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| {{Infobox scientist
| | == 轟音轟音 == |
| | name = W. T. Tutte
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| | image = <!--(filename only)-->
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| | image_size =
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| | alt =
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| | caption =
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| | birth_date = {{Birth date|1917|05|14}}
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| | birth_place = [[Newmarket, Suffolk]], [[England]]
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| | death_date = {{Death date and age|2002|05|02|1917|05|14}}
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| | death_place = [[Kitchener, Ontario|Kitchener]], [[Ontario]], [[Canada]]
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| | residence =
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| | citizenship =
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| | nationality =
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| | fields = [[Mathematics]]
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| | workplaces = [[University of Toronto]]<br>[[University of Waterloo]]
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| | alma_mater = [[Trinity College, Cambridge]] <small>([[Doctor of Philosophy|Ph.D.]])</small>
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| | thesis_title = An Algebraic Theory of Graphs<ref name="MGP">{{MathGenealogy|id=15096}}</ref>
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| | thesis_year = 1948
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| | doctoral_advisor = [[Shaun Wylie]]<ref name="MGP"/>
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| | academic_advisors =
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| | doctoral_students = [[Neil Robertson (mathematician)|Neil Robertson]]<ref name="MGP"/>
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| | notable_students =
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| | known_for = {{Plainlist|
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| *[[BEST theorem]]
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| *[[Peripheral cycle]]
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| *[[Tutte 12-cage]]
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| *[[Tutte embedding]]
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| *[[Tutte graph]]
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| *[[Tutte homotopy theorem]]
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| *[[Tutte matrix]]
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| *[[Tutte polynomial]]
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| *[[Tutte theorem]]
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| *[[Tutte–Berge formula]]
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| *[[Tutte–Coxeter graph]]
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| *[[Cryptanalysis of the Lorenz cipher#Tutte's "1+2 break in"|Tutte's "1+2 break in"]]
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| *Tutte's 1-factor theorem
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| *[[Tutte's fragment]]
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| *[[W. T. Tutte#Tutte's statistical method|Tutte's statistical method]]
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| *Tutte's wheel theorem
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| }}
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| | author_abbrev_bot =
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| | author_abbrev_zoo =
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| | influences =
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| | influenced =
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| | awards = {{Plainlist|
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| * [[Jeffery-Williams Prize]] (1971)
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| * [[Henry Marshall Tory Medal]] (1975)
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| * [[Isaak-Walton-Killam Award]] (1982)
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| * [[CRM-Fields-PIMS prize]] (2001)
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| }}
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| | spouse = Dorothea Mitchell (m. 1949–1994, her death)
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| | signature = <!--(filename only)-->
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| | signature_alt =
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| | footnotes =
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| }}
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| '''William Thomas Tutte''' <small>[[Order of Canada|OC]] [[Royal Society|FRS]] [[Royal Society of Canada|FRSC]]</small>, known as '''Bill Tutte''' ({{IPAc-en|t|ʌ|t}}; May 14, 1917 – May 2, 2002), was a [[United Kingdom|British]], later [[Canadian]], [[cryptanalysis|codebreaker]] and [[mathematician]]. During [[World War II]] he made a brilliant and fundamental advance in [[Cryptanalysis of the Lorenz cipher]], a major [[Nazi Germany|German]] cipher system. The intelligence obtained from these decrypts had a significant impact on the Allied victory in Europe. He also had a number of significant mathematical accomplishments, including foundation work in the fields of [[graph theory]] and [[matroid theory]].<ref name="frs">{{Harvnb|Younger|2012}}</ref><ref name="MacTutorBiog"/>
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| Tutte’s research in the field of graph theory proved to be of remarkable importance. At a time when graph theory was still a primitive subject, Tutte commenced the study of [[matroid]]s and developed them into a theory by expanding from the work that [[Hassler Whitney]] had first developed around the mid 1930s.<ref>{{cite web|last=Johnson|first=Will|title=Matroids|url=http://www.math.washington.edu/~morrow/336_09/papers/Will.pdf|accessdate=5/2/13}}</ref> Even though Tutte’s contributions to graph theory have been influential to modern graph theory and many of his theorems have been used to keep making advances in the field, most of his terminology was not in agreement with their conventional usage and thus his terminology is not used by graph theorists today.<ref name="Hobbs 2004 322">{{cite journal | last = Hobbs | first = Arthur M. | coauthors = [[James Oxley|James G. Oxley]] |date=March 2004 | title = William T. Tutte (1917–2002) | journal = [[Notices of the American Mathematical Society]] | volume = 51 | issue = 3 | page = 322 | url = http://www.ams.org/notices/200403/mem-tutte.pdf | format = PDF}}</ref> "Tutte advanced graph theory from a subject with one text (D. König’s) toward its present extremely active state"<ref name="Hobbs 2004 322"/>
