title: Sukkot

text: In the days of the Temple in Jerusalem, all Israelite, and later Jewish men, women, and children on pilgrimage to Jerusalem for the festival would gather in the Temple courtyard on the first day of Chol HaMoed Sukkot to hear the Jewish king read selections from the Torah. This ceremony, which was mandated in Deuteronomy 31:10–13, was held every seven years, in the year following the Shmita (Sabbatical) year. This ceremony was discontinued after the destruction of the Temple, but it has been revived in Israel since 1952 on a smaller scale.


title: Sukkot

text: During the intermediate days of Sukkot, gatherings of music and dance, known as "Simchat Beit HaShoeivah" (Celebration of the Place of Water-Drawing), take place. This commemorates the celebration that accompanied the drawing of the water for the water-libation on the Altar, an offering unique to Sukkot, when water was carried up the Jerusalem pilgrim road from the Pool of Siloam to the Temple in Jerusalem.


title: Sukkot

text: The seventh day of Sukkot is known as "Hoshana Rabbah" (Great Supplication). This day is marked by a special synagogue service in which seven circuits are made by worshippers holding their Four Species, reciting additional prayers. In addition, a bundle of five willow branches is beaten on the ground.


title: Sukkot

text: The holiday immediately following Sukkot is known as "Shemini Atzeret" ( "Eighth [Day] of Assembly"). Shemini Atzeret is usually viewed as a separate holiday. In the Diaspora a second additional holiday, "Simchat Torah" ("Joy of the Torah"), is celebrated. In the Land of Israel, Simchat Torah is celebrated on Shemini Atzeret. On Shemini Atzeret people leave their sukkah and eat their meals inside the house. Outside the Land of Israel, many eat in the sukkah without making the blessing. The sukkah is not used on Simchat Torah.


title: Sukkot

text: According to , King Jeroboam, first king of the rebellious northern kingdom, instituted a feast on the fifteenth day of the eighth month in imitation of the feast of Sukkot in Judah, and pilgrims went to Bethel instead of Jerusalem to make thanksgiving offerings. Jeroboam feared that continued pilgrimages from the northern kingdom to Jerusalem could lead to pressure for reunion with Judah:


title: Sukkot

text: Sukkot is celebrated by a number of Christian denominations that observe holidays from the Old Testament. These groups base this on the belief that Jesus celebrated Sukkot (see the Gospel of John 7). The holiday is celebrated according to its Hebrew calendar dates. The first mention of observing the holiday by Christian groups dates to the 17th century, among the sect of the Subbotniks in Russia.


title: Sukkot

text: De Moor has suggested that there are links between Sukkot and the Ugaritic New Year festival, in particular the Ugaritic custom of erecting two rows of huts built of branches on the temple roof as temporary dwelling houses for their gods.


title: Sukkot

text: Some have pointed out that the original Thanksgiving holiday had many similarities with Sukkot in the Bible.


title: Psychoanalytic theory

text: Psychoanalytic theory is the theory of personality organization and the dynamics of personality development that guides psychoanalysis, a clinical method for treating psychopathology. First laid out by Sigmund Freud in the late 19th century, psychoanalytic theory has undergone many refinements since his work. The psychoanalytic theory came to full prominence in the last third of the twentieth century as part of the flow of critical discourse regarding psychological treatments after the 1960s, long after Freud's death in 1939. Freud had ceased his analysis of the brain and his physiological studies and shifted his focus to the study of the mind and the related psychological attributes making up the mind, and on treatment using free association and the phenomena of transference. His study emphasized the recognition of childhood events that could influence the mental functioning of adults. His examination of the genetic and then the developmental aspects gave the psychoanalytic theory its characteristics. Starting with his publication of "The Interpretation of Dreams" in 1899, his theories began to gain prominence.


title: Psychoanalytic theory

text: Psychoanalytic and psychoanalytical are used in English. The latter is the older term, and at first, simply meant 'relating to the analysis of the human psyche.' But with the emergence of psychoanalysis as a distinct clinical practice, both terms came to describe that. Although both are still used, today, the normal adjective is psychoanalytic.


title: Psychoanalytic theory

text: A therapeutic method, originated by Sigmund Freud, for treating mental disorders by investigating the interaction of conscious and unconscious elements in the patient's mind and bringing repressed fears and conflicts into the conscious mind, using techniques such as dream interpretation and free association. Also: a system of psychological theory is associated with this method.


title: Psychoanalytic theory

text: Through the scope of a psychoanalytic lens, humans are described as having sexual and aggressive drives. Psychoanalytic theorists believe that human behavior is deterministic. It is governed by irrational forces, and the unconscious, as well as instinctual and biological drives. Due to this deterministic nature, psychoanalytic theorists do not believe in free will.


title: Psychoanalytic theory

text: Freud first began his studies on psychoanalysis in collaboration with Dr. Josef Breuer, especially when it came to the study on Anna O. The relationship between Freud and Breuer was a mix of admiration and competition, based on the fact that they were working together on the Anna O. case and had to balance two different ideas as to her diagnosis and treatment. Today, Breuer can be considered the grandfather of psychoanalysis. Anna O. was subject to both physical and psychological disturbances, such as not being able to drink out of fear. Breuer and Freud both found that hypnosis was a great help in discovering more about Anna O. and her treatment. The research and ideas behind the study on Anna O. were highly referenced in Freud's lectures on the origin and development of psychoanalysis.


title: Psychoanalytic theory

text: These observations led Freud to theorize that the problems faced by hysterical patients could be associated with painful childhood experiences that could not be recalled. The influence of these lost memories shaped the feelings, thoughts, and behaviors of patients. These studies contributed to the development of the psychoanalytic theory.


title: Psychoanalytic theory

text: Sigmund Freud maintained that the personality consists of three different elements, the id, ego, and the superego. The id is the aspect of personality that is driven by internal and basic drives and needs. These are typically instinctual, such as hunger, thirst, and the drive for sex, or libido. The id is also the unconscious and stems from our instinctive abilities. The id acts in accordance with the pleasure principle, in that it avoids pain and seeks pleasure. Due to the instinctual quality of the id, it is impulsive and often unaware of the implications of actions. The ego is driven by the reality principle. The ego works to balance the id and superego, by trying to achieve the id's drive in the most realistic ways. It seeks to rationalize the id's instinct and please the drives that benefit the individual in the long term. It helps separate what is real, and realistic of our drives as well as being realistic about the standards that the superego sets for the individual. Additionally, the Ego is how we view ourselves. This is conscious, but not always true. For example, someone could believe they are the best-looking person in the world, however, this is just an opinion they have and not everyone will agree with that belief. The superego is driven by the morality principle. It acts in connection with the morality of higher thought and action. Instead of instinctively acting like the id, the superego works to act in socially acceptable ways. It employs morality, judging our sense of wrong and right and using guilt to encourage socially acceptable behavior. Furthermore, the Superego comes from the people around us. They affect what we believe in and how we view things, so this can be different depending on how you were raised and the culture you were around. The Superego is also responsible for finding the happy medium between the Id and Ego. The Id can sometimes be overly dominant when there are humanistic urges. The Ego can be very unrealistic in terms of how we view ourselves.


title: Psychoanalytic theory

text: The unconscious is the portion of the mind of which a person is not aware. Freud said that it is the unconscious that exposes the true feelings, emotions, and thoughts of the individual. There are a variety of psychoanalytic techniques used to access and understand the unconscious, ranging from methods like hypnosis, free association, and dream analysis. Dreams allow us to explore the unconscious; according to Freud, they are "the 'royal road' to the unconscious". Dreams are composed of latent and manifest content. Whereas latent content is the underlying meaning of a dream that may not be remembered when a person wakes up, manifest content is the content from the dream that a person remembers upon waking and can be analyzed by a psychoanalytic psychologist. Exploring and understanding the manifest content of dreams can inform the individual of complexes or disorders that may be under the surface of their personality. Dreams can provide access to the unconscious that is not easily accessible.


title: Psychoanalytic theory

text: Freudian slips (also known as parapraxes) occur when the ego and superego do not work properly, exposing the id and internal drives or wants. They are considered mistakes revealing the unconscious. Examples range from calling someone by the wrong name, misinterpreting a spoken or written word, or simply saying the wrong thing.


title: Psychoanalytic theory

text: The ego balances demands of the id, the superego, and of reality to maintain a healthy state of consciousness, where there is only minimal intrapsychic conflict. It thus reacts to protect the individual from stressors and from anxiety by distorting internal or external reality to a lesser or greater extent. This prevents threatening unconscious thoughts and material from entering the consciousness. The ten different defence mechanisms initially enumerated by Anna Freud are: repression, regression, reaction formation, isolation of affect, undoing, projection, introjection, turning against the self, reversal into the opposite, and sublimation. In the same work, however, she details other manoeuvres such as identification with the aggressor and intellectualisation that would later come to be considered defence mechanisms in their own right. Furthermore, this list has been greatly expanded upon by other psychoanalysts, with some authors claiming to enumerate in excess of one hundred defence mechanisms.


title: Psychoanalytic theory

text: Freud's take on the development of the personality (psyche). It is a stage theory that believes progress occurs through stages as the libido is directed to different body parts. The different stages, listed in order of progression, are Oral, Anal, Phallic (Oedipus complex), Latency, Genital. The Genital stage is achieved if people meet all their needs throughout the other stages with enough available sexual energy. Individuals who don't have their needs met in a given stage become fixated, or "stuck" in that stage.


title: Psychoanalytic theory

text: Freud's theory and work with psychosexual development led to Neo-Analytic/ Neo-Freudians who also believed in the importance of the unconscious, dream interpretations, defense mechanisms, and the integral influence of childhood experiences but had objections to the theory as well. They do not support the idea that development of the personality stops at age 6, instead, they believed development spreads across the lifespan. They extended Freud's work and encompassed more influence from the environment and the importance of conscious thought along with the unconscious. The most important theorists are Erik Erikson (Psychosocial Development), Anna Freud, Carl Jung, Alfred Adler and Karen Horney, and including the school of object relations. Erikson's Psychosocial Development theory is based on eight stages of development. The stages are trust vs. mistrust, autonomy vs. shame, initiative vs. guilt, industry vs. inferiority, identity vs. confusion, intimacy vs. isolation, generatively vs. stagnation, and integrity vs. despair. These are important to the psychoanalytic theory because it describes the different stages that people go through life. Each stage has a major impact on their life outcomes since they are going through conflicts at each stage and whichever route they decide to take, will have certain outcomes.


