajāno", and "upekkhā", are mistranslated or understood as particular factors of meditative states, whereas they refer to a particular way of perceiving the sense objects. Polak notes that the qualities of the "jhanas" resemble the "bojjhaṅgā", the seven factors of awakening]], arguing that both sets describe the same essential practice. Polak further notes, elaborating on Vetter, that the onset of the first "dhyana" is described as a quite natural process, due to the preceding efforts to restrain the senses and the nurturing of wholesome states.


title: Buddhist meditation

text: "Upekkhā", equanimity, which is perfected in the fourth "dhyana", is one of the four "Brahma-vihara". While the commentarial tradition downplayed the "Brahma-viharas", Gombrich notes that the Buddhist usage of the "brahma-vihāra", originally referred to an awakened state of mind, and a concrete attitude toward other beings which was equal to "living with Brahman" here and now. The later tradition took those descriptions too literally, linking them to cosmology and understanding them as "living with Brahman" by rebirth in the Brahma-world. According to Gombrich, "the Buddha taught that kindness - what Christians tend to call love - was a way to salvation.


title: Buddhist meditation

text: In addition to the four rūpajhānas, there are also meditative attainments which were later called by the tradition the arūpajhānas, though the early texts do not use the term dhyana for them, calling them "āyatana" (dimension, sphere, base). They are:


title: Buddhist meditation

text: Various early sources mention the attainment of insight after having achieved jhana. In the "Mahasaccaka Sutta", dhyana is followed by insight into the four noble truths. The mention of the four noble truths as constituting "liberating insight" is probably a later addition. Discriminating insight into transiency as a separate path to liberation may be a later development, under pressure of developments in Indian religious thinking, which saw "liberating insight" as essential to liberation. This may also have been due to an over-literal interpretation by later scholastics of the terminology used by the Buddha, and to the problems involved with the practice of "dhyana", and the need to develop an easier method. Collett Cox and Damien Keown question the existence of a dichotomy between dhyana and insight, arguing that samadhi is a key aspect of the later Buddhist process of liberation, which cooperates with insight to remove the āsavas.


title: Buddhist meditation

text: Another important meditation in the early sources are the four Brahmavihāra (divine abodes) which are said to lead to "cetovimutti", a “liberation of the mind”. The four "Brahmavihāra" are:


title: Buddhist meditation

text: According to Anālayo:The effect of cultivating the brahmavihāras as a liberation of the mind finds illustration in a simile which describes a conch blower who is able to make himself heard in all directions. This illustrates how the brahmavihāras are to be developed as a boundless radiation in all directions, as a result of which they cannot be overruled by other more limited karma.The practice of the four divine abodes can be seen as a way to overcome ill-will and sensual desire and to train in the quality of deep concentration (samadhi).


title: Buddhist meditation

text: Traditionally, Eighteen schools of Buddhism are said to have developed after the time of the Buddha. The Sarvastivada school was the most influential, but the Theravada is the only school that still exists.


title: Buddhist meditation

text: The Buddha is said to have identified two paramount mental qualities that arise from wholesome meditative practice:


title: Buddhist meditation

text: The Buddha is said to have extolled serenity and insight as conduits for attaining Nibbana (Pali; Skt.: "Nirvana"), the unconditioned state as in the "Kimsuka Tree Sutta" (SN 35.245), where the Buddha provides an elaborate metaphor in which serenity and insight are "the swift pair of messengers" who deliver the message of Nibbana via the Noble Eightfold Path.


title: Buddhist meditation

text: In the Threefold training, "samatha" is part of "samadhi", the eight limb of the threefold path, together with "sati", mindfulness. According to Mahāsi Sayādaw, tranquility meditation can lead to the attainment of supernatural powers such as psychic powers and mind reading while insight meditation can lead to the realisation of nibbāna.


title: Buddhist meditation

text: In the Pali canon, the Buddha never mentions independent samatha and vipassana meditation practices; instead, samatha and vipassana are two "qualities of mind", to be developed through meditation. Nonetheless, according to the Theravada tradition some meditation practices (such as contemplation of a "kasina" object) favor the development of samatha, others are conducive to the development of vipassana (such as contemplation of the aggregates), while others (such as mindfulness of breathing) are classically used for developing both mental qualities.