| | 後者は今雷雲上空の雲を見るために検索される、顔に、「色」だけでなく、何も心配することはありませんが、興奮の外観があります [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-12.html 腕時計 メンズ casio]。<br><br>'それ'<br>このシーンを見るために<br>、でもXuankongの息子が、また彼の口を開き、すぐに苦笑いし、首を横に振った、それは彼が本当にシャオヤンの手段を過小評価しているようだ [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-8.html カシオ レディース 電波ソーラー腕時計]。<br><br>は雷雲の結束、この世界のエネルギーを伴って、それが同点この時点では、わずかになってきて、恨みの体だったので、それが突然、非常に暴動、土で埋めひどい鉱山となった立ち上がる [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-14.html カシオ腕時計 メンズ]。<br><br>轟音轟音 [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-3.html カシオ 電波時計 腕時計]！<br><br>雷雲は、まもなく凝集した後、最終的にそれが突然ターンの方向で空気に到達したときであっても、それは恐ろしい破壊力、巨大な雲、鮮やかなサンダー圧倒的な爆発ダウンしていた解放し、彼らにすべてのポイントをカウントし始めている悪魔の人形の空気 [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-0.html カシオ 腕時計 バンド]！<br><br>'打ち鳴らす |
| | 相关的主题文章： |
| | <ul> |
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| | <li>[http://www.groundriddim.com/h/cgi/news/news.cgi http://www.groundriddim.com/h/cgi/news/news.cgi]</li> |
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| | <li>[http://a-ca.com/cgi-bin/keijiban/aska.cgi http://a-ca.com/cgi-bin/keijiban/aska.cgi]</li> |
| | |
| | <li>[http://bbs.go19.cn/forum.php?mod=viewthread&tid=995856&fromuid=246228 http://bbs.go19.cn/forum.php?mod=viewthread&tid=995856&fromuid=246228]</li> |
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| | </ul> |
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| ==Early life and education== | | == 第五百六十章断片的燃焼の決定 == |
| Tutte was born in [[Newmarket, Suffolk|Newmarket]] in [[Suffolk]], the son of a [[gardener]]. At the age of 18, he studied [[chemistry]] and [[mathematics]] at [[Trinity College, Cambridge|Trinity College]], [[University of Cambridge|Cambridge University]]. As a student he (along with three of his friends) became the first to solve the problem of [[squaring the square]]. Together the four created the pseudonym [[Blanche Descartes]], under which Tutte published occasionally for years.<ref>{{citation | last1 = Smith | first1 = Cedric A. B. | first2 = Steve | last2 = Abbott | title = The Story of Blanche Descartes | journal = The Mathematical Gazette | issn = 0025-5572 |date=March 2003 | volume = 87 | issue = 508 | pages = 23–33 | jstor = 3620560}}</ref>
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| ==World War II==
| | 中庭の上に影を落として [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-6.html casio 腕時計 説明書]！<br><br>第五百六十章断片的燃焼の決定<br><br>第五百六十章断片的燃焼の決定<br>それが直接の歓声が空をカルマを通して鳴り響いていることだったので<br>突然笑いは、しかし、唯一の数え切れないほどのメンバーを見て、突然人の空大規模なグループで登場驚い見て、やや不明瞭な現状である [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-9.html カシオ 掛け時計]。<br><br>空では、蘇千「色」に直面暗い結び目ミラーが歩行者をこじ開けるように見えた見えた、彼の目はゆっくりと先頭の1着た精錬「医学」部門のローブで停止、瞬間男、目が意志仮想斜視アップがゆっくりとです」と、誰が私が言ったことが判明した」： [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-9.html カシオ 時計 プロトレック]。冷笑薬「皇帝漢鳳ノアールドメインああ」<br>「親切なああ、偉大な長老、真タブーだったが、カジュアルな友人Noireのドメインが送信されましたが、ない時は「ソ連に向け、わずかに笑顔のヒントから、薄い唇、で、漢鳳男として知られています<br>千の笑顔 [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-0.html casio 腕時計]。<br><br>'ハン |
| {{See also|Cryptanalysis of the Lorenz cipher}}
| | 相关的主题文章： |
| [[Image:SZ42-6-wheels-lightened.jpg|right|340px|thumbnail|The Lorenz SZ machines had 12 wheels each with a different number of cams (or "pins").
| | <ul> |
| {|class="wikitable" | border=1 | style="margin: 1em auto 1em auto"
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| |-
| | <li>[http://sh-gmc.com/plus/feedback.php?aid=313 http://sh-gmc.com/plus/feedback.php?aid=313]</li> |
| ! Wheel number
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| |1||2||3||4||5||6||7||8||9||10||11||12
| | <li>[http://50.87.130.157/~xiaocoun/thread-782312-1-1.html http://50.87.130.157/~xiaocoun/thread-782312-1-1.html]</li> |
| |-
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| ! BP wheel name<ref name = "GRoT11B6">{{Harvnb|Good|Michie|Timms|1945|p=6}} in ''1. Introduction: German Tunny''</ref>
| | <li>[http://www.darrenmelrose.com/cgi-bin/guestbook/guestbook.cgi http://www.darrenmelrose.com/cgi-bin/guestbook/guestbook.cgi]</li> |
| | style="text-align:center;"| <math>\psi</math><sub>1</sub>
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| | style="text-align:center;"| <math>\psi</math><sub>2</sub>
| | </ul> |
| | style="text-align:center;"| <math>\psi</math><sub>3</sub>
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| | style="text-align:center;"| <math>\psi</math><sub>4</sub>
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| | style="text-align:center;"| <math>\psi</math><sub>5</sub>
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| | style="text-align:center;"| <math>\mu</math>37
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| | style="text-align:center;"| <math>\mu</math>61
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| | style="text-align:center;"| <math>\chi</math><sub>1</sub>
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| | style="text-align:center;"| <math>\chi</math><sub>2</sub>
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| | style="text-align:center;"| <math>\chi</math><sub>3</sub>
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| | style="text-align:center;"| <math>\chi</math><sub>4</sub>
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| | style="text-align:center;"| <math>\chi</math><sub>5</sub>
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| |-
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| ! Number of cams (pins)
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| |43||47||51||53||59||37||61||41||31||29||26||23
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| |}
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| ]]