title: Psychoanalytic theory

text: Some claim that the theory is lacking in empirical data and too focused on pathology. Other criticisms are that the theory lacks consideration of culture and its influence on personality.


title: Psychoanalytic theory

text: The Psychoanalytic theory comes from Freud and is focused on childhood. This might be an issue since most believe studying children can be inconclusive. One major concern lies in if observed personality will be a lifelong occurrence or if the child will shed it later in life


title: Psychoanalytic theory

text: Psychoanalytic theory is a major influence in Continental philosophy and in aesthetics in particular. Freud is sometimes considered a philosopher. The psychoanalyst Jacques Lacan, and the philosophers Michel Foucault, and Jacques Derrida, have written extensively on how psychoanalysis informs philosophical analysis.


title: Psychoanalytic theory

text: When analyzing literary texts, the psychoanalytic theory could be utilized to decipher or interpret the concealed meaning within a text, or to better understand the author's intentions. Through the analysis of motives, Freud's theory can be used to help clarify the meaning of the writing as well as the actions of the characters within the text.


title: Butane

text: Butane () or "n"-butane is an alkane with the formula CH. Butane is a gas at room temperature and atmospheric pressure. Butane is a highly flammable, colorless, easily liquefied gas that quickly vaporizes at room temperature. The name butane comes from the root but- (from butyric acid, named after the Greek word for butter) and the suffix -ane. It was discovered by the chemist Dr. Walter Snelling in 1912. It was found dissolved in crude petroleum in 1864 by Edmund Ronalds, who was the first to describe its properties.


title: Butane

text: Butane is one of a group of liquefied petroleum gases (LP gases). The others include propane, propylene, butadiene, butylene, isobutylene, and mixtures thereof. Butane burns more cleanly than gasoline and coal.


title: Butane

text: The density of butane is highly dependent on temperature and pressure in the reservoir. For example, the density of liquid phase is 571.8±1 kg/m (for pressures up to 2MPa and temperature 27±0.2 °C), while the density of liquid butane is 625.5±0.7 kg/m (for pressures up to 2MPa and temperature -13±0.2 °C).


title: Butane

text: Butane and Propane were simultaneously discovered in 1912 by an American chemist, Dr. Walter Snelling. Snelling identified these gases as components in gasoline and found that if they were cooled, they could be stored in a volume-reduced liquified state in pressurized containers.


title: Butane

text: Rotation about the central C−C bond produces two different conformations ("trans" and "gauche") for "n"-butane.


title: Butane

text: When oxygen is plentiful, butane burns to form carbon dioxide and water vapor; when oxygen is limited, carbon (soot) or carbon monoxide may also be formed. Butane is denser than air.


title: Butane

text: "n"-Butane, like all hydrocarbons, undergoes free radical chlorination providing both 1-chloro- and 2-chlorobutanes, as well as more highly chlorinated derivatives. The relative rates of the chlorination is partially explained by the differing bond dissociation energies, 425 and 411 kJ/mol for the two types of C-H bonds.


title: Butane

text: Normal butane can be used for gasoline blending, as a fuel gas, fragrance extraction solvent, either alone or in a mixture with propane, and as a feedstock for the manufacture of ethylene and butadiene, a key ingredient of synthetic rubber. Isobutane is primarily used by refineries to enhance (increase) the octane number of motor gasoline.


title: Butane

text: For gasoline blending, n-butane is the main component used to manipulate the Reid vapor pressure (RVP). Since winter fuels require much higher vapor pressure for engines to start, refineries raise the RVP by blending more butane into the fuel. n-Butane has a relatively high research octane number (RON) and motor octane number (MON), which are 93 and 92 respectively.


title: Butane

text: When blended with propane and other hydrocarbons, the mixture may be referred to commercially as liquefied petroleum gas (LPG). It is used as a petrol component, as a feedstock for the production of base petrochemicals in steam cracking, as fuel for cigarette lighters and as a propellant in aerosol sprays such as deodorants.


title: Butane

text: Pure forms of butane, especially isobutane, are used as refrigerants and have largely replaced the ozone-layer-depleting halomethanes in refrigerators, freezers, and air conditioning systems. The operating pressure for butane is lower than for the halomethanes such as Freon-12 (R-12), so R-12 systems such as those in automotive air conditioning systems, when converted to pure butane, will function poorly. A mixture of isobutane and propane is used instead to give cooling system performance comparable to use of R-12.


title: Butane

text: Butane is also used as lighter fuel for a common lighter or butane torch and is sold bottled as a fuel for cooking, barbecues and camping stoves. The global market for butane canisters is dominated by South Korean manufacturers. In the 20th century the Braun (company) of Germany made a cordless hair styling device product that used butane as its heat source to produce steam.


title: Butane

text: As fuel, it is often mixed with small amounts of mercaptans to give the unburned gas an offensive smell easily detected by the human nose. In this way, butane leaks can easily be identified. While hydrogen sulfide and mercaptans are toxic, they are present in levels so low that suffocation and fire hazard by the butane becomes a concern far before toxicity. Most commercially available butane also contains some contaminant oil, which can be removed by filtration and will otherwise leave a deposit at the point of ignition and may eventually block the uniform flow of gas.


title: Butane

text: The butane used as a solvent for fragrance extraction does not contain these contaminants and butane gas can cause gas explosions in poorly ventilated areas if leaks go unnoticed and are ignited by spark or flame. Purified butane is used as a solvent in the industrial extraction of cannabis oils.


title: Butane

text: Inhalation of butane can cause euphoria, drowsiness, unconsciousness, asphyxia, cardiac arrhythmia, fluctuations in blood pressure and temporary memory loss, when abused directly from a highly pressurized container, and can result in death from asphyxiation and ventricular fibrillation. It enters the blood supply and within seconds produces intoxication. Butane is the most commonly abused volatile substance in the UK, and was the cause of 52% of solvent related deaths in 2000. By spraying butane directly into the throat, the jet of fluid can cool rapidly to by expansion, causing prolonged laryngospasm. "Sudden sniffer's death" syndrome, first described by Bass in 1970, is the most common single cause of solvent related death, resulting in 55% of known fatal cases.


title: Innuendo (album)

text: Innuendo is the fourteenth studio album by the British rock band Queen, released on 4 February 1991 by Parlophone in the United Kingdom and it is the band's first studio album to be released by Hollywood Records in the United States. Produced by David Richards and the band, it was the band's last album to be released in lead singer Freddie Mercury's lifetime, and their most recent one to be composed of entirely new material. It reached the No. 1 spot on the UK album charts for two weeks, and also peaked at No. 1 in Italy, the Netherlands, Germany, and Switzerland, staying at No. 1 for three weeks, four weeks, six weeks, and eight weeks, respectively. It was the first Queen album to go Gold in the US upon its release since "The Works" in 1984.


title: Innuendo (album)

text: The album was recorded between March 1989 and November 1990. In the spring of 1987, Mercury had been diagnosed with AIDS, although he kept his illness a secret from the public and denied numerous media reports that he was seriously ill. The band and producers were aiming for a November or December release date in order to catch the crucial Christmas market, but Mercury's declining health meant that the release of the album did not take place until February 1991. Stylistically, "Innuendo" is in some sense a return to Queen's roots, with its harder rock sound, complex musical composition (title track), psychedelic effects ("I'm Going Slightly Mad"), and strong vocals from Mercury ranging three octaves (F2-F5). Nine months after the album was released, Mercury died of AIDS-derived bronchopneumonia.


title: Innuendo (album)

text: The album cover was designed by Queen and Richard Gray. The booklets and single covers from the album are by Grandville, or are inspired by his illustrations. "Innuendo" was voted the 94th greatest album of all time in a national 2006 BBC poll.


title: Innuendo (album)

text: Queen released their thirteenth album, "The Miracle", in May 1989, but unlike their previous albums, they did not conduct a live tour. Freddie Mercury conducted an interview with BBC Radio 1, where he said that he wanted to break from the "album – tour – album – tour" routine. He had privately been diagnosed as HIV positive in 1987, and was now diagnosed with AIDS, which was not yet publicised; however, rumours had been spreading since 1988 about Mercury's health and of the possibility that he had the disease, with speculation fuelled by a clear physical decline in his appearance, particularly weight loss. While he kept quiet due to his personal rule not to talk to the media, the other band members denied the rumours; at one point, band member Roger Taylor told reporters that "he is healthy and working". In February 1990, Queen won the Brit Award for Outstanding Contribution to British Music. While Mercury accepted the award for the band at the Dominion Theatre, Brian May spoke for the band. Mercury's increasingly gaunt appearance at the ceremony sparked further speculation from the public about his health, which persisted throughout 1990. The 1990 BRIT Awards would be Mercury's final public appearance.


title: Innuendo (album)

text: Mercury did not speak publicly about his health, saying that he did not want to sell his music out of the people's sympathy. He was determined to continue working on music with Queen for as long as he could, saying that he would "keep working until I fucking drop". Mercury was persistently bothered by reporters at his London home, making it difficult for the band to record music. As a result, the band relocated to Mountain Studios in Montreux, where the safer and more peaceful atmosphere allowed the band to concentrate. Early in recording, the band decided again that all work would be credited to Queen as a whole instead of to individual contributing members; May said that the decision made a significant impact in the recording process, while Taylor said that it helped eliminate much of the egotistical struggles that would normally cause bands to break up.


title: Innuendo (album)

text: The album was released in the US under a new label, the Disney-owned Hollywood Records, in an effort to garner greater exposure there. Hollywood had also secured the rights to Queen's Elektra and Capitol back catalogs, and began reissuing albums early in 1991, marking Queen's 20th anniversary.


title: Innuendo (album)

text: "Innuendo" began as a jam session in Switzerland amongst Brian May, Roger Taylor and John Deacon in spring 1989. Freddie Mercury was upstairs and heard them playing the beat, and turned it into a song, creating the melody and starting off the lyrics. From then on all four worked on polishing the track and Taylor took over the lyrics (which were written as a tribute to Led Zeppelin and their song "Kashmir"). The middle section, written by Mercury, was included later and it featured a synth-orchestra programmed by producer David Richards and a flamenco interlude played by Yes guitarist Steve Howe, who had come to visit them and was asked to play. "Innuendo" was released as a single in January 1991, debuting at No. 1 in the UK.