title: Buddhist meditation

text: In the "Four Ways to Arahantship Sutta" (AN 4.170), Ven. Ananda reports that people attain arahantship using serenity and insight in one of three ways:


title: Buddhist meditation

text: While the Nikayas state that the pursuit of vipassana can precede the pursuit of samatha, according to the Burmese Vipassana movement "vipassana" be based upon the achievement of stabilizing "access concentration" (Pali: "upacara samadhi"). According to the Theravada tradition, through the meditative development of serenity, one is able to suppress obscuring hindrances; and, with the suppression of the hindrances, it is through the meditative development of insight that one gains liberating wisdom.


title: Buddhist meditation

text: The oldest material of the Theravāda tradition on meditation can be found in the Pali Nikayas, and in texts such as the Patisambhidamagga which provide commentary to meditation suttas like the Anapanasati sutta.


title: Buddhist meditation

text: An early Theravāda meditation manual is the Vimuttimagga ('Path of Freedom', 1st or 2nd century). The most influential presentation though, is that of the 5th-century "Visuddhimagga" ('Path of Purification') of Buddhaghoṣa, which seems to have been influenced by the earlier Vimuttimagga in his presentation.


title: Buddhist meditation

text: The "Visuddhimagga" doctrine reflects Theravāda Abhidhamma scholasticism, which includes several innovations and interpretations not found in the earliest discourses ("suttas") of the Buddha. Buddhaghosa's "Visuddhimagga" includes non-canonical instructions on Theravada meditation, such as "ways of guarding the mental image (nimitta)," which point to later developments in Theravada meditation.


title: Buddhist meditation

text: The text is centered around "kasina"-meditation, a form of concentration-meditation in which the mind is focused on a (mental) object. According to Thanissaro Bhikkhu, "[t]he text then tries to fit all other meditation methods into the mold of kasina practice, so that they too give rise to countersigns, but even by its own admission, breath meditation does not fit well into the mold." In its emphasis on "kasina"-meditation, the "Visuddhimagga" departs from the Pali Canon, in which "dhyana" is the central meditative practice, indicating that what "jhana means in the commentaries is something quite different from what it means in the Canon."


title: Buddhist meditation

text: The "Visuddhimagga" describes forty meditation subjects, most being described in the early texts. Buddhaghoṣa advises that, for the purpose of developing concentration and consciousness, a person should "apprehend from among the forty meditation subjects one that suits his own temperament" with the advice of a "good friend" ("kalyāṇa-mittatā") who is knowledgeable in the different meditation subjects (Ch. III, § 28). Buddhaghoṣa subsequently elaborates on the forty meditation subjects as follows (Ch. III, §104; Chs. IV–XI):


title: Buddhist meditation

text: When one overlays Buddhaghosa's 40 meditative subjects for the development of concentration with the Buddha's foundations of mindfulness, three practices are found to be in common: breath meditation, foulness meditation (which is similar to the Sattipatthana Sutta's cemetery contemplations, and to contemplation of bodily repulsiveness), and contemplation of the four elements. According to Pali commentaries, breath meditation can lead one to the equanimous fourth jhanic absorption. Contemplation of foulness can lead to the attainment of the first jhana, and contemplation of the four elements culminates in pre-jhana access concentration.


title: Buddhist meditation

text: The role of samatha in Buddhist practice, and the exact meaning of "samatha", are points of contention and investigation in contemporary Theravada and western "vipassanan". Burmese "vipassana" teachers have tended to disregard "samatha" as unnecessary, while Thai teachers see "samatha" and "vipassana" as intertwined.


title: Buddhist meditation

text: The exact meaning of "samatha" is also not clear, and westerners have started to question the receive wisdom on this. While "samatha" is usually equated with the "jhanas" in the commentarial tradition, scholars and practitioners have pointed out that "jhana" is more than a narrowing of the focus of the mind. While the second "jhana" may be characterized by "samadhi-ji", "born of concentration," the first "jhana" sets in quite naturally as a result of sense-restraint, while the third and fourth "jhana" are characterized by mindfulness and equanimity. Sati, sense-restraint and mindfulness are necessary preceding practices, while insight may mark the point where one enters the "stream" of development which results in "vimukti", release.