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| Soon after the outbreak of [[World War II]], Tutte's tutor, Patrick Duff, suggested him for war work at the [[Government Code and Cypher School]] at [[Bletchley Park]] (BP). He was interviewed and sent on a training course in London before going to Bletchley Park, where he joined the Research Section. At first he worked on the [[Boris Hagelin|Hagelin]] cipher that was being used by the Italian Navy. This was a [[Rotor machine|rotor cipher]] machine that was available commercially, so the mechanics of enciphering was known, and decrypting messages only required working out how the machine was set up.<ref>{{Harvnb|Tutte|2006|pp=352–353}}</ref>
| | == 「今日、物事は == |
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| In the summer of 1941, Tutte was transferred to work on a teleprinter cipher system that had been dubbed "Tunny".<ref>{{Harvnb|Tutte|2006|p=355}}</ref> Telegraphy used the [[bit|5-bit]] [[ITA2|International Telegraphy Alphabet No. 2]] (ITA2). Other than that messages were preceded by a 12-letter [[Cryptanalysis#Indicator|indicator]], which implied a 12-wheel rotor cipher machine, nothing was known about the mechanism of enciphering. The first step, therefore, had to be to diagnose the machine by establishing the logical structure and hence the functioning of the machine. Tutte played a pivotal role in achieving this, and it was not until shortly before the allied victory in Europe in 1945, that Bletchley Park acquired a Tunny [[Lorenz cipher]] machine.<ref name=Sale>{{Citation | last = Sale | first = Tony | author-link = Anthony Sale | title = The Lorenz Cipher and how Bletchley Park broke it | url = http://www.codesandciphers.org.uk/lorenz/fish.htm | accessdate = 21 October 2010 }}</ref> Tutte's breakthroughs led eventually to bulk decrypting of Tunny-enciphered messages between German High Command [[Oberkommando der Wehrmacht|(OKW)]] in Berlin and their army commands throughout occupied Europe, that played a crucial part in shortening the war.<ref>{{Harvnb|Hinsley|1993|p=8}}</ref>
| | ではない、彼は再び火の蓮の破壊のうち最後の最後での結束の神秘的に気づいていないならば、彼はまた、少なくともでなければなりませんでしたないように、、話す、しかしMeimouはこの勝利が、いくつかの怒り徐シャオヤンを破って気絶するだけでなく、獲得していない生鮮古い悪魔が重傷を負っていることを意味します [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-10.html casio電波腕時計]。<br><br>「今日、物事は！古代の悪魔を終えないかもしれない、あなたが私の手に入らない、次回は、それ以外の場合は、あなたがこの感覚を試してみましょう！ [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-14.html カシオ 時計 電波 ソーラー] '<br><br>薫の子供の手が少し震えて、そしてちょうどシャオヤンの目にはそっとフィールドに、様ひらひら蝶のよう、、身長なびくを微笑んでうなずいた [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-14.html カシオ腕時計 メンズ]。<br><br>広場に、Tongxuanの長老たちは少し冷たい頬を見て、子供を吸って、また叫びを助けることが笑顔ができなかった、と言った： [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-13.html カシオ アナログ 腕時計] 'まあ、あなたがの発生、古代部族のあなたの優れたステータスでいることを知っているべき物事の種類、驚くべきことではないが、シャオヤン彼はまた、それ以外の場合は、本当に誰部族を認識することは困難であり、この挑戦を必要とします |
| | 相关的主题文章： |
| | <ul> |
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| | <li>[http://www.jackyphoto.com/plus/feedback.php?aid=113 http://www.jackyphoto.com/plus/feedback.php?aid=113]</li> |
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| | <li>[http://dlzhengxing.com/plus/feedback.php?aid=109 http://dlzhengxing.com/plus/feedback.php?aid=109]</li> |
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| | <li>[http://51busad.com/plus/feedback.php?aid=199 http://51busad.com/plus/feedback.php?aid=199]</li> |
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| ===Diagnosing the cipher machine=== | | == 殺人は900を == |
| On 31 August 1941, two versions of the same message were sent using identical keys which constituted a "[[Cryptanalysis#Depth|depth]]". This allowed [[John Tiltman]], Bletchley Park's veteran and remarkably gifted cryptanalyst, to deduce that it was a [[Gilbert Vernam|Vernam cipher]] which uses the [[Exclusive or|Exclusive Or (XOR)]] function (symbolised by "⊕"), and to extract the two messages and hence obtain the obscuring key. After a fruitless period of Research Section cryptanalysts trying to work out how the Tunny machine worked, this and some other keys were handed to Tutte who was asked to "see what you can make of these".<ref>{{Harvnb|Tutte|2006|p=354}}</ref>
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| At his training course, Tutte had been taught the [[Kasiski examination]] technique of writing out a key on squared paper, starting a new row after a defined number of characters that was suspected of being the frequency of repetition of the key.<ref>{{Harvnb|Bauer|2006|p=375}}</ref> If this number was correct, the columns of the matrix would show more repetitions of sequences of characters than chance alone. Tutte knew that the Tunny indicators used 25 letters (excluding J) for 11 of the positions, but only 23 letters for the other. He therefore tried Kasiski's technique on the first impulse of the key characters, using a repetition of 25 × 23 = 575. He did not observe a large number of column repetitions with this period, but he did observe the phenomenon on a diagonal. He therefore tried again with 574, which showed up repeats in the columns. Recognising that the [[prime factor]]s of this number are 2, 7 and 41, he tried again with a period of 41 and "got a rectangle of dots and crosses that was replete with repetitions".<ref>{{Harvnb|Tutte|2006|pp=356–357}}</ref>
| | シャオヤンは彼女の手のひらに冷たい汗で覆われていた狙ったもの、そのダース以上の強い皇室闘争作るために周りを見回して、背後に続いて、彼らは実践的でなければならない場合には、私もシャオヤン、すべての避難所のエッジああを持って怖いです [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-5.html gps 腕時計 カシオ]。<br>ツリー小岩二つのドア、それがうつ状態になるまでのタイトな周囲の雰囲気、その微妙な足音にますます近いと<br>、それはそれは人々が感じて呼吸停止のようなものだったので、一般的には人間の心を踏むようなものです [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-2.html 腕時計 casio]。<br><br>ペースは再び静かに落下、シャオヤンツリーを見て、扉未満10メートル離れていた、とギャングゆうがゆっくり危険なアークがあると同時に、恐ろしい寒盛彼の目を狭め、ホッと、急に鳴ります [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-9.html カシオ 時計 プロトレック]。<br><br>「みんなが協力し、精神的な北極キツネがそれを引き継ぐ、一日は、血液の山の湖が私たちのコピーを持つことができます！ [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-0.html casio 腕時計] '<br>殺人は900を<br>と第七十章はホッキョクギツネの原因となった<br>殺人は900を<br>と第七十章はホッキョクギツネの原因となった |
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| | |
| | <li>[http://www.aaeafrica.org/cgi-bin/home/index.cgi http://www.aaeafrica.org/cgi-bin/home/index.cgi]</li> |
| | |