title: Innuendo (album)

text: "I'm Going Slightly Mad" was begun in Mercury's London house, after he had the idea of writing a song about madness, inspired by Noël Coward's camp one-liners. Most of the lyrics like "banana tree" or "one needle", came from both him and his friend Peter Straker, who stayed up all night in Mercury's kitchen, devising ever more outlandish lines. The music is Mercury's and is one of the earliest songs the band were working on in Montreux when Steve Howe came in.


title: Innuendo (album)

text: The video that accompanied the song saw Mercury dressed in a costume suit with wild hair, white gloves, long pointing shoes and extremely heavy make up, filmed in black and white. Whilst Queen fans were thoroughly amused by the band in the video, in the documentary, "Champions of the World", Taylor confessed, from the band's perspective, the video was marred by Mercury's appearance having to be camouflaged by costume and make-up, as Taylor admitted Mercury looked "pretty ill, at that point."


title: Innuendo (album)

text: "Headlong" was written by May at the studio they had in Switzerland. He recorded it for his debut solo album, "Back to the Light", which he was making at the same time, but after hearing Mercury sing it, decided it worked better as a Queen song.


title: Innuendo (album)

text: "I Can't Live with You" was also written for May's solo album. He gave it to the band as well since Taylor, Deacon and Mercury were fond of the track. Drums were programmed on synth by May, and the keyboard-pads were added by the producer.


title: Innuendo (album)

text: An alternative version of this song appeared on the 1997 compilation album "Queen Rocks", billed as the "'97 Rocks Retake". It was said to be more along the lines of how May and Taylor originally wanted the track to sound, with a harder, guitar-driven rock edge. May has stated in an interview that most of the original demo is in the recording, making the song "impossible" to mix.


title: Innuendo (album)

text: "Don't Try So Hard" came from Mercury. The intro "rain" is actually the pre-set sound of the Korg M1, which appears when it is switched on ("00: Universe").


title: Innuendo (album)

text: "Ride the Wild Wind" was composed by Taylor, who recorded a demo with his own vocals. The album version is sung by Mercury with Taylor on backing vocals. The song is a sort of sequel of Taylor's "A Night at the Opera" composition, "I'm in Love with My Car", which focused on Taylor's passion for cars and racing. This time, the song involved all of the other members, that gave life to a fast song with beating drums and rhythmic bass line, eerily note-for-note similar to The Smiths' "Shakespeare's Sister", which create the sensation of speed and engine's roar. In the mid-part, a May solo, which accentuates the sense of high velocity, and also gives the song a heavier sound. In some parts, a racing car can be heard.


title: Innuendo (album)

text: "All God's People" was co-written by Mercury and Mike Moran, initially as part of Mercury's "Barcelona" project under the title "Africa by Night". He'd asked May to play guitar, then one thing led to another and the entire band played. The keyboard parts were played by Moran. Similar to "Somebody to Love" from "A Day at the Races", "All God's People" has a strong gospel influence.


title: Innuendo (album)

text: "These Are the Days of Our Lives" was written by Taylor. Keyboards were programmed by all band members in the studio, and conga percussion was recorded by David Richards. The music video for this song was Mercury's last appearance in a video medium, and with his knowing farewell look straight at the camera, Mercury whispers "I still love you" at the end of the song. By the time the video was made, it had become impossible to disguise that Mercury was seriously ill. The video was filmed in colour, but converted to black and white to minimise Mercury's frail appearance. At a later date, colour footage of the band making the video was released, revealing just how ill Mercury was at the time.


title: Innuendo (album)

text: "Delilah" is a song Mercury penned for his favourite female calico cat named Delilah. Although Mercury had about 11 cats, Delilah was special. May recorded his solo using a talk box. Taylor later admitted he is not fond of the song, stating "I hate 'Delilah'. That's just not me."


title: Innuendo (album)

text: The fly-away rocker "The Hitman" was started by Mercury. The original version was apparently on keyboards and in a different key. May took Mercury's riff (not uncommon), changed the key and recorded a demo of the heavy version. Deacon then re-arranged the structure and they all filled the gaps in lyrics and recorded it. All of the backing vocals were done by May. The demo version is sung by May, with Mercury making spoken comments (like "Bite the bullet baby!").


title: Innuendo (album)

text: "Bijou" was an idea Mercury and May had of making a song "inside-out", having guitar doing the verses and the vocal doing the break. Mercury put the chords, title and lyrics, and the two of them worked on the guitar parts. Mercury sang the first line and then May transferred the melody to his Red Special. The song was finished without any input from Taylor or Deacon. May later credited Jeff Beck's 1989 song "Where Were You" as the inspiration for the arrangement of "Bijou." The inspiration for the song itself is twofold, Brian May; “The vocal is a succinct and very precise little verse, a little gem, a "Bijou" - a jewel buried at the heart of the piece: hence the name of the song.” “My Mum was given a budgie by a friend - it became a great companion for her after she lost my Dad. She called it "Bijou" and she would spend hours talking to it! ..It was her little Bijou.” In 2008, Queen + Paul Rodgers performed this song in their shows of the Rock the Cosmos Tour by May playing the verse live and then having Mercury's studio vocals play while a screen showed footage from the band's Wembley concert in 1986, with the visuals put in sync with the tape.


title: Innuendo (album)

text: "The Show Must Go On" was written by May, based on a chord sequence he had been working on. May decided to use the sequence, and both he and Mercury decided the theme of the lyrics and wrote the first verse together. From then on May finished the lyrics, completed the vocal melody and wrote the bridge, inspired by "Pachelbel's Canon". Some keys and ideas were suggested by the producer too. The song chronicles the effort of Mercury continuing to perform despite approaching the end of his life.


title: Innuendo (album)

text: The song was initially not released as a single as part of promotion for the "Innuendo" album, but was released in October 1991 as the band launched their "Greatest Hits II" album. The video for the song featured a compilation of clips from all their videos since 1982, in support of the "Greatest Hits II" album. Due to Mercury's critical health at the time of its production, a fresh appearance by the band in a video was not possible. The track is a personal favourite of fellow British artist Elton John, who performed the song at the Freddie Mercury Tribute Concert with the remaining members of Queen, and Tony Iommi playing rhythm guitar. A different live version featuring John on vocals later appeared on Queen's "Greatest Hits III" album.


title: Innuendo (album)

text: "Innuendo" was the lead single from the album in most countries, except for the US where "Headlong" was released to radio as a promo prior to the album's release. The single was released on 14 January 1991 in Europe and in March 1991 in the US as a promo single, becoming Queen's third UK No. 1 single. The song also achieved modest success in the US, charting at No. 17 on "Billboard"'s Mainstream Rock Tracks chart. Still, the length and style of the track limited its appeal, and it only spent one week at No. 1 in the UK and quickly slid down the chart, spending only six weeks in the top 75. (B-side on 7 inch release: "Bijou").


title: Innuendo (album)

text: "I'm Going Slightly Mad" was released on 4 March 1991. The song reached No. 1 in Hong Kong and reached No. 22 on the UK charts. (B-side on 7 inch release: "The Hitman" in some countries, in others it was "Lost Opportunity", which was a non-album cut).


title: Innuendo (album)

text: "Headlong" was released as a promotional single in January 1991 in the US and as a single on 13 May 1991 in the UK. It entered the UK charts at No. 14, and reached No. 3 on the US "Billboard" Mainstream Rock Tracks chart. (B-side on 12 inch release: "All God's People" in some countries, in others, "Lost Opportunity" and in a few, "The Hitman". The 12" and CD also feature "Mad the Swine").


title: Innuendo (album)

text: "I Can't Live with You" was released as a promo single to radio stations in the US. This two-track promo single, completely remixed by Brian Malouf, uses slightly different lead vocal tracks by Mercury, louder and tighter harmony tracks, and reprogrammed synth drums, resulting in a much more punchy and "over the top" poppy version than included on the album. It reached No. 28 on the US Mainstream Rock Tracks chart.


title: Innuendo (album)

text: "These Are the Days of Our Lives" was first released in the US on Mercury's birthday, 5 September 1991 on cassette and to radio. In the UK it was released in December 1991 following Mercury's death, as a double A-side with "Bohemian Rhapsody". The single was the UK's Christmas No. 1 of 1991.


title: Innuendo (album)

text: "The Show Must Go On" was released on 14 October 1991 in the UK. The single was taken from the album, although it had not been released as a single from "Innuendo", and was released as promotion for the "Greatest Hits II" album ("Classic Queen" in the US/Canada), and peaked at No. 16 on the UK charts. After Mercury's death in November, the song re-entered the British charts and spent as many weeks in the top 75 as it had upon its original release. This single was released just six weeks before Mercury died. In 1992, the song was released as a double A-side with "Bohemian Rhapsody" in the US and reached No. 2 in the US. (The original B-side in October 1991 was "Keep Yourself Alive").


title: Innuendo (album)

text: In 1991, Chuck Eddy of "Rolling Stone" wrote that "Innuendo" was "the group's most playful top-to-bottom pile since "The Game"" and "there's no getting around the new album's craft", which he suggested meant the band were "finally satisfied with their lot in life", but he added ""Innuendo" is so lightweight you'll forget it as soon as it's over — which, with this band, should go without saying anyway". However, in 2016, writing for the same publication, Ron Hart described it as "Queen's last masterpiece" and an album which "boldly confronted mortality," likening it to David Bowie's final album "Blackstar".


title: Innuendo (album)

text: "People" wrote "If this is cartoon rock and roll, at least it's good and brazenly cartoonish." The "Orange County Register" observed "Queen dispenses with any stylistic variations or flirtations with dance music and offers its basic sound: lots of Mercury vocal leaps, fuzzed-out May guitar, choral overdubs and a sense of orchestral importance mixed with straightforward hard rock", concluding that it was a "mixed bag". The "LA Times" wrote "Given the bombast and harsh assault of Queen's biggest hits, it's a shock to find that the heart of... "Innuendo", is made of soft, sweet, sticky, sentimental goo", but added "The goo actually goes down well" and "Queen hasn't forgotten how to rock."