title: Buddhist meditation

text: According to Anālayo, the jhanas are crucial meditative states which lead to the abandonment of hindrances such as lust and aversion; however, they are not sufficient for the attainment of liberating insight. Some early texts also warn meditators against becoming attached to them, and therefore forgetting the need for the further practice of insight. According to Anālayo, "either one undertakes such insight contemplation while still being in the attainment, or else one does so retrospectively, after having emerged from the absorption itself but while still being in a mental condition close to it in concentrative depth."


title: Buddhist meditation

text: The position that insight can be practiced from within jhana, according to the early texts, is endorsed by Gunaratna, Crangle and Shankaman. Anālayo meanwhile argues, that the evidence from the early texts suggest that "contemplation of the impermanent nature of the mental constituents of an absorption takes place before or on emerging from the attainment".


title: Buddhist meditation

text: Particularly influential from the twentieth century onward has been the Burmese Vipassana movement, especially the "New Burmese Method" or "Vipassanā School" approach to "samatha" and "vipassanā" developed by Mingun Sayadaw and U Nārada and popularized by Mahasi Sayadaw. Here "samatha" is considered an optional but not necessary component of the practice—"vipassanā" is possible without it. Another Burmese method popularized in the west, notably that of Pa-Auk sayadaw Bhaddanta Āciṇṇa, uphold the emphasis on "samatha" explicit in the commentarial tradition of the "Visuddhimagga". Other Burmese traditions, derived from Ledi Sayadaw via Sayagyi U Ba Khin and popularized in the west by Mother Sayamagyi and S. N. Goenka, takes a similar approach. These Burmese traditions have been influential on Western Theravada-oriented teachers, notably Joseph Goldstein, Sharon Salzberg and Jack Kornfield.


title: Buddhist meditation

text: There are also other less well known Burmese meditation methods, such as the system developed by U Vimala, which focuses on knowledge of dependent origination and cittanupassana (mindfulness of the mind). Likewise, Sayadaw U Tejaniya's method also focuses on mindfulness of the mind.


title: Buddhist meditation

text: Also influential is the Thai Forest Tradition deriving from Mun Bhuridatta and popularized by Ajahn Chah, which, in contrast, stresses the inseparability of the two practices, and the essential necessity of both practices. Other noted practitioners in this tradition include Ajahn Thate and Ajahn Maha Bua, among others. There are other forms of Thai Buddhist meditation associated with particular teachers, including Buddhadasa Bhikkhu's presentation of anapanasati, Ajahn Lee's breath meditation method (which influenced his American student Thanissaro) and the "dynamic meditation" of Luangpor Teean Cittasubho.


title: Buddhist meditation

text: There are other less mainstream forms of Theravada meditation practiced in Thailand which include the vijja dhammakaya meditation developed by Luang Pu Sodh Candasaro and the meditation of former supreme patriarch Suk Kai Thuean (1733–1822). Newell notes that these two forms of modern Thai meditation share certain features in common with tantric practices such as the use of visualizations and centrality of maps of the body.


title: Buddhist meditation

text: A less common type of meditation is practiced in Cambodia and Laos by followers of Borān kammaṭṭhāna ('ancient practices') tradition. This form of meditation includes the use of mantras and visualizations.


title: Buddhist meditation

text: The now defunct Sarvāstivāda tradition, and its related sub-schools like the Sautrāntika and the Vaibhāṣika, were the most influential Buddhists in North India and Central Asia. Their highly complex Abhidharma treatises, such as the Mahavibhasa, the Sravakabhumi and the Abhidharmakosha, contain new developments in meditative theory which had a major influence on meditation as practiced in East Asian Mahayana and Tibetan Buddhism. Individuals known as "yogācāras ("yoga practitioners")" were influential in the development of Sarvāstivāda meditation praxis, and some modern scholars such as Yin Shun believe they were also influential in the development of Mahayana meditation. The "Dhyāna sutras" () or "meditation summaries" () are a group of early Buddhist meditation texts which are mostly based on the Yogacara meditation teachings of the Sarvāstivāda school of Kashmir circa 1st-4th centuries CE, which focus on the concrete details of the meditative practice of the Yogacarins of northern Gandhara and Kashmir. Most of the texts only survive in Chinese and were key works in the development of the Buddhist meditation practices of Chinese Buddhism.


