Editing Claude Shannon (section)

===Wartime research===
Shannon had worked at [[Bell Labs]] for a few months in the summer of 1937,<ref>{{Cite book |last=Gertner |first=Jon |title=The idea factory: Bell Labs and the great age of American innovation |date=2013 |publisher=Penguin Books |isbn=978-0-14-312279-1 |location=London |pages=118}}</ref> and returned there to work on [[fire-control system]]s and [[cryptography]] during [[World War II]], under a contract with section D-2 (Control Systems section) of the [[National Defense Research Committee]] (NDRC).

Shannon is credited with the invention of [[signal-flow graph]]s, in 1942. He discovered the topological gain formula while investigating the functional operation of an analog computer.<ref>{{Cite book|title = NASAP-70 User's and Programmer's manual|last1 = Okrent|first1 = Howard|publisher = School of Engineering and Applied Science, University of California at Los Angeles|year = 1970|location = Los Angeles, California|pages = 3–9|first2 = Lawrence P.|last2 = McNamee|url=https://ntrs.nasa.gov/citations/19710025849|chapter-url = https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710025849.pdf|chapter = 3. 3 Flowgraph Theory|access-date = March 4, 2016}}</ref>

For two months early in 1943, Shannon came into contact with the leading British mathematician [[Alan Turing]]. Turing had been posted to Washington to share with the [[U.S. Navy]]'s cryptanalytic service the methods used by the [[Government Code and Cypher School]] at [[Bletchley Park]] to break the cyphers used by the ''[[Kriegsmarine]]'' [[U-boat]]s in the north [[Atlantic Ocean]].<ref name=Hodges1992>{{Citation | last = Hodges | first = Andrew | author-link = Andrew Hodges | year = 1992 | title = Alan Turing: The Enigma | location = London | publisher = [[Vintage Books|Vintage]] | pages = 243–252 | isbn = 978-0-09-911641-7}}</ref> He was also interested in the encipherment of speech and to this end spent time at Bell Labs. Shannon and Turing met at teatime in the cafeteria.<ref name=Hodges1992 /> Turing showed Shannon his 1936 paper that defined what is now known as the "[[universal Turing machine]]".<ref>{{Citation | last= Turing | first= A.M. | publication-date = 1937 | year = 1936 | title = On Computable Numbers, with an Application to the Entscheidungsproblem | periodical = Proceedings of the London Mathematical Society | series = 2 | volume = 42 | pages = 230–65 | doi= 10.1112/plms/s2-42.1.230 | s2cid= 73712 }}</ref><ref>{{citation | last = Turing | first = A.M. | publication-date = 1937 | title = On Computable Numbers, with an Application to the Entscheidungsproblem: A correction | periodical = Proceedings of the London Mathematical Society | series = 2 | volume = 43 | pages = 544–6 | doi = 10.1112/plms/s2-43.6.544 | year = 1938 | issue = 6 }}</ref> This impressed Shannon, as many of its ideas complemented his own.

Shannon and his team developed anti-aircraft systems that tracked enemy missiles and planes, while also determining the paths for intercepting missiles.<ref>{{Cite book |url=https://books.google.com/books?id=58ySAwAAQBAJ&pg=PA183 |title=Computing: A Historical and Technical Perspective |date=2014 |publisher=CRC Press |isbn=978-1-4822-2741-3 |editor-last=Igarashi |editor-first=Yoshihide |edition= |location=Boca Raton, Florida |pages=183}}</ref>

In 1945, as the war was coming to an end, the NDRC was issuing a summary of technical reports as a last step prior to its eventual closing down. Inside the volume on fire control, a special essay titled ''Data Smoothing and Prediction in Fire-Control Systems'', coauthored by Shannon, [[Ralph Beebe Blackman]], and [[Hendrik Wade Bode]], formally treated the problem of smoothing the data in fire-control by analogy with "the problem of separating a signal from interfering noise in communications systems."<ref>{{cite book|isbn=0801880572|pages=319–320|title=Between Human and Machine: Feedback, Control, and Computing Before Cybernetics|last1=Mindell|first1=David A.|date=October 15, 2004|publisher=JHU Press }}</ref> In other words, it modeled the problem in terms of [[Data processing|data]] and [[signal processing]] and thus heralded the coming of the [[Information Age]].

Shannon's work on cryptography was even more closely related to his later publications on [[communication theory]].<ref>{{cite book |last=Kahn |first=David |author-link=David Kahn (writer) |title=The Codebreakers: The Comprehensive History of Secret Communication from Ancient Times to the Internet |title-link=The Codebreakers |date=1966 |publisher=Macmillan and Sons |isbn=0684831309 |pages=743–751}}</ref> At the close of the war, he prepared a classified memorandum for [[Bell Telephone Labs]] entitled "A Mathematical Theory of Cryptography", dated September 1945. A declassified version of this paper was published in 1949 as "[[Communication Theory of Secrecy Systems]]" in the ''[[Bell System Technical Journal]]''. This paper incorporated many of the concepts and mathematical formulations that also appeared in his ''[[A Mathematical Theory of Communication]]''. Shannon said that his wartime insights into communication theory and cryptography developed simultaneously, and that "they were so close together you couldn't separate them".<ref>quoted in Kahn, ''The Codebreakers'', p. 744.</ref> In a footnote near the beginning of the classified report, Shannon announced his intention to "develop these results … in a forthcoming memorandum on the transmission of information."<ref>Quoted in Erico Marui Guizzo, [http://dspace.mit.edu/bitstream/1721.1/39429/1/54526133.pdf "The Essential Message: Claude Shannon and the Making of Information Theory"], {{webarchive |url=https://web.archive.org/web/20080528182200/http://dspace.mit.edu/bitstream/1721.1/39429/1/54526133.pdf |date=May 28, 2008 }} unpublished MS thesis, Massachusetts Institute of Technology, 2003, p. 21.</ref>

While he was at Bell Labs, Shannon proved that the [[cryptographic]] [[one-time pad]] is unbreakable in his classified research that was later published in 1949. The same article also proved that any unbreakable system must have essentially the same characteristics as the one-time pad: the key must be truly random, as large as the plaintext, never reused in whole or part, and kept secret.<ref>{{cite journal|doi=10.1002/j.1538-7305.1949.tb00928.x|title=Communication Theory of Secrecy Systems|year=1949|last1=Shannon|first1=C. E.|journal=Bell System Technical Journal|volume=28|issue=4|pages=656–715}}</ref>