title: Innuendo (album)

text: In a retrospective review, AllMusic wrote ""Innuendo" was a fitting way to end one of rock's most successful careers". For "Classic Rock" in 2016, Malcolm Dome ranked it as Queen's ninth greatest album, writing that ""Innuendo" had a lot of intelligent humour and pathos about it." He praised the title track's "brilliantly synthesised orchestrations" and added "Perhaps most poignant of all is the low key yet mesmerising 'These Are The Days Of Our Lives', which ended with Mercury’s whispered paean 'I still love you', which was moving in its simplicity." Dome concluded "The album summed up how Queen could draw people close, yet still keep them at a convenient distance."


title: Innuendo (album)

text: All tracks credited to Queen, except "All God's People" credited to Queen and Mike Moran. All lead vocals by Freddie Mercury.


title: Innuendo (album)

text: "Innuendo" was re-released on vinyl on 25 September 2015 by Virgin EMI Records and Hollywood Records, alongside all of Queen's other studio albums. This was the first time the album had been presented on vinyl in full, spread across 2 LPs. Just as the original LP had an altered track listing, the 2 LP version swapped the placement of “I Can’t Live With You” and “These Are the Days of Our Lives” to have a more equal amount of time on each side of vinyl.


title: Cryptanalysis of the Enigma

text: Cryptanalysis of the Enigma ciphering system enabled the western Allies in World War II to read substantial amounts of Morse-coded radio communications of the Axis powers that had been enciphered using Enigma machines. This yielded military intelligence which, along with that from other decrypted Axis radio and teleprinter transmissions, was given the codename "Ultra".


title: Cryptanalysis of the Enigma

text: The Enigma machines were a family of portable cipher machines with rotor scramblers. Good operating procedures, properly enforced, would have made the plugboard Enigma machine unbreakable. However, most of the German military forces, secret services, and civilian agencies that used Enigma employed poor operating procedures, and it was these poor procedures that allowed the Enigma machines to be reverse-engineered and the ciphers to be read.


title: Cryptanalysis of the Enigma

text: The German plugboard-equipped Enigma became Nazi Germany's principal crypto-system. In December 1932 it was "broken" by mathematician Marian Rejewski at the Polish General Staff's Cipher Bureau, using mathematical permutation group theory combined with French-supplied intelligence material obtained from a German spy. By 1938 Rejewski had invented a device, the cryptologic bomb, and Henryk Zygalski had devised his sheets, to make the cipher-breaking more efficient. Five weeks before the outbreak of World War II, in late July 1939, at a conference just south of Warsaw, the Polish Cipher Bureau shared its Enigma-breaking techniques and technology with the French and British.


title: Cryptanalysis of the Enigma

text: During the German invasion of Poland, core Polish Cipher Bureau personnel were evacuated via Romania to France, where they established the "PC Bruno" signals intelligence station with French facilities support. Successful cooperation among the Poles, the French, and the British at Bletchley Park continued until June 1940, when France surrendered to the Germans.


title: Cryptanalysis of the Enigma

text: From this beginning, the British Government Code and Cypher School (GC&CS) at Bletchley Park built up an extensive cryptanalytic capability. Initially the decryption was mainly of "Luftwaffe" (German air force) and a few "Heer" (German army) messages, as the "Kriegsmarine" (German navy) employed much more secure procedures for using Enigma. Alan Turing, a Cambridge University mathematician and logician, provided much of the original thinking that led to upgrading of the Polish cryptologic bomb used in decrypting German Enigma ciphers. However, the "Kriegsmarine" introduced an Enigma version with a fourth rotor for its U-boats, resulting in a prolonged period when these messages could not be decrypted. With the capture of cipher keys and the use of much faster US Navy bombes, regular, rapid reading of U-boat messages resumed.


title: Cryptanalysis of the Enigma

text: The Enigma machines produced a polyalphabetic substitution cipher. During World War I, inventors in several countries realized that a purely random key sequence, containing no repetitive pattern, would, in principle, make a polyalphabetic substitution cipher unbreakable. This led to the development of rotor cipher machines which alter each character in the plaintext to produce the ciphertext, by means of a scrambler comprising a set of "rotors" that alter the electrical path from character to character, between the input device and the output device. This constant altering of the electrical pathway produces a very long period before the pattern—the key sequence or substitution alphabet—repeats.


title: Cryptanalysis of the Enigma

text: Decrypting enciphered messages involves three stages, defined somewhat differently in that era than in modern cryptography. First, there is the "identification" of the system in use, in this case Enigma; second, "breaking" the system by establishing exactly how encryption takes place, and third, "solving", which involves finding the way that the machine was set up for an individual message, "i.e." the "message key". Today, it is often assumed that an attacker knows how the encipherment process works (see Kerckhoffs's principle) and "breaking" is often used for "solving" a key. Enigma machines, however, had so many potential internal wiring states that reconstructing the machine, independent of particular settings, was a very difficult task.


title: Cryptanalysis of the Enigma

text: The Enigma rotor cipher machine was potentially an excellent system. It generated a polyalphabetic substitution cipher, with a period before repetition of the substitution alphabet that was much longer than any message, or set of messages, sent with the same key.


title: Cryptanalysis of the Enigma

text: A major weakness of the system, however, was that no letter could be enciphered to itself. This meant that some possible solutions could quickly be eliminated because of the same letter appearing in the same place in both the ciphertext and the putative piece of plaintext. Comparing the possible plaintext "Keine besonderen Ereignisse" (literally, "no special occurrences"—perhaps better translated as "nothing to report"; a phrase regularly used by one German outpost in North Africa), with a section of ciphertext, might produce the following:


title: Cryptanalysis of the Enigma

text: The mechanism of the Enigma consisted of a keyboard connected to a battery and a current entry plate or wheel (German: "Eintrittswalze"), at the right hand end of the scrambler (usually via a plugboard in the military versions). This contained a set of 26 contacts that made electrical connection with the set of 26 spring-loaded pins on the right hand rotor. The internal wiring of the core of each rotor provided an electrical pathway from the pins on one side to different connection points on the other. The left hand side of each rotor made electrical connection with the rotor to its left. The leftmost rotor then made contact with the reflector (German: "Umkehrwalze"). The reflector provided a set of thirteen paired connections to return the current back through the scrambler rotors, and eventually to the lampboard where a lamp under a letter was illuminated.


title: Cryptanalysis of the Enigma

text: Whenever a key on the keyboard was pressed, the stepping motion was actuated, advancing the rightmost rotor one position. Because it moved with each key pressed it is sometimes called the "fast rotor". When a notch on that rotor engaged with a pawl on the middle rotor, that too moved; and similarly with the leftmost ('slow') rotor.


title: Cryptanalysis of the Enigma

text: There are a huge number of ways that the connections within each scrambler rotor—and between the entry plate and the keyboard or plugboard or lampboard—could be arranged. For the reflector plate there are fewer, but still a large number of options to its possible wirings.


title: Cryptanalysis of the Enigma

text: Each scrambler rotor could be set to any one of its 26 starting positions (any letter of the alphabet). For the Enigma machines with only three rotors, their sequence in the scrambler—which was known as the "wheel order (WO)" to Allied cryptanalysts—could be selected from the six that are possible.


title: Cryptanalysis of the Enigma

text: Later Enigma models included an "alphabet ring" like a tyre around the core of each rotor. This could be set in any one of 26 positions in relation to the rotor's core. The ring contained one or more notches that engaged with a pawl that advanced the next rotor to the left.


title: Cryptanalysis of the Enigma

text: Later still, the three rotors for the scrambler were selected from a set of five or, in the case of the German Navy, eight rotors. The alphabet rings of rotors VI, VII and VIII contained two notches which, despite shortening the period of the substitution alphabet, made decryption more difficult.


title: Cryptanalysis of the Enigma

text: Most military Enigmas also featured a plugboard (German: "Steckerbrett"). This altered the electrical pathway between the keyboard and the entry wheel of the scrambler and, in the opposite direction, between the scrambler and the lampboard. It did this by exchanging letters reciprocally, so that if "A" was plugged to "G" then pressing key "A" would lead to current entering the scrambler at the "G" position, and if "G" was pressed the current would enter at "A". The same connections applied for the current on the way out to the lamp panel.


title: Cryptanalysis of the Enigma

text: Discovering the logical structure of the machine may be called "breaking" it, a one-off process except when changes or additions were made to the machines. Finding the internal and external settings for one or more messages may be called "solving" – although breaking is often used for this process as well.


title: Cryptanalysis of the Enigma

text: The various Enigma models provided different levels of security. The presence of a plugboard ("Steckerbrett") substantially increased the security of the encipherment. Each pair of letters that were connected together by a plugboard lead were referred to as "stecker partners", and the letters that remained unconnected were said to be "self-steckered". In general, the unsteckered Enigma was used for commercial and diplomatic traffic and could be broken relatively easily using hand methods, while attacking versions with a plugboard was much more difficult. The British read unsteckered Enigma messages sent during the Spanish Civil War, and also some Italian naval traffic enciphered early in World War II.


title: Cryptanalysis of the Enigma

text: The strength of the security of the ciphers that were produced by the Enigma machine was a product of the large numbers associated with the scrambling process.


title: Cryptanalysis of the Enigma

text: However, the way that Enigma was used by the Germans meant that, if the settings for one day (or whatever period was represented by each row of the setting sheet) were established, the rest of the messages for that network on that day could quickly be deciphered.


title: Cryptanalysis of the Enigma

text: Enigma featured the major operational convenience of being symmetrical (or self-inverse). This meant that decipherment worked in the same way as encipherment, so that when the ciphertext was typed in, the sequence of lamps that lit yielded the plaintext.


title: Cryptanalysis of the Enigma

text: Identical setting of the machines at the transmitting and receiving ends was achieved by key setting procedures. These varied from time to time and across different networks. They consisted of "setting sheets" in a "codebook". which were distributed to all users of a network, and were changed regularly. The message key was transmitted in an "indicator" as part of the message preamble. The word "key" was also used at Bletchley Park to describe the network that used the same Enigma setting sheets. Initially these were recorded using coloured pencils and were given the names "red", "light blue" etc., and later the names of birds such as "kestrel". During World War II the settings for most networks lasted for 24 hours, although towards the end of the war, some were changed more frequently. The sheets had columns specifying, for each day of the month, the rotors to be used and their positions, the ring positions and the plugboard connections. For security, the dates were in reverse chronological order down the page, so that each row could be cut off and destroyed when it was finished with.