title: Buddhist meditation

text: According to K.L. Dhammajoti, the Sarvāstivāda meditation practitioner begins with samatha meditations, divided into the fivefold mental stillings, each being recommended as useful for particular personality types:


title: Buddhist meditation

text: Contemplation of the impure, and mindfulness of breathing, was particularly important in this system; they were known as the 'gateways to immortality' ("amrta-dvāra"). The Sarvāstivāda system practiced breath meditation using the same sixteen aspect model used in the "anapanasati sutta," but also introduced a unique six aspect system which consists of:


title: Buddhist meditation

text: This sixfold breathing meditation method was influential in East Asia, and expanded upon by the Chinese Tiantai meditation master Zhiyi.


title: Buddhist meditation

text: After the practitioner has achieved tranquility, Sarvāstivāda Abhidharma then recommends one proceeds to practice the four applications of mindfulness ("smrti-upasthāna") in two ways. First they contemplate each specific characteristic of the four applications of mindfulness, and then they contemplate all four collectively.


title: Buddhist meditation

text: In spite of this systematic division of "samatha" and "vipasyana", the Sarvāstivāda Abhidharmikas held that the two practices are not mutually exclusive. The Mahavibhasa for example remarks that, regarding the six aspects of mindfulness of breathing, "there is no fixed rule here — all may come under "samatha" or all may come under "vipasyana"." The Sarvāstivāda Abhidharmikas also held that attaining the dhyānas was necessary for the development of insight and wisdom.


title: Buddhist meditation

text: Mahāyāna practice is centered on the path of the bodhisattva, a being which is aiming for full Buddhahood. Meditation ("dhyāna") is one of the transcendent virtues ("paramitas") which a bodhisattva must perfect in order to reach Buddhahood, and thus, it is central to Mahāyāna Buddhist praxis.


title: Buddhist meditation

text: Indian Mahāyāna Buddhism was initially a network of loosely connected groups and associations, each drawing upon various Buddhist texts, doctrines and meditation methods. Because of this, there is no single set of Indian Mahāyāna practices which can be said to apply to all Indian Mahāyānists, nor is there is a single set of texts which were used by all of them.


title: Buddhist meditation

text: Textual evidence shows that many Mahāyāna Buddhists in northern India as well as in Central Asia practiced meditation in a similar way to that of the Sarvāstivāda school outlined above. This can be seen in what is probably the most comprehensive and largest Indian Mahāyāna treatise on meditation practice, the "Yogācārabhūmi-Śāstra" (compiled c. 4th century), a compendium which explains in detail Yogācāra meditation theory, and outlines numerous meditation methods as well as related advice"." Among the topics discussed are the various early Buddhist meditation topics such as the four "dhyānas", the different kinds of "samādhi", the development of insight ("vipaśyanā") and tranquility ("śamatha"), the four foundations of mindfulness ("smṛtyupasthāna"), the five hindrances ("nivaraṇa"), and classic Buddhist meditations such as the contemplation of unattractiveness ("aśubhasaṃjnā"), impermanence ("anitya"), suffering ("duḥkha"), and contemplation death ("maraṇasaṃjñā"). Other works of the Yogācāra school, such as Asaṅga's "Abhidharmasamuccaya," and Vasubandhu's "Madhyāntavibhāga-bhāsya" also discuss meditation topics such as mindfulness, "smṛtyupasthāna," the 37 wings to awakening"," and "samadhi".


title: Buddhist meditation

text: Some Mahāyāna sutras also teach early Buddhist meditation practices. For example, the "Mahāratnakūṭa Sūtra" and the "Mahāprajñāpāramitā Sūtra" both teach the four foundations of mindfulness.