| | <li>[http://www.siyotech.com/home.php?mod=space&uid=31713&do=blog&quickforward=1&id=1632364 http://www.siyotech.com/home.php?mod=space&uid=31713&do=blog&quickforward=1&id=1632364]</li> |
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| | </ul> |
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| It was clear, however, that the first impulse of the key was more complicated than that produced by a single wheel of 41 key impulses. Tutte called this component of the key <math>\chi</math><sub>1</sub> (''chi''<sub>1</sub>). He figured that there was another component, which was XOR-ed with this, that did not always change with each new character, and that this was the product of a wheel that he called <math>\psi</math><sub>1</sub> (''psi''<sub>1</sub>). The same applied for each of the five impulses (<math>\chi</math><sub>1</sub><math>\chi</math><sub>2</sub><math>\chi</math><sub>3</sub><math>\chi</math><sub>4</sub><math>\chi</math><sub>5</sub> and <math>\psi</math><sub>1</sub><math>\psi</math><sub>2</sub><math>\psi</math><sub>3</sub><math>\psi</math><sub>4</sub><math>\psi</math><sub>5</sub>). So for a single character, the whole key '''K''' consisted of two components:
| | == エネルギー」ブーム '潮解約し、移動の終わりに == |
| :::: <big>K</big> = <big><math>\chi</math> ⊕ <math>\psi</math> </big>
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| At Bletchley Park mark impulses were signified by '''x''' and space impulses by '''•'''.<ref>In more recent terminology, each impulse would be termed a "[[bit]]" with a mark being binary 1 and a space being binary 0. Punched paper tape had a hole for a mark and no hole for a space.</ref> For example the letter "H" would be coded as '''••x•x'''.<ref>{{Harvnb|Copeland|2006|pp=348, 349}}</ref> Tutte's derivation of the ''chi'' and ''psi'' components was made possible by the fact that dots were more likely than not to be followed by dots, and crosses more likely than not to be followed by crosses. This was a product of a weakness in the German key setting, which they later eliminated. Once Tutte had made this breakthrough, the rest of the Research Section joined in to study the other impulses, and it was established that the five ''chi'' wheels all advanced with each new character and that the five ''psi'' wheels all moved together under the control of two ''mu'' or "motor" wheels. Over the following two months, Tutte and other members of the Research Section worked out the complete logical structure of the machine with its set of wheels bearing cams that could either be in a position (raised) that added '''x''' to the stream of key characters, or in the alternative position that added in '''•'''.<ref>{{Harvnb|Tutte|2006|p=357}}</ref>
| | それはすべての古代部族の「色」に直面したので、すぐに、すぐに開いて広げ、突然隆起アップしている [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-1.html カシオ 腕時計 チタン]。<br><br>「魂天国！ [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-10.html カシオ 腕時計 スタンダード] '<br>魂天を見つめ<br>区人民元顔」色 [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-9.html カシオ 時計 プロトレック] '冷たい目は、空の「色」の多くの瞬間に突然暗い、世界のエネルギーは、その跡は、時計のように、遠くから、天と地をつなぐ、口笛での広大であるしかし、エネルギーの終わりではなく、「ブーム」のXi一般、音波の「潮」を急いでノンストップ。<br>そのようなエネルギーとして、ばかりでなく、人間のプロポーションの手の届かない、天と地のビジョン、シーンの鎬「スイング」のようなものを成形することが、今、それはまれな世紀であるhuanhangrnエネルギー」ブーム [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-8.html 時計 メンズ カシオ] '一般的には西、、、'チャオ「西が、それは、移動原生代の心で凝縮し、9つの神聖な強さで、実際にはとてもひどいです<br>エネルギー」ブーム [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-12.html 時計 カシオ] '潮解約し、移動の終わりに<br>光景、それはそれはヤンと他の4つの魂であっても、圧力を分散 |
| | 相关的主题文章： |
| | <ul> |
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| | <li>[http://cloud.d1xy.com/forum.php?mod=viewthread&tid=202119 http://cloud.d1xy.com/forum.php?mod=viewthread&tid=202119]</li> |
| | |
| | <li>[http://www.m-hy.com/home.php?mod=space&uid=16516 http://www.m-hy.com/home.php?mod=space&uid=16516]</li> |
| | |
| | <li>[http://www.xiongmaoche.com/bbs/forum.php?mod=viewthread&tid=1934178 http://www.xiongmaoche.com/bbs/forum.php?mod=viewthread&tid=1934178]</li> |
| | |
| | </ul> |
|
| |
|
| Diagnosing the functioning of the Tunny machine in this way was a truly remarkable cryptanalytical achievement which, in the citation for Tutte's induction as an Officer of the Order of Canada, was described as: {{quote|<big>one of the greatest intellectual feats of World War II</big><ref name="MacTutorBiog">{{Harvnb|O'Connor|Robertson|2003}} <!-- {{cite web | url = http://www.codesandciphers.org.uk/lorenz/fish.htm | title = The Lorenz Cipher and how Bletchley Park broke it | publisher = Codesandciphers.org.uk | date=1941-08-30 | accessdate=2011-10-26 }}--></ref>}}
| | == 裁判所にそれを雷ではない == |
|
| |
|
| ===Tutte's statistical method===
| | 'ああ、ハング家族はいつも私のためにあらゆる可能な方法で、北の街の日を支配したかったことはほぼ同じ強さは、何も所有しないため、漢は常に過去を嫌いますが、ハング陳は最近、嵐から返された北の裁判所が、これは彼がなっていると述べたノースタワーキャビネットの弟子たちは、以前の位置と比較して、かなり異なるし、それによって、ハング家族の威信は市の北部多く、今日、多くの中立勢力のように上下に移動されていること、したがって、洪水のホーム側に投資されている。 [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-3.html casio 腕時計 レディース] 'ハンカイはため息をついて言った。<br><br>'雷ノースタワー？裁判所にそれを雷ではない？'漢雪に対してささやいウェンヤン、ヤンシャオ疑問 [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-2.html 腕時計 casio] '混乱'は尋ねた。<br><br>「雷裁判所はセントラルノースフィールドの角に位置して、東と西地区裁判所に分割され、北風と雷裁判所こと、それが北の3000の都市の西峰山脈の日数を超えているが、香港の陳は、それは風と雷ノースタワーキャビネットとは弟子。 [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-12.html カシオ 腕時計 ソーラー] 'ハン雪は説明した。<br><br>シャオヤンこの幾分突然、すぐに驚いて再び強風と雷裁判所その光の力 |
| {{See also|Cryptanalysis of the Lorenz cipher#Tutte's "1+2 break in"|label 1=Tutte's "1+2 break in"}}
| | 相关的主题文章： |
| To decrypt a Tunny message required knowledge not only of the logical functioning of the machine, but the start positions of each rotor for the particular message. The search was on for a process that would manipulate the ciphertext or key to produce a frequency distribution of characters that departed from the uniformity that the enciphering process aimed to achieve. While on secondment to the Research Section in July 1942, [[Alan Turing]] worked out that the XOR combination of the values of successive characters in a stream of ciphertext and key, emphasised any departures from a uniform distribution. The resultant stream (symbolised by the Greek letter "delta" '''Δ''') was called the [[Cryptanalysis of the Lorenz cipher#Differencing|difference]] because XOR is the same as modulo 2 subtraction.