title: Cryptanalysis of the Enigma

text: Up until 15 September 1938, the transmitting operator indicated to the receiving operator(s) how to set their rotors, by choosing a three letter "message key" (the key specific to that message) and enciphering it twice using the specified initial ring positions (the "Grundstellung"). The resultant 6-letter indicator, was then transmitted before the enciphered text of the message. Suppose that the specified "Grundstellung" was "RAO", and the chosen 3-letter message key was "IHL", the operator would set the rotors to "RAO" and encipher "IHL" twice. The resultant ciphertext, "DQYQQT", would be transmitted, at which point the rotors would be changed to the message key ("IHL") and then the message itself enciphered. The receiving operator would use the specified "Grundstellung RAO" to decipher the first six letters, yielding "IHLIHL". The receiving operator, seeing the repeated message key would know that there had been no corruption and use "IHL" to decipher the message.


title: Cryptanalysis of the Enigma

text: The weakness in this indicator procedure came from two factors. First, use of a global "Grundstellung" —this was changed in September 1938 so that the operator selected his initial position to encrypt the message key, and sent the initial position in clear followed by the enciphered message key. The second problem was the repetition of message key within the indicator, which was a serious security flaw. The message setting was encoded twice, resulting in a relation between first and fourth, second and fifth, and third and sixth character. This security problem enabled the Polish Cipher Bureau to break into the pre-war Enigma system as early as 1932. On 1 May 1940 the Germans changed the procedures to encipher the message key only once.


title: Cryptanalysis of the Enigma

text: In 1927, the UK openly purchased a commercial Enigma. Its operation was analysed and reported. Although a leading British cryptographer, Dilly Knox (a veteran of World War I and the cryptanalytical activities of the Royal Navy's Room 40), worked on decipherment he had only the messages he generated himself to practice with. After Germany supplied modified commercial machines to the Nationalist side in the Spanish Civil War, and with the Italian Navy (who were also aiding the Nationalists) using a version of the commercial Enigma that did not have a plugboard, Britain could intercept the radio broadcast messages. In April 1937 Knox made his first decryption of an Enigma encryption using a technique that he called "buttoning up" to discover the rotor wirings and another that he called "rodding" to solve messages. This relied heavily on cribs and on a crossword-solver's expertise in Italian, as it yielded a limited number of spaced-out letters at a time.


title: Cryptanalysis of the Enigma

text: Britain had no ability to read the messages broadcast by Germany, which used the military Enigma machine.


title: Cryptanalysis of the Enigma

text: In the 1920s the German military began using a 3-rotor Enigma, whose security was increased in 1930 by the addition of a plugboard. The Polish Cipher Bureau sought to break it due to the threat that Poland faced from Germany, but its early attempts did not succeed. Near the beginning of 1929, the Polish Cipher Bureau realized that mathematicians may make good codebreakers; the bureau invited math students at Poznań University to take a class on cryptology. After the class, the Bureau recruited some students to work part-time at a Bureau branch set up in Poznań for the students. The branch operated for some time. On 1 September 1932, 27-year-old Polish mathematician Marian Rejewski and two fellow Poznań University mathematics graduates, Henryk Zygalski and Jerzy Różycki, joined the Bureau full-time and moved to Warsaw. Their first task was to reconstruct a four-letter German naval cipher.


title: Cryptanalysis of the Enigma

text: Marian Rejewski quickly spotted the Germans' major procedural weaknesses of specifying a single indicator setting ("Grundstellung") for all messages on a network for a day, and repeating the operator's chosen "message key" in the enciphered 6-letter indicator. Those procedural mistakes allowed Rejewski to decipher the message keys without knowing any of the machine's wirings. In the above example of "DQYQQT" being the enciphered indicator, it is known that the first letter "D" and the fourth letter "Q" represent the same letter, enciphered three positions apart in the scrambler sequence. Similarly with "Q" and "Q" in the second and fifth positions, and "Y" and "T" in the third and sixth. Rejewski exploited this fact by collecting a sufficient set of messages enciphered with the same indicator setting, and assembling three tables for the 1,4, the 2,5, and the 3,6 pairings. Each of these tables might look something like the following:


title: Cryptanalysis of the Enigma

text: A path from one first letter to the corresponding fourth letter, then from that letter as the first letter to its corresponding fourth letter, and so on until the first letter recurs, traces out a cycle group. The following table contains six cycle groups.


title: Cryptanalysis of the Enigma

text: Rejewski recognized that a cycle group must pair with another group of the same length. Even though Rejewski did not know the rotor wirings or the plugboard permutation, the German mistake allowed him to reduce the number of possible substitution ciphers to a small number. For the 1,4 pairing above, there are only possibilities for the substitution ciphers at positions 1 and 4.


title: Cryptanalysis of the Enigma

text: Rejewski also exploited cipher clerk laziness. Scores of messages would be enciphered by several cipher clerks, but some of those messages would have the same encrypted indicator. That meant that both clerks happened to choose the same three letter starting position. Such a collision should be rare with randomly selected starting positions, but lazy cipher clerks often chose starting positions such as "AAA", "BBB", or "CCC". Those security mistakes allowed Rejewski to solve each of the six permutations used to encipher the indicator.


title: Cryptanalysis of the Enigma

text: That solution was an extraordinary feat. Rejewski did it without knowing the plugboard permutation or the rotor wirings. Even after solving for the six permutations, Rejewski did not know how the plugboard was set or the positions of the rotors. Knowing the six permutations also did not allow Rejewski to read any messages.


title: Cryptanalysis of the Enigma

text: Before Rejewski started work on the Enigma, the French had a spy, Hans-Thilo Schmidt, who worked at Germany's Cipher Office in Berlin and had access to some Enigma documents. Even with the help of those documents, the French did not make progress on breaking the Enigma. The French decided to share the material with their British and Polish allies. In a December 1931 meeting, the French provided Gwido Langer, head of the Polish Cipher Bureau, with copies of some Enigma material. Langer asked the French for more material, and Gustave Bertrand of French Military Intelligence quickly obliged; Bertrand provided additional material in May and September 1932. The documents included two German manuals and two pages of Enigma daily keys.


title: Cryptanalysis of the Enigma

text: In December 1932, the Bureau provided Rejewski with some German manuals and monthly keys. The material enabled Rejewski to achieve "one of the most important breakthroughs in cryptologic history" by using the theory of permutations and groups to work out the Enigma scrambler wiring.


title: Cryptanalysis of the Enigma

text: Rejewski could look at a day's cipher traffic and solve for the permutations at the six sequential positions used to encipher the indicator. Since Rejewski had the cipher key for the day, he knew and could factor out the plugboard permutation. He assumed the keyboard permutation was the same as the commercial Enigma, so he factored that out. He knew the rotor order, the ring settings, and the starting position. He developed a set of equations that would allow him to solve for the rightmost rotor wiring assuming the two rotors to the left did not move.


title: Cryptanalysis of the Enigma

text: He attempted to solve the equations, but failed with inconsistent results. After some thought, he realized one of his assumptions must be wrong.


title: Cryptanalysis of the Enigma

text: Rejewski found that the connections between the military Enigma's keyboard and the entry ring were not, as in the commercial Enigma, in the order of the keys on a German typewriter. He made an inspired correct guess that it was in alphabetical order. Britain's Dilly Knox was astonished when he learned, in July 1939, that the arrangement was so simple.


title: Cryptanalysis of the Enigma

text: With the new assumption, Rejewski succeeded in solving the wiring of the rightmost rotor. The next month's cipher traffic used a different rotor in the rightmost position, so Rejewski used the same equations to solve for its wiring. With those rotors known, the remaining third rotor and the reflector wiring were determined. Without capturing a single rotor to reverse engineer, Rejewski had determined the logical structure of the machine.


title: Cryptanalysis of the Enigma

text: The Polish Cipher Bureau then had some Enigma machine replicas made; the replicas were called "Enigma doubles".


title: Cryptanalysis of the Enigma

text: The Poles now had the machine's wiring secrets, but they still needed to determine the daily keys for the cipher traffic. The Poles would examine the Enigma traffic and use the method of characteristics to determine the six permutations used for the indicator. The Poles would then use the grill method to determine the rightmost rotor and its position. That search would be complicated by the plugboard permutation, but that permutation only swapped six pairs of letters — not enough to disrupt the search. The grill method also determined the plugboard wiring. The grill method could also be used to determine the middle and left rotors and their setting (and those tasks were simpler because there was no plugboard), but the Poles eventually compiled a catalog of the possible permutations (reflector and 2 leftmost rotor permutations), so they could just look up the answer.


title: Cryptanalysis of the Enigma

text: The only remaining secret of the daily key would be the ring settings, and the Poles would attack that problem with brute force. Most messages would start with the three letters "ANX" ("an" is German for "to" and the "X" character was used as a space). It may take almost trials, but that was doable. Once the ring settings were found, the Poles could read the day's traffic.


title: Cryptanalysis of the Enigma

text: The Germans made it easy for the Poles in the beginning. The rotor order only changed every quarter, so the Poles would not have to search for the rotor order. Later the Germans changed it every month, but that would not cause much trouble, either. Eventually, the Germans would change the rotor order every day, and late in the war (after Poland had been overrun) the rotor order might be changed during the day.


title: Cryptanalysis of the Enigma

text: Rejewski realised that, although the letters in the cycle groups were changed by the plugboard, the number and lengths of the cycles were unaffected—in the example above, six cycle groups with lengths of 9, 9, 3, 3, 1 and 1. He described this invariant structure as the "characteristic" of the indicator setting. There were only 105,456 possible rotor settings. The Poles therefore set about creating a "card catalog" of these cycle patterns.


title: Cryptanalysis of the Enigma

text: The cycle-length method would avoid using the grill. The card catalog would index the cycle-length for all starting positions (except for turnovers that occurred while enciphering an indicator). The day's traffic would be examined to discover the cycles in the permutations. The card catalog would be consulted to find the possible starting positions. There are roughly 1 million possible cycle-length combinations and only 105,456 starting positions. Having found a starting position, the Poles would use an Enigma double to determine the cycles at that starting position without a plugboard. The Poles would then compare those cycles to the cycles with the (unknown) plugboard and solve for the plugboard permutation (a simple substitution cipher). Then the Poles could find the remaining secret of the ring settings with the ANX method.