title: Buddhist meditation

text: The "Prajñāpāramitā Sutras" are some of the earliest Mahāyāna sutras. Their teachings center on the bodhisattva path (viz. the "paramitas"), the most important of which is the perfection of transcendent knowledge or "prajñāpāramitā." This knowledge is associated with the early Buddhist practice of the three "samādhis" (meditative concentrations)":" emptiness ("śūnyatā"), signlessness ("animitta"), and wishlessness or desirelessness ("apraṇihita"). These three "samadhis" are also mentioned in the "Mahāprajñāpāramitōpadeśa" (Ch. "Dà zhìdù lùn"), chapter X. In the "Prajñāpāramitā Sutras", "prajñāpāramitā" is described as a kind of "samādhi" which is also a deep understanding of reality arising from meditative insight that is totally non-conceptual and completely unattached to any person, thing or idea. The "Aṣṭasāhasrikā Prajñāpāramitā," possibly the earliest of these texts"," also equates "prajñāpāramitā" with what it terms the "aniyato" (unrestricted) "samādhi," “the "samādhi" of not taking up ("aparigṛhīta") any dharma”, and “the "samādhi" of not grasping at ("anupādāna") any dharma” (as a self)"." According to Shi Huifeng, this meditative concentration:entails not only not clinging to the five aggregates as representative of all phenomena, but also not clinging to the very notion of the five aggregates, their existence or non-existence, their impermanence or eternality, their being dissatisfactory or satisfactory, their emptiness or self-hood, their generation or cessation, and so forth with other antithetical pairs. To so mistakenly perceive the aggregates is to “course in a sign” ("nimite carati; xíng xiāng" 行相), i.e. to engage in the signs and conceptualization of phenomena, and not to course in "Prajñāpāramitā". Even to perceive of oneself as a bodhisattva who courses, or the "Prajñāpāramitā" in which one courses, are likewise coursing in signs.Other Indian Mahāyāna texts show new innovative methods which were unique to Mahāyāna Buddhism. Texts such as the Pure Land sutras, the "Akṣobhya-vyūha Sūtra" and the "Pratyutpanna Samādhi Sūtra" teach meditations on a particular Buddha (such as Amitābha or Akshobhya). Through the repetition of their name or some other phrase and certain visualization methods, one is said to be able to meet a Buddha face to face or at least to be reborn in a Buddha field (also known as "Pure land") like Abhirati and Sukhavati after death. The "Pratyutpanna sutra" for example, states that if one practices recollection of the Buddha ("Buddhānusmṛti") by visualizing a Buddha in their Buddha field and developing this "samadhi" for some seven days, one may be able to meet this Buddha in a vision or a dream so as to learn the Dharma from them. Alternatively, being reborn in one of their Buddha fields allows one to meet a Buddha and study directly with them, allowing one to reach Buddhahood faster. A set of sutras known as the Visualization Sutras also depict similar innovative practices using mental imagery. These practices been seen by some scholars as a possible explanation for the source of certain Mahāyāna sutras which are seen traditionally as direct visionary revelations from the Buddhas in their pure lands.


title: Buddhist meditation

text: Another popular practice was the memorization and recitation of various texts, such as sutras, mantras and dharanis. According to Akira Hirakawa, the practice of reciting "dharanis" (chants or incantations) became very important in Indian Mahāyāna. These chants were believed to have "the power to preserve good and prevent evil", as well as being useful to attain meditative concentration or "samadhi". Important Mahāyāna sutras such as the "Lotus Sutra", "Heart Sutra" and others prominently include "dharanis". Ryûichi Abé states that dharanis are also prominent in the "Prajñāpāramitā Sutras" wherein the Buddha "praises dharani incantation, along with the cultivation of "samadhi", as virtuous activity of a bodhisattva". They are also listed in the "Mahāprajñāpāramitōpadeśa", chapter X, as an important quality of a bodhisattva.


title: Buddhist meditation

text: A later Mahāyāna work which discusses meditation practice is Shantideva's "Bodhicaryāvatāra" (8th century) which depicts how a bodhisattva's meditation was understood in the later period of Indian Mahāyāna. Shantideva begins by stating that isolating the body and the mind from the world (i.e. from discursive thoughts) is necessary for the practice of meditation, which must begin with the practice of tranquility ("śamatha"). He promotes classic practices like meditating on corpses and living in forests, but these are preliminary to the Mahāyāna practices which initially focus on generating "bodhicitta," a mind intent on awakening for the benefit of all beings. An important of part of this practice is to cultivate and practice the understanding that oneself and other beings are actually the same, and thus all suffering must be removed, not just "mine". This meditation is termed by Shantideva "the exchange of self and other" and it is seen by him as the apex of meditation, since it simultaneously provides a basis for ethical action and cultivates insight into the nature of reality, i.e. emptiness.


