Mathematical Solution of the Enigma Cipher
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To What Extent Did British Advancements in Cryptanalysis During World War II Influence the Development of Computer Technology?
Portland State University PDXScholar Young Historians Conference Young Historians Conference 2016 Apr 28th, 9:00 AM - 10:15 AM To What Extent Did British Advancements in Cryptanalysis During World War II Influence the Development of Computer Technology? Hayley A. LeBlanc Sunset High School Follow this and additional works at: https://pdxscholar.library.pdx.edu/younghistorians Part of the European History Commons, and the History of Science, Technology, and Medicine Commons Let us know how access to this document benefits ou.y LeBlanc, Hayley A., "To What Extent Did British Advancements in Cryptanalysis During World War II Influence the Development of Computer Technology?" (2016). Young Historians Conference. 1. https://pdxscholar.library.pdx.edu/younghistorians/2016/oralpres/1 This Event is brought to you for free and open access. It has been accepted for inclusion in Young Historians Conference by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. To what extent did British advancements in cryptanalysis during World War 2 influence the development of computer technology? Hayley LeBlanc 1936 words 1 Table of Contents Section A: Plan of Investigation…………………………………………………………………..3 Section B: Summary of Evidence………………………………………………………………....4 Section C: Evaluation of Sources…………………………………………………………………6 Section D: Analysis………………………………………………………………………………..7 Section E: Conclusion……………………………………………………………………………10 Section F: List of Sources………………………………………………………………………..11 Appendix A: Explanation of the Enigma Machine……………………………………….……...13 Appendix B: Glossary of Cryptology Terms.…………………………………………………....16 2 Section A: Plan of Investigation This investigation will focus on the advancements made in the field of computing by British codebreakers working on German ciphers during World War 2 (19391945). -
Breaking the Enigma Cipher
Marian Rejewski An Application of the Theory of Permutations in Breaking the Enigma Cipher Applicaciones Mathematicae. 16, No. 4, Warsaw 1980. Received on 13.5.1977 Introduction. Cryptology, i.e., the science on ciphers, has applied since the very beginning some mathematical methods, mainly the elements of probability theory and statistics. Mechanical and electromechanical ciphering devices, introduced to practice in the twenties of our century, broadened considerably the field of applications of mathematics in cryptology. This is particularly true for the theory of permutations, known since over a hundred years(1), called formerly the theory of substitutions. Its application by Polish cryptologists enabled, in turn of years 1932–33, to break the German Enigma cipher, which subsequently exerted a considerable influence on the course of the 1939–1945 war operation upon the European and African as well as the Far East war theatres (see [1]–[4]). The present paper is intended to show, necessarily in great brevity and simplification, some aspects of the Enigma cipher breaking, those in particular which used the theory of permutations. This paper, being not a systematic outline of the process of breaking the Enigma cipher, presents however its important part. It should be mentioned that the present paper is the first publication on the mathematical background of the Enigma cipher breaking. There exist, however, several reports related to this topic by the same author: one – written in 1942 – can be found in the General Wladyslaw Sikorski Historical Institute in London, and the other – written in 1967 – is deposited in the Military Historical Institute in Warsaw. -
41760779079990.Pdf