| | <ul> |
| | | |
| The reason that this provided a way into Tunny, was that although the frequency distribution of characters in the ciphertext could not be distinguished from a random stream, the same was not true for a version of the ciphertext from which the ''chi'' element of the key had been removed. This is because, where the plaintext contained a repeated character and the ''psi'' wheels did not move on, the differenced ''psi'' character ('''Δ'''<math>\psi</math>) would be the null character ('<span style="font-size:140%;">'''/'''</span> ' at Bletchley Park). When XOR-ed with any character, this character has no effect. Repeated characters in the plaintext were more frequent both because of the characteristics of German (EE, TT, LL and SS are relatively common),<ref>{{Citation | last = Singh | first = Simon | author-link = Simon Singh | title = The Black Chamber | url = http://www.simonsingh.net/The_Black_Chamber/hintsandtips.html | accessdate = 28 April 2012 }}</ref> and because telegraphists frequently repeated the figures-shift and letters-shift characters<ref>[[Max Newman|Newman]] c. 1944 p. 387</ref> as their loss in an ordinary telegraph message could lead to gibberish.<ref>{{Harvnb|Carter|2004|p = 3}}</ref>
| | <li>[http://592bbs.net/forum.php?mod=viewthread&tid=233521 http://592bbs.net/forum.php?mod=viewthread&tid=233521]</li> |
| | | |
| To quote the General Report on Tunny:<blockquote>Turingery introduced the principle that the key differenced at one, now called '''ΔΚ''', could yield information unobtainable from ordinary key. This '''Δ''' principle was to be the fundamental basis of nearly all statistical methods of wheel-breaking and setting.<ref name="GRoT11B6"/></blockquote>
| | <li>[http://www.athensmasons.org/cgi/hamguestbook/guestbook.cgi http://www.athensmasons.org/cgi/hamguestbook/guestbook.cgi]</li> |
| | | |
| Tutte exploited this amplification of non-uniformity in the differenced values<ref>For this reason Tutte's 1 + 2 method is sometimes called the "double delta" method.</ref> and by November 1942 had produced a way of discovering wheel starting points of the Tunny machine which became known as the "Statistical Method".<ref>{{Harvnb|Tutte|1998|pp=7–8}}</ref> The essence of this method was to find the initial settings of the ''chi'' component of the key by exhaustively trying all positions of its combination with the ciphertext, and looking for evidence of the non-uniformity that reflected the characteristics of the original plaintext.<ref>{{Harvnb|Good|Michie|Timms|1945|pp=321–322}} in ''44. Hand Statistical Methods: Setting - Statistical Methods''</ref><ref>{{Harvnb|Budiansky|2006|pp=58–59}}</ref> Because any repeated characters in the plaintext would always generate '''•''', and similarly ∆<math>\psi</math><sub>1</sub> ⊕ ∆<math>\psi</math><sub>2</sub> would generate '''•''' whenever the ''psi'' wheels did not move on, and about half of the time when they did - some 70% overall.
| | <li>[http://kaxiouguangbobiao.hutoubang.com/home.php?mod=space&uid=334504 http://kaxiouguangbobiao.hutoubang.com/home.php?mod=space&uid=334504]</li> |
| | | |
| As well as applying differencing to the full 5-bit characters of the ITA2 code, Tutte applied it to the individual impulses (bits).<ref>The five impulses or bits of the coded characters are sometimes referred to as five levels.</ref> The current ''chi'' wheel cam settings needed to have been established to allow the relevant sequence of characters of the ''chi'' wheels to be generated. It was totally impracticable to generate the 22 million characters from all five of the ''chi'' wheels, so it was initially limited to 41 × 31 = 1271 from the first two. After explaining his findings to [[Max Newman]], Newman was given the job of developing an automated approach to comparing ciphertext and key to look for departures from randomness. The first machine was dubbed [[Heath Robinson (codebreaking machine)|Heath Robinson]] but the much faster [[Colossus computer]] soon took over.<ref>{{Harvnb|Copeland|2011}}</ref>
| | </ul> |
| | |
| Because of this work, Canada's [[Communications Security Establishment]] named an internal organisation aimed at promoting research into cryptology, the [[Tutte Institute for Mathematics and Computing]]<ref>[http://www.cse-cst.gc.ca/tutte/index-eng.html The Tutte Institute for Mathematics and Computing]. Canada.</ref> (TIMC) in his honour in 2011.<ref>{{cite news|last=Freeze|first=Colin|title=Top secret institute comes out of the shadows to recruit top talent|url=http://www.theglobeandmail.com/news/national/bloggins/article2154310/|accessdate=7 September 2011|newspaper=Globe and Mail|date=7 September 2011|location=Toronto}}</ref>
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| ==Doctorate and career==
| |
| Tutte completed a doctorate in mathematics from [[University of Cambridge|Cambridge]] in 1948 under the supervision of [[Shaun Wylie]], who had also worked at Bletchley Park on TUNNY. The same year, invited by [[Harold Scott MacDonald Coxeter]], he accepted a position at the [[University of Toronto]]. In 1962, he moved to the [[University of Waterloo]] in [[Waterloo, Ontario|Waterloo]], [[Ontario]] where he stayed for the rest of his academic career. He officially retired in 1985 but remained active as an emeritus professor. Tutte was instrumental in helping to found the [http://www.math.uwaterloo.ca/CandO_Dept/ Department of Combinatorics and Optimization] at the University of Waterloo.