title: Cryptanalysis of the Enigma

text: Rejewski, in 1934 or 1935, devised a machine to facilitate making the catalog and called it a "cyclometer". This "comprised two sets of rotors... connected by wires through which electric current could run. Rotor N in the second set was three letters out of phase with respect to rotor N in the first set, whereas rotors L and M in the second set were always set the same way as rotors L and M in the first set". Preparation of this catalog, using the cyclometer, was, said Rejewski, "laborious and took over a year, but when it was ready, obtaining daily keys was a question of [some fifteen] minutes".


title: Cryptanalysis of the Enigma

text: However, on 1 November 1937, the Germans changed the Enigma reflector, necessitating the production of a new catalog—"a task which [says Rejewski] consumed, on account of our greater experience, probably somewhat less than a year's time".


title: Cryptanalysis of the Enigma

text: This characteristics method stopped working for German naval Enigma messages on 1 May 1937, when the indicator procedure was changed to one involving special codebooks (see German Navy 3-rotor Enigma below). Worse still, on 15 September 1938 it stopped working for German army and air force messages because operators were then required to choose their own "Grundstellung" (initial rotor setting) for each message. Although German army message keys would still be double-enciphered, the day's keys would not be double-enciphered at the same initial setting, so the characteristic could no longer be found or exploited.


title: Cryptanalysis of the Enigma

text: Although the characteristics method no longer worked, the inclusion of the enciphered message key twice gave rise to a phenomenon that the cryptanalyst Henryk Zygalski was able to exploit. Sometimes (about one message in eight) one of the repeated letters in the message key enciphered to the same letter on both occasions. These occurrences were called "samiczki" (in English, "females"—a term later used at Bletchley Park).


title: Cryptanalysis of the Enigma

text: Only a limited number of scrambler settings would give rise to females, and these would have been identifiable from the card catalog. If the first six letters of the ciphertext were SZVSIK", this would be termed a 1-4 female; if "WHOEHS", a 2-5 female; and if "ASWCRW, a 3-6 female. The method was called "Netz" (from "Netzverfahren", "net method"), or the Zygalski sheet method as it used perforated sheets that he devised, although at Bletchley Park Zygalski's name was not used for security reasons. About ten females from a day's messages were required for success.


title: Cryptanalysis of the Enigma

text: There was a set of 26 of these sheets for each of the six possible sequences "wheel orders". Each sheet was for the left (slowest-moving) rotor. The 51×51 matrices on the sheets represented the 676 possible starting positions of the middle and right rotors. The sheets contained about 1000 holes in the positions in which a female could occur. The set of sheets for that day's messages would be appropriately positioned on top of each other in the perforated sheets apparatus. Rejewski wrote about how the device was operated:


title: Cryptanalysis of the Enigma

text: The holes in the sheets were painstakingly cut with razor blades and in the three months before the next major setback, the sets of sheets for only two of the possible six wheel orders had been produced.


title: Cryptanalysis of the Enigma

text: After Rejewski's characteristics method became useless, he invented an electro-mechanical device that was dubbed the "bomba kryptologiczna" or "cryptologic bomb". Each machine contained six sets of Enigma rotors for the six positions of the repeated three-letter key. Like the Zygalski sheet method, the "bomba" relied on the occurrence of "females", but required only three instead of about ten for the sheet method. Six "bomby" were constructed, one for each of the then possible "wheel orders". Each "bomba" conducted an exhaustive (brute-force) analysis of the 17,576 possible message keys.


title: Cryptanalysis of the Enigma

text: The cipher message transmitted the "Grundstellung" in the clear, so when a "bomba" found a match, it revealed the rotor order, the rotor positions, and the ring settings. The only remaining secret was the plugboard permutation.


title: Cryptanalysis of the Enigma

text: On 15 December 1938, the German Army increased the complexity of Enigma enciphering by introducing two additional rotors (IV and V). This increased the number of possible "wheel orders" from 6 to 60. The Poles could then read only the small minority of messages that used neither of the two new rotors. They did not have the resources to commission 54 more bombs or produce 58 sets of Zygalski sheets. Other Enigma users received the two new rotors at the same time. However, until 1 July 1939 the "Sicherheitsdienst" (SD)—the intelligence agency of the SS and the Nazi Party—continued to use its machines in the old way with the same indicator setting for all messages. This allowed Rejewski to reuse his previous method, and by about the turn of the year he had worked out the wirings of the two new rotors. On 1 January 1939, the Germans increased the number of plugboard connections from between five and eight to between seven and ten, which made other methods of decryption even more difficult.


title: Cryptanalysis of the Enigma

text: Rejewski wrote, in a 1979 critique of appendix 1, volume 1 (1979), of the official history of British Intelligence in the Second World War:


title: Cryptanalysis of the Enigma

text: As the likelihood of war increased in 1939, Britain and France pledged support for Poland in the event of action that threatened its independence. In April, Germany withdrew from the German–Polish Non-Aggression Pact of January 1934. The Polish General Staff, realizing what was likely to happen, decided to share their work on Enigma decryption with their western allies. Marian Rejewski later wrote:


title: Cryptanalysis of the Enigma

text: At a conference near Warsaw on 26 and 27 July 1939, the Poles revealed to the French and British that they had broken Enigma and pledged to give each a Polish-reconstructed Enigma, along with details of their Enigma-solving techniques and equipment, including Zygalski's perforated sheets and Rejewski's cryptologic bomb. In return, the British pledged to prepare two full sets of Zygalski sheets for all 60 possible wheel orders. Dilly Knox was a member of the British delegation. He commented on the fragility of the Polish system's reliance on the repetition in the indicator, because it might "at any moment be cancelled". In August two Polish Enigma doubles were sent to Paris, whence Gustave Bertrand took one to London, handing it to Stewart Menzies of Britain's Secret Intelligence Service at Victoria Station.


title: Cryptanalysis of the Enigma

text: Peter Calvocoressi, who became head of the Luftwaffe section in Hut 3, wrote of the Polish contribution:


title: Cryptanalysis of the Enigma

text: On 5 September 1939 the Cipher Bureau began preparations to evacuate key personnel and equipment from Warsaw. Soon a special evacuation train, the Echelon F, transported them eastward, then south. By the time the Cipher Bureau was ordered to cross the border into allied Romania on 17 September, they had destroyed all sensitive documents and equipment and were down to a single very crowded truck. The vehicle was confiscated at the border by a Romanian officer, who separated the military from the civilian personnel. Taking advantage of the confusion, the three mathematicians ignored the Romanian's instructions. They anticipated that in an internment camp they might be identified by the Romanian security police, in which the German Abwehr and SD had informers.


title: Cryptanalysis of the Enigma

text: The mathematicians went to the nearest railroad station, exchanged money, bought tickets, and boarded the first train headed south. After a dozen or so hours, they reached Bucharest, at the other end of Romania. There they went to the British embassy. Told by the British to "come back in a few days", they next tried the French embassy, introducing themselves as "friends of Bolek" (Bertrand's Polish code name) and asking to speak with a French military officer. A French Army colonel telephoned Paris and then issued instructions for the three Poles to be assisted in evacuating to Paris.


title: Cryptanalysis of the Enigma

text: On 20 October 1939, at "PC Bruno" outside Paris, the Polish cryptologists resumed work on German Enigma ciphers, in collaboration with Bletchley Park.


title: Cryptanalysis of the Enigma

text: "PC Bruno" and Bletchley Park worked together closely, communicating via a telegraph line secured by the use of Enigma doubles. In January 1940 Alan Turing spent several days at "PC Bruno" conferring with his Polish colleagues. He had brought the Poles a full set of Zygalski sheets that had been punched at Bletchley Park by John Jeffreys using Polish-supplied information, and on 17 January 1940, the Poles made the first break into wartime Enigma traffic—that from 28 October 1939. From that time, until the Fall of France in June 1940, 17 percent of the Enigma keys that were found by the allies, were solved at "PC Bruno".


title: Cryptanalysis of the Enigma

text: Just before opening their 10 May 1940 offensive against the Low Countries and France, the Germans made the feared change in the indicator procedure, discontinuing the duplication of the enciphered message key. This meant that the Zygalski sheet method no longer worked. Instead, the cryptanalysts had to rely on exploiting the operator weaknesses described below, particularly the cillies and the Herivel tip.


title: Cryptanalysis of the Enigma

text: After the June Franco-German armistice, the Polish cryptological team resumed work in France's southern "Free Zone", although probably not on Enigma. Marian Rejewski and Henryk Zygalski, after many travails, perilous journeys and Spanish imprisonment, finally made it to Britain, where they were inducted into the Polish Army and put to work breaking German "SS" and "SD" hand ciphers at a Polish signals facility in Boxmoor. Due to their having been in occupied France, it was thought too risky to invite them to work at Bletchley Park.


title: Cryptanalysis of the Enigma

text: After the German occupation of Vichy France, several of those who had worked at "PC Bruno" were captured by the Germans. Despite the dire circumstances in which some of them were held, none betrayed the secret of Enigma's decryption.


title: Cryptanalysis of the Enigma

text: Apart from some less-than-ideal inherent characteristics of the Enigma, in practice the system's greatest weakness was the way that it was used. The basic principle of this sort of enciphering machine is that it should deliver a very long stream of transformations that are difficult for a cryptanalyst to predict. Some of the instructions to operators, however, and their sloppy habits, had the opposite effect. Without these operating shortcomings, Enigma would, almost certainly, not have been broken.


title: Cryptanalysis of the Enigma

text: The set of shortcomings that the Polish cryptanalysts exploited to such great effect included the following:


title: Cryptanalysis of the Enigma

text: Other useful shortcomings that were discovered by the British and later the American cryptanalysts included the following, many of which depended on frequent solving of a particular network:


title: Cryptanalysis of the Enigma

text: Mavis Lever, a member of Dilly Knox's team, recalled an occasion when there was an extraordinary message.


title: Cryptanalysis of the Enigma

text: Postwar debriefings of German cryptographic specialists, conducted as part of project TICOM, tend to support the view that the Germans were well aware that the un-steckered Enigma was theoretically solvable, but thought that the steckered Enigma had not been solved.