title: Buddhist meditation

text: Another late Indian Mahāyāna meditation text is Kamalaśīla's "Bhāvanākrama" ("stages of meditation", 9th century), which teaches insight ("vipaśyanā") and tranquility ("śamatha") from a Yogācāra-Madhyamaka perspective.


title: Buddhist meditation

text: The meditation forms practiced during the initial stages of Chinese Buddhism did not differ much from those of Indian Mahayana Buddhism, though they did contain developments that could have arisen in Central Asia.


title: Buddhist meditation

text: The works of the Chinese translator An Shigao (安世高, 147-168 CE) are some of the earliest meditation texts used by Chinese Buddhism and their focus is mindfulness of breathing ("annabanna" 安那般那). The Chinese translator and scholar Kumarajiva (344–413 CE) transmitted various meditation works, including a meditation treatise titled "The Sūtra Concerned with Samādhi in Sitting Meditation" (坐禅三昧经, T.614, K.991) which teaches the Sarvāstivāda system of fivefold mental stillings. These texts are known as the Dhyāna sutras. They reflect the meditation practices of Kashmiri Buddhists, influenced by Sarvāstivāda and Sautrantika meditation teachings, but also by Mahayana Buddhism.


title: Buddhist meditation

text: The East Asian Yogācāra school or "Consciousness only school" (Ch. "Wéishí-zōng"), known in Japan as the "Hossō" school was a very influential tradition of Chinese Buddhism. They practiced several forms of meditation. According to Alan Sponberg, they included a class of visualization exercises, one of which centered on constructing a mental image of the Bodhisattva (and presumed future Buddha) Maitreya in Tusita heaven. A biography the Chinese Yogācāra master and translator Xuanzang depicts him practicing this kind of meditation. The goal of this practice seems to have been rebirth in Tusita heaven, so as to meet Maitreya and study Buddhism under him.


title: Buddhist meditation

text: Another method of meditation practiced in Chinese Yogācāra is called "the five level discernment of "vijñapti-mātra"" (impressions only), introduced by Xuanzang's disciple, Kuījī (632–682), which became one of the most important East Asian Yogācāra teachings. According to Alan Sponberg, this kind of vipasyana meditation was an attempt "to penetrate the true nature of reality by understanding the three aspects of existence in five successive steps or stages". These progressive stages or ways of seeing ("kuan") the world are:


title: Buddhist meditation

text: In China it has been traditionally held that the meditation methods used by the Tiantai school are the most systematic and comprehensive of all. In addition to its doctrinal basis in Indian Buddhist texts, the Tiantai school also emphasizes use of its own meditation texts which emphasize the principles of śamatha and vipaśyanā. Of these texts, Zhiyi's "Concise Śamathavipaśyanā" (小止観), "Mohe Zhiguan" (摩訶止観, Sanskrit "Mahāśamathavipaśyanā"), and "Six Subtle Dharma Gates" (六妙法門) are the most widely read in China. Rujun Wu identifies the work "Mahā-śamatha-vipaśyanā" of Zhiyi as the seminal meditation text of the Tiantai school. Regarding the functions of śamatha and vipaśyanā in meditation, Zhiyi writes in his work "Concise Śamatha-vipaśyanā":


title: Buddhist meditation

text: The Tiantai school also places a great emphasis on "ānāpānasmṛti," or mindfulness of breathing, in accordance with the principles of śamatha and vipaśyanā. Zhiyi classifies breathing into four main categories: panting (喘), unhurried breathing (風), deep and quiet breathing (氣), and stillness or rest (息). Zhiyi holds that the first three kinds of breathing are incorrect, while the fourth is correct, and that the breathing should reach stillness and rest. Zhiyi also outlines four kinds of samadhi in his "Mohe Zhiguan", and ten modes of practicing vipaśyanā.