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| His mathematical career concentrated on [[combinatorics]], especially [[graph theory]], which he is credited as having helped create in its modern form, and [[matroid theory]], to which he made profound contributions; one colleague <!-- Dr. Younger --> described him as "the leading mathematician in combinatorics for three decades". He was editor in chief of ''The Journal of Combinatorial Theory'' when it was started, and served on the editorial boards of several other mathematical research journals.
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| His work in graph theory includes the structure of cycle and cut spaces, size of [[maximum matching]]s and existence of [[k-factor (graph theory)|''k''-factor]]s in graphs, and [[Hamiltonian path|Hamiltonian]] and non-Hamiltonian graphs. He disproved [[Tait's conjecture]] using the construction known as [[Tutte's fragment]]. The eventual proof of the [[four color theorem]] made use of his earlier work. The graph polynomial he called the "dichromate" has become famous and influential under the name ''[[Tutte polynomial]]'' and serves as the prototype of combinatorial invariants that are universal for all invariants that satisfy a specified reduction law.
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| The first major advances in matroid theory were made by Tutte in his 1948 Cambridge Ph.D. thesis which formed the basis of an important sequence of papers published over the next two decades. Tutte's work in graph theory and matroid theory has been profoundly influential on the development of both the content and direction of these two fields.<ref name="Hobbs 2004 322"/> In matroid theory he discovered the highly sophisticated [[homotopy theorem]] as well as founding the studies of [[matroid|chain group]]s and [[regular matroid]]s, about which he proved deep results.
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| In addition, Tutte developed an algorithm for determining whether a given binary matroid is graphic. The algorithm makes use of the fact that a planar graph is simply a graph whose circuit-matroid, the dual of its [[Dual matroid|bond-matroid]], is graphic.<ref>W.T Tutte. An algorithm for determining whether a given binary matroid is graphic, ''Proceedings of the London Mathematical Society'', '''11'''(1960)905-917</ref>
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| Tutte wrote a paper entitled ''How to Draw a Graph'' in which he proves that any face in a 3-connected graph is enclosed by a [[peripheral cycle]]. Using this fact, Tutte developed an alternative proof to show that every Kuratowski graph is non-planar by showing that''K''<sub>5</sub> and ''K''<sub>3,3</sub> each have three distinct peripheral cycles with a common edge. In addition to using peripheral cycles to prove that the Kuratowski graphs are non-planar, Tutte proved that there exists a convex embedding of any simple 3-connected graph and devised an algorithm which constructs the plane drawing by solving a linear system. This algorithm makes use of the [[barycentric coordinates (mathematics)|barycentric]] mappings of the peripheral circuits of a simple 3-connected graph.<ref>W.T. Tutte. How to draw a graph. Proceedings of the London Mathematical Society, 13(3):743-768, 1963.</ref> The findings published in this paper have proved to be of much significance because the algorithms that Tutte developed have become popular planar graph drawing methods. In 1997, [http://www.ifi.uio.no/~michaelf/papers/papers.htm Michael S. Floater] published a paper entitled ''Parameterization and smooth approximation of surface triangulations'' which extends Tutte’s original theorem on the existence of a plane drawing of a 3-connected graph bounded by a convex polygon. Floater shows that a plane drawing of a 3-connected graph can be drawn without the boundary necessarily being a convex polygon.<ref>M.S. Floater. Parameterization and smooth approximation of surface triangulations. Computer
| |
| Aided Geometric Design, 14:231–250, 1997.</ref>
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| | |
| One of the reasons for which Tutte’s embedding is popular is that the necessary computations that are carried out by his algorithms are simple and guarantee a one-to-one correspondence of a graph and its embedding onto the Euclidean plane which is of importance when paramterizing a three dimensional mesh to the plane in geometric modeling. “ Tutte's theorem is the basis for solutions to other computer graphics problems, such as [[Morphing#Present use of morphing|morphing]]<ref>Steven J. Gortle; Craig Gotsman; Dylan Thurston. Discrete One-Forms on Meshes and Applications to 3D Mesh Parameterization, ''Computer Aided Geometric Design'', 23(2006)83-112</ref>
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| Tutte was mainly responsible for developing the theory of enumeration of planar graphs, which has close links with chromatic and dichromatic polynomials. This work involved some innovated techniques of his own invention, requiring considerable manipulative dexterity in handling power series (whose coefficients count appropriate kinds of graphs) and the functions arising as their sums, as well as geometrical dexterity in extracting these power series from the graph-theoretic situation.<ref>Paul Erdos, A Note on Some of Professor Tutte's Mathematical Work, Graph Theory and Related Topics (eds. J.A Bondy and U. S. R Murty), Academic Press, New York, 1979, pp. xxvii.</ref>
| |
| | |
| ==Positions, honours and awards==
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| Tutte's work in WW2 and subsequently in combinatorics brought him various positions, honours and awards:
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| * 1958, Fellow of the [[Royal Society of Canada]] (FRSC);
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| * 1971, [[Jeffery-Williams Prize]] by the [[Canadian Mathematical Society]];
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| * 1975, [[Henry Marshall Tory Medal]] by the Royal Society of Canada;
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| * 1977, A conference on Graph Theory and Related Topics was held at the [[University of Waterloo]] in his honour on the occasion of his sixtieth birthday;
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| * 1982, [[Isaak-Walton-Killam Award]] by the [[Canada Council]];
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| * 1987, [[Fellow of the Royal Society]] (FRS);
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| * 1990-1996, First President of the [[Institute of Combinatorics and its Applications]];<ref>{{cite web |title=The Institute of Combinatorics & Its Applications |url=http://www.theica.org/ |publisher=ICA |accessdate=2013-09-28}}</ref>
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| * 1998, Appointed honorary director of the [[Centre for Applied Cryptographic Research]] at the University of Waterloo;<ref>{{cite web |title=Tutte honoured by cryptographic centre |url=http://www.adm.uwaterloo.ca/infonews/release/1998/107%20Tutte%20honored%20by%20new%20Centre%20for%20Applied%20Cryptographic%20Research,%20June%2017,%201998.html
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| |publisher=University of Waterloo |accessdate=2013-09-28}}</ref>
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| * 2001, Officer of the [[Order of Canada]] (OC);
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| * 2001, [[CRM-Fields-PIMS prize]].