title: Cryptanalysis of the Enigma

text: The term "crib" was used at Bletchley Park to denote any "known plaintext" or "suspected plaintext" at some point in an enciphered message.


title: Cryptanalysis of the Enigma

text: Britain's Government Code and Cipher School (GC&CS), before its move to Bletchley Park, had realised the value of recruiting mathematicians and logicians to work in codebreaking teams. Alan Turing, a Cambridge University mathematician with an interest in cryptology and in machines for implementing logical operations—and who was regarded by many as a genius—had started work for GC&CS on a part-time basis from about the time of the Munich Crisis in 1938. Gordon Welchman, another Cambridge mathematician, had also received initial training in 1938, and they both reported to Bletchley Park on 4 September 1939, the day after Britain declared war on Germany.


title: Cryptanalysis of the Enigma

text: Most of the Polish success had relied on the repetition within the indicator. But as soon as Turing moved to Bletchley Park—where he initially joined Dilly Knox in the research section—he set about seeking methods that did not rely on this weakness, as they correctly anticipated that the German Army and Air Force might follow the German Navy in improving their indicator system.


title: Cryptanalysis of the Enigma

text: The Poles had used an early form of crib-based decryption in the days when only six leads were used on the plugboard. The technique became known as the "Forty Weepy Weepy" method for the following reason. When a message was a continuation of a previous one, the plaintext would start with "FORT" (from "Fortsetzung", meaning "continuation") followed by the time of the first message given twice bracketed by the letter "Y". At this time numerals were represented by the letters on the top row of the Enigma keyboard. So, "continuation of message sent at 2330" was represented as "FORTYWEEPYYWEEPY".


title: Cryptanalysis of the Enigma

text: "Cribs" were fundamental to the British approach to solving Enigma keys, but guessing the plaintext for a message was a highly skilled business. So in 1940 Stuart Milner-Barry set up a special "Crib Room" in Hut 8.


title: Cryptanalysis of the Enigma

text: Foremost amongst the knowledge needed for identifying cribs was the text of previous decrypts. Bletchley Park maintained detailed indexes of message preambles, of every person, of every ship, of every unit, of every weapon, of every technical term and of repeated phrases such as forms of address and other German military jargon. For each message the traffic analysis recorded the radio frequency, the date and time of intercept, and the preamble—which contained the network-identifying discriminant, the time of origin of the message, the callsign of the originating and receiving stations, and the indicator setting. This allowed cross referencing of a new message with a previous one. Thus, as Derek Taunt, another Cambridge mathematician-cryptanalyst wrote, the truism that "nothing succeeds like success" is particularly apposite here.


title: Cryptanalysis of the Enigma

text: Stereotypical messages included "Keine besonderen Ereignisse" (literally, "no special occurrences"—perhaps better translated as "nothing to report"), "An die Gruppe" ("to the group") and a number that came from weather stations such as "weub null seqs null null" ("weather survey 0600"). This was actually rendered as "WEUBYYNULLSEQSNULLNULL". The word "WEUB" being short for "Wetterübersicht", "YY" was used as a separator and "SEQS" was common abbreviation of "sechs" (German for "six"). As another example, Field Marshal Erwin Rommel's Quartermaster started all of his messages to his commander with the same formal introduction.


title: Cryptanalysis of the Enigma

text: With a combination of probable plaintext fragment and the fact that no letter could be enciphered as itself, a corresponding ciphertext fragment could often be tested by trying every possible alignment of the crib against the ciphertext, a procedure known as "crib-dragging". This, however, was only one aspect of the processes of solving a key. Derek Taunt has written that the three cardinal personal qualities that were in demand for cryptanalysis were (1) a creative imagination, (2) a well-developed critical faculty, and (3) a habit of meticulousness. Skill at solving crossword puzzles was famously tested in recruiting some cryptanalysts. This was useful in working out plugboard settings when a possible solution was being examined. For example, if the crib was the word "WETTER" (German for "weather") and a possible decrypt before the plugboard settings had been discovered, was "TEWWER", it is easy to see that "T" with "W" are "stecker partners". These examples, although illustrative of the principles, greatly over-simplify the cryptanalysts' tasks.


title: Cryptanalysis of the Enigma

text: A fruitful source of cribs was re-encipherments of messages that had previously been decrypted either from a lower-level manual cipher or from another Enigma network. This was called a "kiss" and happened particularly with German naval messages being sent in the "dockyard cipher" and repeated "verbatim" in an Enigma cipher. One German agent in Britain, Nathalie Sergueiew, code named "Treasure", who had been "turned" to work for the Allies, was very verbose in her messages back to Germany, which were then re-transmitted on the "Abwehr" Enigma network. She was kept going by MI5 because this provided long cribs, not because of her usefulness as an agent to feed incorrect information to the "Abwehr".


title: Cryptanalysis of the Enigma

text: Occasionally, when there was a particularly urgent need to solve German naval Enigma keys, such as when an Arctic convoy was about to depart, mines would be laid by the RAF in a defined position, whose grid reference in the German naval system did not contain any of the words (such as "sechs" or "sieben") for which abbreviations or alternatives were sometimes used. The warning message about the mines and then the "all clear" message, would be transmitted both using the "dockyard cipher" and the U-boat Enigma network. This process of "planting" a crib was called "gardening".


title: Cryptanalysis of the Enigma

text: Although "cillies" were not actually cribs, the "chit-chat" in clear that Enigma operators indulged in amongst themselves, often gave a clue as to the cillies that they might generate.


title: Cryptanalysis of the Enigma

text: When captured German Enigma operators revealed that they had been instructed to encipher numbers by spelling them out rather than using the top row of the keyboard, Alan Turing reviewed decrypted messages and determined that the word "eins" ("one") appeared in 90% of messages. Turing automated the crib process, creating the "Eins Catalogue", which assumed that "eins" was encoded at all positions in the plaintext. The catalogue included every possible rotor position for "EINS" with that day's "wheel order" and plugboard connections.


title: Cryptanalysis of the Enigma

text: The British bombe was an electromechanical device designed by Alan Turing soon after he arrived at Bletchley Park in September 1939. Harold "Doc" Keen of the British Tabulating Machine Company (BTM) in Letchworth ( from Bletchley) was the engineer who turned Turing's ideas into a working machine—under the codename CANTAB. Turing's specification developed the ideas of the Poles' "bomba kryptologiczna" but was designed for the much more general crib-based decryption.


title: Cryptanalysis of the Enigma

text: The bombe helped to identify the "wheel order", the initial positions of the rotor cores, and the "stecker partner" of a specified letter. This was achieved by examining all 17,576 possible scrambler positions for a set of "wheel orders" on a comparison between a crib and the ciphertext, so as to eliminate possibilities that contradicted the Enigma's known characteristics. In the words of Gordon Welchman "the task of the bombe was simply to reduce the assumptions of "wheel order" and scrambler positions that required 'further analysis' to a manageable number."


title: Cryptanalysis of the Enigma

text: The demountable drums on the front of the bombe were wired identically to the connections made by Enigma's different rotors. Unlike them, however, the input and output contacts for the left-hand and the right-hand sides were separate, making 104 contacts between each drum and the rest of the machine. This allowed a set of scramblers to be connected in series by means of 26-way cables. Electrical connections between the rotating drums' wiring and the rear plugboard were by means of metal brushes. When the bombe detected a scrambler position with no contradictions, it stopped and the operator would note the position before restarting it.


title: Cryptanalysis of the Enigma

text: Although Welchman had been given the task of studying Enigma traffic callsigns and discriminants, he knew from Turing about the bombe design and early in 1940, before the first pre-production bombe was delivered, he showed him an idea to increase its effectiveness. It exploited the reciprocity in plugboard connections, to reduce considerably the number of scrambler settings that needed to be considered further. This became known as the "diagonal board" and was subsequently incorporated to great effect in all the bombes.


title: Cryptanalysis of the Enigma

text: A cryptanalyst would prepare a crib for comparison with the ciphertext. This was a complicated and sophisticated task, which later took the Americans some time to master. As well as the crib, a decision as to which of the many possible "wheel orders" could be omitted had to be made. Turing's Banburismus was used in making this major economy. The cryptanalyst would then compile a "menu" which specified the connections of the cables of the patch panels on the back of the machine, and a particular letter whose "stecker partner" was sought. The menu reflected the relationships between the letters of the crib and those of the ciphertext. Some of these formed loops (or "closures" as Turing called them) in a similar way to the "cycles" that the Poles had exploited.


title: Cryptanalysis of the Enigma

text: The reciprocal nature of the plugboard meant that no letter could be connected to more than one other letter. When there was a contradiction of two different letters apparently being "stecker partners" with the letter in the menu, the bombe would detect this, and move on. If, however, this happened with a letter that was not part of the menu, a false stop could occur. In refining down the set of stops for further examination, the cryptanalyst would eliminate stops that contained such a contradiction. The other plugboard connections and the settings of the alphabet rings would then be worked out before the scrambler positions at the possible true stops were tried out on Typex machines that had been adapted to mimic Enigmas. All the remaining stops would correctly decrypt the crib, but only the true stop would produce the correct plaintext of the whole message.


title: Cryptanalysis of the Enigma

text: To avoid wasting scarce bombe time on menus that were likely to yield an excessive number of false stops, Turing performed a lengthy probability analysis (without any electronic aids) of the estimated number of stops per rotor order. It was adopted as standard practice only to use menus that were estimated to produce no more than four stops per "wheel order". This allowed an 8-letter crib for a 3-closure menu, an 11-letter crib for a 2-closure menu and a 14-letter crib for a menu with only one closure. If there was no closure, at least 16 letters were required in the crib. The longer the crib, however, the more likely it was that "turn-over" of the middle rotor would have occurred.


title: Cryptanalysis of the Enigma

text: The production model 3-rotor bombes contained 36 scramblers arranged in three banks of twelve. Each bank was used for a different "wheel order" by fitting it with the drums that corresponded to the Enigma rotors being tested. The first bombe was named "Victory" and was delivered to Bletchley Park on 18 March 1940. The next one, which included the diagonal board, was delivered on 8 August 1940. It was referred to as a "spider bombe" and was named "Agnus Dei" which soon became "Agnes" and then "Aggie". The production of British bombes was relatively slow at first, with only five bombes being in use in June 1941, 15 by the year end, 30 by September 1942, 49 by January 1943 but eventually 210 at the end of the war.