.CONFIS~Ti;~691 BBS'l'RIOHJB· THE DISTBIBUTION OF THIS SPECIAL TEXT WILL BE RESTRICTED TO REGULARLY ENROLLED EXTENSION COURSE STUDENTS, 'l'O MILITARY PERSONNEL, AND TO OTHER PERSONS COMING WITHIN THE MEANING OF THE PHRASE "FOR OFFICIAL USE ONLY/, ·. ARMY EXTENSION COURSES ~,· ·~~cY-l~~ I!LA)f'~'~ ~ \_ -·----------;-- --·· SPECIAL TEXT No. 166 ADVANCED MILITARY CRYPTOGRAPHY Szcoxn (19'3) EDmox PREPARED UNDER THE DIRECTION OF THE CHIEF SIGNAL OFFICER FOR USE WITH 'I1fE ARMY EXTENSION COURSES .',; ,_ • RSS'fRI<ffRB document contains information affecting the nat1 defense of the United States within the meaning of die · nage Act (U.S. C. -Y,. ~:>· 50: 31, 32). The transmission o · ocument · · or the revelation of its contents in any nl:an any unauthorized person is prohibited. + UNITED STATES GOVERNMENT PRINTING OFFICE ~ (o ~ ~ WASHINGTON : 19'3 . ,. 7.~0NFIDENTIAL Peclassified and approved for release by NSA on 01-14-2014 pursuant to E.O. 1352§ REF ID:A64691 ,·J/ 30 April 1959 Th.is document is re-graded "eEm'!BBrff " of DOD Directive 5200.l dated 8 ~ UP and by autharity of the Directar '2t1:.!i Security ~ncy. ' Paul~w~ S. Willard Colonel, AOC Adjutant Ge.nera.J. • ~· WAR DEPARTMENT, • WAsmNGTON, Februa1"JI S, 1948. Tbis revision of Special Text No. 166, Advanced Milita.ry Cryptog raphy (1935), for use with the Anny Extension Courses, is published for the information and guidance of all concerned. BY ORDEB OF THE SlilCBlilTAB.Y OF wAB! :,. G. o. M.ARSHAT,T., General, Ohiejoj8f4. OFFICIAL! JAMES A. ULIO, Major Gemral, 7?i.e Adjut,ant Geneml,. (XI) • SPECIAL TEXT NO. -
Polska Myśl Techniczna W Ii Wojnie Światowej
CENTRALNA BIBLIOTEKA WOJSKOWA IM. MARSZAŁKA JÓZEFA PIŁSUDSKIEGO POLSKA MYŚL TECHNICZNA W II WOJNIE ŚWIATOWEJ W 70. ROCZNICĘ ZAKOŃCZENIA DZIAŁAŃ WOJENNYCH W EUROPIE MATERIAŁY POKONFERENCYJNE poD REDAkcJą NAUkoWą DR. JANA TARCZYńSkiEGO WARSZAWA 2015 Konferencja naukowa Polska myśl techniczna w II wojnie światowej. W 70. rocznicę zakończenia działań wojennych w Europie Komitet naukowy: inż. Krzysztof Barbarski – Prezes Instytutu Polskiego i Muzeum im. gen. Sikorskiego w Londynie dr inż. Leszek Bogdan – Dyrektor Wojskowego Instytutu Techniki Inżynieryjnej im. profesora Józefa Kosackiego mgr inż. Piotr Dudek – Prezes Stowarzyszenia Techników Polskich w Wielkiej Brytanii gen. dyw. prof. dr hab. inż. Zygmunt Mierczyk – Rektor-Komendant Wojskowej Akademii Technicznej im. Jarosława Dąbrowskiego płk mgr inż. Marek Malawski – Szef Inspektoratu Implementacji Innowacyjnych Technologii Obronnych Ministerstwa Obrony Narodowej mgr inż. Ewa Mańkiewicz-Cudny – Prezes Federacji Stowarzyszeń Naukowo-Technicznych – Naczelnej Organizacji Technicznej prof. dr hab. Bolesław Orłowski – Honorowy Członek – założyciel Polskiego Towarzystwa Historii Techniki – Instytut Historii Nauki Polskiej Akademii Nauk kmdr prof. dr hab. Tomasz Szubrycht – Rektor-Komendant Akademii Marynarki Wojennej im. Bohaterów Westerplatte dr Jan Tarczyński – Dyrektor Centralnej Biblioteki Wojskowej im. Marszałka Józefa Piłsudskiego prof. dr hab. Leszek Zasztowt – Dyrektor Instytutu Historii Nauki Polskiej Akademii Nauk dr Czesław Andrzej Żak – Dyrektor Centralnego Archiwum Wojskowego im. -
Cryptographyorhioohulmuoft CRYPTOGRAPHY OR the HISTORY, PRINCIPLES, and PRACTICE of CIPHER-WRITING
Digitized by the Internet Archive in 2007 with funding from IVIicrosoft Corporation http://www.archive.org/details/cryptographyorhiOOhulmuoft CRYPTOGRAPHY OR THE HISTORY, PRINCIPLES, AND PRACTICE OF CIPHER-WRITING ^ w >TOGRA OR The History, Principles, and Practice OF CIPHER-WRITING e<^ BY Fl^EDWARD HULME, F.L.S., F.S.A U\ AUTHOR OF "familiar WILD FLOWERS," " MYTHLAND," " NATURAL HISTORY LORE AND LEGEND," "the birth and development OF ORNAMENT," " WAYSIDK SKETCHES," ETC Heres noiv mystery and hieroglyphic Ben Jonson— The Alchemysi. LONDON WARWICK HOUSE, SALISBURY SQUARE, E.C NEW YORK AND MELBOURNE — CONTENTS CHAPTER I PAGE Meaning of cryptography—Objections to its study—Its legitimate use and value—Historic examples of its employment—Deliglit in the mysterious—Many other ways of conveying secret information—Symbolism of action—The spoken word imprisoned and dispatched —A matter not necessarily secret because one cannot understand it — Egyptian hieroglypliics — Chinese characters—Indian mutiny Greek—Ancient Biblical cryptogram — Sheshach of