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| Asteroid [[14989 Tutte]] (1997 UB7) and the [[Tutte Institute for Mathematics and Computing]] were named in his honour.
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| | |
| ==Personal life and death==
| |
| The opportunity to work at the University of Waterloo appealed to Tutte because it offered the possibility of advancement. It also happened that both William and Dorothea enjoyed natural settings and the overall rural environment that was offered by Waterloo was of interest to Tutte and his wife. Tutte accepted the position and he and Dorothea bought a house in the small nearby town of West Montrose, Ontario. Both Bill and Dorothea enjoyed spending time in their garden and allowing others to enjoy the beautiful scenery that was contained within their property. They also had an extensive knowledge of all the birds in their garden, they could name every bird they encountered. Dorothea was a keen hiker and Bill organized hiking trips. Even near the end of his life Bill still was an avid walker, he could out-walk colleagues 20 years younger.<ref name="Hobbs 2004 322"/><ref>{{cite web| title=Bill Tutte | url=http://www-gap.dcs.st-and.ac.uk/~history/Obits2/Tutte_Telegraph.html|publisher=Telegraph Group Limited}}</ref> After his wife died in 1994, he returned to live in Newmarket, but then returned to Waterloo in 2000, where he died two years later.<ref>{{Citation | last = van der Vat | first = Dan | author-link = Dan van der Vat | title = Obituary: William Tutte | place =London | publisher = The Guardian | date = 10 May 2002 | url = http://www.guardian.co.uk/news/2002/may/10/guardianobituaries.obituaries | accessdate = 28 April 2013 }}</ref>
| |
| | |
| ==Books==
| |
| *{{citation |last=Tutte |first=W. T.
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| |title=Connectivity in graphs |series=Mathematical expositions |volume=15
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| |location=Toronto, Ontario |publisher=University of Toronto Press |year=1966 |zbl=0146.45603}}
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| *{{citation |last=Tutte |first=W. T.
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| |title=Introduction to the theory of matroids
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| |series=Modern analytic and computational methods in science and mathematics |volume=37
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| |location=New York |publisher=American Elsevier Publishing Company |year=1971 |zbl=0231.05027}}
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| *{{citation |last=Tutte |first=W. T.
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| |title=Graph theory |series=Encyclopedia of mathematics and its applications |volume=21
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| |location=Menlo Park, California |publisher=Addison-Wesley Publishing Company |year=1984 |zbl=0554.05001}}
| |
| *{{citation |last=Tutte |first=W. T.
| |
| |title=Graph theory as I have known it |series=Oxford lecture series in mathematics and its applications |volume=11
| |
| |location=Oxford |publisher=Clarendon Press |year=1998 |zbl=0915.05041}}
| |
| | |
| == See also ==
| |
| *[[Systolic geometry]]
| |
| | |
| == References ==
| |
| {{reflist|colwidth=30em}}
| |
| | |
| ==Sources==
| |
| * {{Citation | last = Bauer | first = Friedrich L. | author-link = Friedrich L. Bauer | title = The Tiltman Break | year = 2006 }} Appendix 5 in {{Harvnb|Copeland|2006|pp=370–377}}
| |
| * {{Citation | last = Copeland | first = B. Jack | author-link = Jack Copeland | title = Colossus and the Dawning of the Computer Age | page = }} in {{Harvnb|Erskine|Smith|2011|pp=305–327}}
| |
| * {{Citation | editor-last = Erskine | editor-first = Ralph | editor2-last = Smith | editor2-first = Michael | editor2-link = Michael Smith (newspaper reporter) | title = The Bletchley Park Codebreakers | publisher = Biteback Publishing Ltd | origyear = 2001 | year = 2011 | isbn = 978-1-84954-078-0}} Updated and extended version of ''Action This Day: From Breaking of the Enigma Code to the Birth of the Modern Computer'' Bantam Press 2001
| |
| * {{Citation | last = Good | first = Jack | author-link = I. J. Good | last2 = Michie | first2 = Donald | author2-link = Donald Michie | last3 = Timms | first3 = Geoffrey | title = General Report on Tunny: With Emphasis on Statistical Methods | year = 1945 | id = UK Public Record Office HW 25/4 and HW 25/5 | url = http://www.alanturing.net/turing_archive/archive/index/tunnyreportindex.html | accessdate = 15 September 2010 }} That version is a facsimile copy, but there is a transcript of much of this document in '.pdf' format at: {{Citation | last = Sale | first = Tony | author-link = Anthony Sale | title = Part of the "General Report on Tunny", the Newmanry History, formatted by Tony Sale| year = 2001 | url = http://www.codesandciphers.org.uk/documents/newman/newman.pdf | accessdate = 20 September 2010 }}, and a web transcript of Part 1 at: {{Citation | last = Ellsbury | first = Graham | title = General Report on Tunny With Emphasis on Statistical Methods | url = http://www.ellsbury.com/tunny/tunny-001.htm | accessdate = 3 November 2010 }}
| |
| * {{Citation | last = Good | first = Jack | author-link = I. J. Good | title = Enigma and Fish | year = 1993 }} in {{Harvnb|Hinsley|Stripp|1993|pp=149–166 }}
| |
| * {{Citation | editor-last = Hinsley | editor-first = F.H. | editor-link = Harry Hinsley | editor2-last = Stripp | editor2-first = Alan | year = 1993 | origyear = 1992 | title = Codebreakers: The inside story of Bletchley Park | publication-place = Oxford | publisher = Oxford University Press | isbn = 978-0-19-280132-6 }}
| |
| *{{Citation | last = O'Connor | first = J J | last2 = Robertson | first2 = E F | author2-link = Edmund F. Robertson | title = MacTutor Biography: William Thomas Tutte | publisher = University of St Andrews | year = 2003 | url = http://www-history.mcs.st-and.ac.uk/Biographies/Tutte.html | accessdate = 28 April 2013 }}