title: Cryptanalysis of the Enigma

text: A refinement that was developed for use on messages from those networks that disallowed the plugboard ("Stecker") connection of adjacent letters, was the "Consecutive Stecker Knock Out". This was fitted to 40 bombes and produced a useful reduction in false stops.


title: Cryptanalysis of the Enigma

text: Initially the bombes were operated by ex-BTM servicemen, but in March 1941 the first detachment of members of the Women's Royal Naval Service (known as "Wrens") arrived at Bletchley Park to become bombe operators. By 1945 there were some 2,000 Wrens operating the bombes. Because of the risk of bombing, relatively few of the bombes were located at Bletchley Park. The largest two outstations were at Eastcote (some 110 bombes and 800 Wrens) and Stanmore (some 50 bombes and 500 Wrens). There were also bombe outstations at Wavendon, Adstock and Gayhurst. Communication with Bletchley Park was by teleprinter links.


title: Cryptanalysis of the Enigma

text: When the German Navy started using 4-rotor Enigmas, about sixty 4-rotor bombes were produced at Letchworth, some with the assistance of the General Post Office. The NCR-manufactured US Navy 4-rotor bombes were, however, very fast and the most successful. They were extensively used by Bletchley Park over teleprinter links (using the Combined Cipher Machine) to OP-20-G for both 3-rotor and 4-rotor jobs.


title: Cryptanalysis of the Enigma

text: Although the German army, SS, police, and railway all used Enigma with similar procedures, it was the "Luftwaffe" (Air Force) that was the first and most fruitful source of Ultra intelligence during the war. The messages were decrypted in Hut 6 at Bletchley Park and turned into intelligence reports in Hut 3. The network code-named 'Red' at Bletchley Park was broken regularly and quickly from 22 May 1940 until the end of hostilities. Indeed, the Air Force section of Hut 3 expected the new day's Enigma settings to have been established in Hut 6 by breakfast time. The relative ease of solving this network's settings was a product of plentiful cribs and frequent German operating mistakes. Luftwaffe chief Hermann Göring was known to use it for trivial communications, including informing squadron commanders to make sure the pilots he was going to decorate had been properly deloused. Such messages became known as "Göring funnies" to the staff at Bletchley Park.


title: Cryptanalysis of the Enigma

text: Dilly Knox's last great cryptanalytical success, before his untimely death in February 1943, was the solving of the "Abwehr" Enigma in 1941. Intercepts of traffic which had an 8-letter indicator sequence before the usual 5-letter groups led to the suspicion that a 4-rotor machine was being used. The assumption was correctly made that the indicator consisted of a 4-letter message key enciphered twice. The machine itself was similar to a Model G Enigma, with three conventional rotors, though it did not have a plug board. The principal difference to the model G was that it was equipped with a reflector that was advanced by the stepping mechanism once it had been set by hand to its starting position (in all other variants, the reflector was fixed). Collecting a set of enciphered message keys for a particular day allowed "cycles" (or "boxes" as Knox called them) to be assembled in a similar way to the method used by the Poles in the 1930s.


title: Cryptanalysis of the Enigma

text: Knox was able to derive, using his "buttoning up" procedure, some of the wiring of the rotor that had been loaded in the fast position on that day. Progressively he was able to derive the wiring of all three rotors. Once that had been done, he was able to work out the wiring of the reflector. Deriving the indicator setting for that day was achieved using Knox's time-consuming "rodding" procedure. This involved a great deal of trial and error, imagination and crossword puzzle-solving skills, but was helped by "cillies".


title: Cryptanalysis of the Enigma

text: The "Abwehr" was the intelligence and counter-espionage service of the German High Command. The spies that it placed in enemy countries used a lower level cipher (which was broken by Oliver Strachey's section at Bletchley Park) for their transmissions. However, the messages were often then re-transmitted word-for-word on the "Abwehr's" internal Enigma networks, which gave the best possible crib for deciphering that day's indicator setting. Interception and analysis of "Abwehr" transmissions led to the remarkable state of affairs that allowed MI5 to give a categorical assurance that all the German spies in Britain were controlled as double agents working for the Allies under the Double Cross System.


title: Cryptanalysis of the Enigma

text: In the summer of 1940 following the Franco-German armistice, most Army Enigma traffic was travelling by land lines rather than radio and so was not available to Bletchley Park. The air Battle of Britain was crucial, so it was not surprising that the concentration of scarce resources was on "Luftwaffe" and "Abwehr" traffic. It was not until early in 1941 that the first breaks were made into German Army Enigma traffic, and it was the spring of 1942 before it was broken reliably, albeit often with some delay. It is unclear whether the German Army Enigma operators made deciphering more difficult by making fewer operating mistakes.


title: Cryptanalysis of the Enigma

text: The German Navy used Enigma in the same way as the German Army and Air Force until 1 May 1937 when they changed to a substantially different system. This used the same sort of setting sheet but, importantly, it included the ground key for a period of two, sometimes three days. The message setting was concealed in the indicator by selecting a trigram from a book (the "Kenngruppenbuch", or K-Book) and performing a bigram substitution on it. This defeated the Poles, although they suspected some sort of bigram substitution.


title: Cryptanalysis of the Enigma

text: The procedure for the naval sending operator was as follows. First they selected a trigram from the K-Book, say YLA. They then looked in the appropriate columns of the K-Book and selected another trigram, say YVT, and wrote it in the boxes at the top of the message form:


title: Cryptanalysis of the Enigma

text: and wrote down the resultant pairs, UB, LK, RS and PW which were transmitted as two four letter groups at the start and end of the enciphered message. The receiving operator performed the converse procedure to obtain the message key for setting his Enigma rotors.


title: Cryptanalysis of the Enigma

text: As well as these "Kriegsmarine" procedures being much more secure than those of the German Army and Air Force, the German Navy Enigma introduced three more rotors (VI, VII and VIII), early in 1940. The choice of three rotors from eight meant that there were a total of 336 possible permutations of rotors and their positions.


title: Cryptanalysis of the Enigma

text: Alan Turing decided to take responsibility for German naval Enigma because "no one else was doing anything about it and I could have it to myself". He established Hut 8 with Peter Twinn and two "girls". Turing used the indicators and message settings for traffic from 1–8 May 1937 that the Poles had worked out, and some very elegant deductions to diagnose the complete indicator system. After the messages were deciphered they were translated for transmission to the Admiralty in Hut 4.


title: Cryptanalysis of the Enigma

text: The first break of wartime traffic was in December 1939, into signals that had been intercepted in November 1938, when only three rotors and six plugboard leads had been in use. It used "Forty Weepy Weepy" cribs.


title: Cryptanalysis of the Enigma

text: A captured German "Funkmaat" ("radio operator") named Meyer had revealed that numerals were now spelt out as words. EINS, the German for "one", was present in about 90% of genuine German Navy messages. An EINS catalogue was compiled consisting of the encipherment of EINS at all 105,456 rotor settings. These were compared with the ciphertext, and when matches were found, about a quarter of them yielded the correct plaintext. Later this process was automated in Mr Freeborn's section using Hollerith equipment. When the ground key was known, this EINS-ing procedure could yield three bigrams for the tables that were then gradually assembled.


title: Cryptanalysis of the Enigma

text: Further progress required more information from German Enigma users. This was achieved through a succession of "pinches", the capture of Enigma parts and codebooks. The first of these was on 12 February 1940, when rotors VI and VII, whose wiring was at that time unknown, were captured from the , by minesweeper .


title: Cryptanalysis of the Enigma

text: On 26 April 1940, the Narvik-bound German patrol boat "VP2623", disguised as a Dutch trawler named "Polares", was captured by . This yielded an instruction manual, codebook sheets and a record of some transmissions, which provided complete cribs. This confirmed that Turing's deductions about the trigram/bigram process were correct and allowed a total of six days' messages to be broken, the last of these using the first of the bombes. However, the numerous possible rotor sequences, together with a paucity of usable cribs, made the methods used against the Army and Air Force Enigma messages of very limited value with respect to the Navy messages.


title: Cryptanalysis of the Enigma

text: At the end of 1939, Turing extended the clock method invented by the Polish cryptanalyst Jerzy Różycki. Turing's method became known as "Banburismus". Turing said that at that stage "I was not sure that it would work in practice, and was not in fact sure until some days had actually broken." Banburismus used large cards printed in Banbury (hence the Banburismus name) to discover correlations and a statistical scoring system to determine likely rotor orders ("Walzenlage") to be tried on the bombes. The practice conserved scarce bombe time and allowed more messages to be attacked. In practice, the 336 possible rotor orders could be reduced to perhaps 18 to be run on the bombes. Knowledge of the bigrams was essential for Banburismus, and building up the tables took a long time. This lack of visible progress led to Frank Birch, head of the Naval Section, to write on 21 August 1940 to Edward Travis, Deputy Director of Bletchley Park:


title: Cryptanalysis of the Enigma

text: Schemes for capturing Enigma material were conceived including, in September 1940, Operation Ruthless by Lieutenant Commander Ian Fleming (author of the James Bond novels). When this was cancelled, Birch told Fleming that "Turing and Twinn came to me like undertakers cheated of a nice corpse..."


title: Cryptanalysis of the Enigma

text: A major advance came through Operation Claymore, a commando raid on the Lofoten Islands on 4 March 1941. The German armed trawler "Krebs" was captured, including the complete Enigma keys for February, but no bigram tables or K-book. However, the material was sufficient to reconstruct the bigram tables by "EINS-ing", and by late March they were almost complete.


title: Cryptanalysis of the Enigma

text: Banburismus then started to become extremely useful. Hut 8 was expanded and moved to 24-hour working, and a crib room was established. The story of Banburismus for the next two years was one of improving methods, of struggling to get sufficient staff, and of a steady growth in the relative and absolute importance of cribbing as the increasing numbers of bombes made the running of cribs ever faster. Of value in this period were further "pinches" such as those from the German weather ships "München" and "Lauenburg" and the submarines and .


title: Cryptanalysis of the Enigma

text: Despite the introduction of the 4-rotor Enigma for Atlantic U-boats, the analysis of traffic enciphered with the 3-rotor Enigma proved of immense value to the Allied navies. Banburismus was used until July 1943, when it became more efficient to use the many more bombes that had become available.