Jeremiah — Sir Henry Eawlinson thereon—Statements for and against Julius Caesar's secret code—The waxed tablet of Demaratus—Difference between hidden and secret writing—The shaven head a writing tablet—Charle- magne and Alfred the Great as cryptographic experts —Mediaeval authorities—Trithemius the Benedictine " — " Steganographia —Dabbling in the black art Dr. Dee—Batista Porta's book on "Natural Majick" —Invisible writing—Chemical methods by vitriol, alum, etc. —Writing on glass or crystal—Papal In- quisition—Disappearing writing—Messages wrapped round rollers—Two methods—A slave's back the writing surface—Chemical methods of no great value ordinarily—Disadvantages of use— Action of light and heat—Chloride of cobalt, sulphate of copper, etc. -
Enigma Cryptanalysis - Beginnings
Enigma Cryptanalysis - Beginnings Gaurish Korpal∗ [email protected] July 15, 2015 Abstract Any message may be hidden in two basic ways. The methods of steganography conceal the very existence of the message, for example invisible inks and microdots. The methods of cryptography, on the other hand, do not conceal the presence of a secret message but render it unintelligible as ciphertext, to outsiders by various transformations of the plaintext. Breaking ciphers require ingenuity, creativity and a little math. In this article our focus will be on breaking Enigma ciphers. The skill involved in breaking ciphers is called cryptanalysis. Keywords. Enigma, cryptanalysis, cypher, Caesar, Vigen`ere,Rejewski, Zygalski, Bomba, Bombe 1 Cipher not Code A code is a mapping from some meaningful unit (word, sentence, phrase) into something else (usually a shorter group of symbols). A code requires a codebook, it is simply a list of these mappings. For example we could make up a code where the word Apple is written as 67, historical example of this is \Zimmermann Telegram Code" for more details refer [7]. Ciphers do not involve meaning. Instead they are mechanical operations (known as algorithms) which are performed on the individual or small chunks of letters. A code is stored as a mapping in a codebook, while ciphers transform individual symbols according to an algorithm. It was definitively stated in 1883 by the Dutch linguist Auguste Kerckhoffs von Nieuwenhof in his book La Cryptographie militaire: Kerckhoffs' Principle: The security of a cryptosystem must not depend on keeping secret the crypto-algorithm. The security depends only on keeping secret the key. -
The Enigma History and Mathematics
The Enigma History and Mathematics by Stephanie Faint A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Master of Mathematics m Pure Mathematics Waterloo, Ontario, Canada, 1999 @Stephanie Faint 1999 I hereby declare that I am the sole author of this thesis. I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research. I further authorize the University of Waterloo to reproduce this thesis by pho tocopying or by other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research. 11 The University of Waterloo requires the signatures of all persons using or pho tocopying this thesis. Please sign below, and give address and date. ill Abstract In this thesis we look at 'the solution to the German code machine, the Enigma machine. This solution was originally found by Polish cryptologists. We look at the solution from a historical perspective, but most importantly, from a mathematical point of view. Although there are no complete records of the Polish solution, we try to reconstruct what was done, sometimes filling in blanks, and sometimes finding a more mathematical way than was originally found. We also look at whether the solution would have been possible without the help of information obtained from a German spy. IV Acknowledgements I would like to thank all of the people who helped me write this thesis, and who encouraged me to keep going with it. In particular, I would like to thank my friends and fellow grad students for their support, especially Nico Spronk and Philippe Larocque for their help with latex. -
Introduction