title: Buddhist meditation

text: One of the adaptations by the Japanese Tendai school was the introduction of Mikkyō (esoteric practices) into Tendai Buddhism, which was later named "Taimitsu" by Ennin. Eventually, according to Tendai Taimitsu doctrine, the esoteric rituals came to be considered of equal importance with the exoteric teachings of the Lotus Sutra. Therefore, by chanting mantras, maintaining mudras, or performing certain meditations, one is able to see that the sense experiences are the teachings of Buddha, have faith that one is inherently an enlightened being, and one can attain enlightenment within this very body. The origins of Taimitsu are found in China, similar to the lineage that Kūkai encountered in his visit to Tang China and Saichō's disciples were encouraged to study under Kūkai.


title: Buddhist meditation

text: The Huayan school was a major school of Chinese Buddhism, which also strongly influenced Chan Buddhism. An important element of their meditation theory and practice is what was called the "Fourfold Dharmadhatu" ("sifajie", 四法界). Dharmadhatu (法界) is the goal of the bodhisattva's practice, the ultimate nature of reality or deepest truth which must be known and realized through meditation. According to Fox, the Fourfold Dharmadhatu is "four cognitive approaches to the world, four ways of apprehending reality". Huayan meditation is meant to progressively ascend through these four "increasingly more holographic perspectives on a single phenomenological manifold."


title: Buddhist meditation

text: According to Paul Williams, the reading and recitation of the Avatamsaka sutra was also a central practice for the tradition, for monks and laity.


title: Buddhist meditation

text: In Pure Land Buddhism, repeating the name of Amitābha is traditionally a form of mindfulness of the Buddha (Skt. ""). This term was translated into Chinese as "nianfo" (), by which it is popularly known in English. The practice is described as calling the buddha to mind by repeating his name, to enable the practitioner to bring all his or her attention upon that Buddha ("samādhi"). This may be done vocally or mentally, and with or without the use of Buddhist prayer beads. Those who practice this method often commit to a fixed set of repetitions per day, often from 50,000 to over 500,000.


title: Buddhist meditation

text: Repeating the Pure Land Rebirth dhāraṇī is another method in Pure Land Buddhism. Similar to the mindfulness practice of repeating the name of Amitābha Buddha, this dhāraṇī is another method of meditation and recitation in Pure Land Buddhism. The repetition of this dhāraṇī is said to be very popular among traditional Chinese Buddhists.


title: Buddhist meditation

text: Another practice found in Pure Land Buddhism is meditative contemplation and visualization of Amitābha, his attendant bodhisattvas, and the Pure Land. The basis of this is found in the "Amitāyurdhyāna Sūtra" ("Amitābha Meditation Sūtra").


title: Buddhist meditation

text: During sitting meditation (坐禅, Ch. "zuòchán," Jp. "zazen", Ko. "jwaseon"), practitioners usually assume a position such as the lotus position, half-lotus, Burmese, or seiza, often using the dhyāna mudrā. Often, a square or round cushion placed on a padded mat is used to sit on; in some other cases, a chair may be used. Various techniques and meditation forms are used in the different Zen traditions. Mindfulness of breathing is a common practice, used to develop mental focus and concentration.


title: Buddhist meditation

text: Another common form of sitting meditation is called "Silent illumination" (Ch. "mòzhào," Jp". mokushō"). This practice was traditionally promoted by the Caodong school of Chinese Chan and is associated with Hongzhi Zhengjue (1091—1157). In Hongzhi's practice of "nondual objectless meditation" the mediator strives to be aware of the totality of phenomena instead of focusing on a single object, without any interference, conceptualizing, grasping, goal seeking, or subject-object duality. This practice is also popular in the major schools of Japanese Zen, but especially Sōtō, where it is more widely known as "Shikantaza (Ch. zhǐguǎn dǎzuò, "Just sitting")."


title: Buddhist meditation

text: During the Sòng dynasty, a new meditation method was popularized by figures such as Dahui, which was called "kanhua chan" ("observing the phrase" meditation) which referred to contemplation on a single word or phrase (called the "huatou", "critical phrase") of a "gōng'àn" (Koan). In Chinese Chan and Korean Seon, this practice of "observing the "huatou"" ("hwadu" in Korean) is a widely practiced method.