| |
| * {{Citation | last = Tutte | first = W. T. | author-link = W. T. Tutte | title = Fish and I | date = 19 June 1998 | url = http://www.usna.edu/Users/math/wdj/_files/documents/papers/cryptoday/tutte_fish.pdf | accessdate = 7 April 2012 }} Transcript of a lecture given by Prof. Tutte at the [[University of Waterloo]]
| |
| * {{Citation | last = Tutte | first = William T. | authorlink = W. T. Tutte | year = 2006 | title = My Work at Bletchley Park }} Appendix 4 in {{Harvnb|Copeland|2006|pp=352–369}}
| |
| * {{Citation | last = Ward | first = Mark | title = Code-cracking machine returned to life | publisher = BBC News | url = http://www.bbc.co.uk/news/technology-13566878 | accessdate = 28 April 2013 | date=27 May 2011}}
| |
| * {{Citation | last = Younger | first = D. H. | title = Biographical Memoirs of Fellows of the Royal Society: William Thomas Tutte. 14 May 1917 — 2 May 2002 | publisher = The Royal Society | year = 2012 | doi = 10.1098/rsbm.2012.0036 | url = http://rsbm.royalsocietypublishing.org/content/58/283 | accessdate = 28 April 2013 }}
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| == External links ==
| |
| * [[Rowland L. Brooks|Brooks, R. L.]]; [[Cedric Smith (statistician)|Smith, C. A. B.]]; [[Arthur Harold Stone|Stone, A. H.]]; and Tutte, W. T. "The Dissection of Rectangles into Squares." ''Duke Math. J.'' 7, 312-340, 1940
| |
| * [http://www.math.uwaterloo.ca/CandO_Dept/William_Tutte/tutte.shtml Professor William T. Tutte]
| |
| * {{Citation | last1 = Hobbs | first1 = Arthur | last2 = Oxley | first2 = James | author2-link = James Oxley | title = William T. Tutte (1917-2002) | journal = Notices of the American Mathematical Society | volume = 51 | issue = 3 | pages = 320–330 | publisher = American Mathematical Society | location = Providence, RI | date = March 2004 | url = http://www.ams.org/notices/200403/mem-tutte.pdf |format=PDF| issn = 1088-9477}}
| |
| *{{MathGenealogy |id=15096}}
| |
| * [http://www.math.binghamton.edu/zaslav/Oldcourses/580.S04/tutte.html William Tutte, 84, Mathematician and Code-breaker, Dies] - Obituary from [[The New York Times]]
| |
| * [http://www.guardian.co.uk/obituaries/story/0,3604,712971,00.html William Tutte: Unsung mathematical mastermind] - Obituary from [[The Guardian]]
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| * [http://www.crm.umontreal.ca/prix/recipients.html#2001 CRM-Fields-PIMS Prize - 2001 - William T. Tutte]
| |
| * [http://www.fields.utoronto.ca/audio/01-02/CRM-Fields/tutte/ "60 Years in the Nets" - a lecture (audio recording) given at the Fields Institute on October 25, 2001 to mark the receipt of the 2001 CRM-Fields Prize]
| |
| * [http://frode.home.cern.ch/frode/crypto/tutte.html Tutte's paper on the Fish cipher]
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| * [http://www.math.niu.edu/%7Erusin/known-math/97/tutte Tutte's disproof of Tait's conjecture]
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| * [http://www.telegraph.co.uk/history/world-war-two/9765962/Bletchleys-forgotten-heroes.html "Bletchley's forgotten heroes"], Ian Douglas, ''[[The Daily Telegraph|The Telegraph]]'', 25 December 2012
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| {{Authority control|VIAF=9915493}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Tutte, William Thomas
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Codebreaker and mathematician
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| | DATE OF BIRTH = 1917-05-14
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| | PLACE OF BIRTH = [[Newmarket, Suffolk]], [[England]]
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| | DATE OF DEATH = 2002-05-02
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| | PLACE OF DEATH = [[Kitchener, Ontario|Kitchener]], [[Ontario]], [[Canada]]
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| }}
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| {{DEFAULTSORT:Tutte, William Thomas}}
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| [[Category:1917 births]]
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| [[Category:2002 deaths]]
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| [[Category:People from Newmarket, Suffolk]]
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| [[Category:Alumni of Trinity College, Cambridge]]
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| [[Category:People associated with Bletchley Park]]
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| [[Category:British cryptographers]]
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| [[Category:Cipher-machine cryptographers]]
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| [[Category:English mathematicians]]
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| [[Category:Canadian mathematicians]]
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| [[Category:20th-century mathematicians]]
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| [[Category:Graph theorists]]
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| [[Category:Graph drawing people]]
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| [[Category:Combinatorialists]]
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| [[Category:University of Toronto faculty]]
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| [[Category:University of Waterloo faculty]]
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| [[Category:Officers of the Order of Canada]]
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| [[Category:British expatriate academics in Canada]]
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| [[Category:Fellows of the Royal Society]]
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| [[Category:Fellows of the Royal Society of Canada]]
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