ON SOME KNOWN POSSIBLE APPLICATIONS OF QUASIGROUPS IN CRYPTOLOGY Victor Shcherbacov Abstract. It is surveyed known (published) possible application of binary and n-ary quasigroups in cryptology. Mathematics Subject Classification: 20N05, 94A60. Key words and phrases: Cryptology, cryptography, cipher, key, quasigroup, n-ary quasigroup. Introduction Almost all results obtained in branch of application of quasigroups in cryptology and coding theory to the end of eighties years of the XX-th century are described in [20, 21]. In the present survey the main attention is devoted more late articles in this direction. Basic facts on quasigroup theory it is possible to find in [5, 6, 7, 64]. Information on basic fact in cryptology it is possible to find in many books see, for example, [3, 11, 60, 54]. Cryptology is a science that consists form two parts: cryptography and cryptanalysis. Cryp- tography is a science on methods of transformation (ciphering) of information with the purpose of a protection this information from an unlawful user. Cryptanalysis is a science on methods and ways of breaking down of ciphers ([32]). In some sense cryptography is a \defense", i.e. this is a science on construction of new ciphers, but cryptanalysis is an \attack", i.e. this is a science and some kind \art", a set of methods on breaking of ciphers. This situation is similar to situation with intelligence and contr-intelligence. These two objects (cryptography and cryptanalysis) are very closed and there does not exist a good cryptographer that do not know methods of cryptanalysis. It is clear, that cryptology depends from a level of development of a society and a level of development of technology. -
Cryptology: an Historical Introduction DRAFT
Cryptology: An Historical Introduction DRAFT Jim Sauerberg February 5, 2013 2 Copyright 2013 All rights reserved Jim Sauerberg Saint Mary's College Contents List of Figures 8 1 Caesar Ciphers 9 1.1 Saint Cyr Slide . 12 1.2 Running Down the Alphabet . 14 1.3 Frequency Analysis . 15 1.4 Linquist's Method . 20 1.5 Summary . 22 1.6 Topics and Techniques . 22 1.7 Exercises . 23 2 Cryptologic Terms 29 3 The Introduction of Numbers 31 3.1 The Remainder Operator . 33 3.2 Modular Arithmetic . 38 3.3 Decimation Ciphers . 40 3.4 Deciphering Decimation Ciphers . 42 3.5 Multiplication vs. Addition . 44 3.6 Koblitz's Kid-RSA and Public Key Codes . 44 3.7 Summary . 48 3.8 Topics and Techniques . 48 3.9 Exercises . 49 4 The Euclidean Algorithm 55 4.1 Linear Ciphers . 55 4.2 GCD's and the Euclidean Algorithm . 56 4.3 Multiplicative Inverses . 59 4.4 Deciphering Decimation and Linear Ciphers . 63 4.5 Breaking Decimation and Linear Ciphers . 65 4.6 Summary . 67 4.7 Topics and Techniques . 67 4.8 Exercises . 68 3 4 CONTENTS 5 Monoalphabetic Ciphers 71 5.1 Keyword Ciphers . 72 5.2 Keyword Mixed Ciphers . 73 5.3 Keyword Transposed Ciphers . 74 5.4 Interrupted Keyword Ciphers . 75 5.5 Frequency Counts and Exhaustion . 76 5.6 Basic Letter Characteristics . 77 5.7 Aristocrats . 78 5.8 Summary . 80 5.9 Topics and Techniques . 81 5.10 Exercises . 81 6 Decrypting Monoalphabetic Ciphers 89 6.1 Letter Interactions . 90 6.2 Decrypting Monoalphabetic Ciphers . -
Agnes Meyer Driscoll Vs. the Enigma and the Bombe Colin Burke
Colin Burke 1-2001 © Agnes Meyer Driscoll vs. the Enigma and the Bombe Colin Burke ABSTRACT: Documents in Britain‘s National Archives/ Public Record Office and in the U.S. National Archive‘s Record Groups RG457 and RG38 indicate that in mid-1941 the United States Navy‘s codebreaking organization, OP-20-G ignored an opportunity to gain full knowledge of Britain‘s anti-Enigma methods and machines. Spending a year and one-half working on what it felt was a unique and much more effective method– but one that failed--OP-20-G‘s, staff, at a critical time in U.S.- British relations ,did not inform America‘s decision makers of Britain‘s willingness to share its crypto-secrets . As a result, American leaders believed that England‘s GC&CS had deliberately withheld vital information that would have allowed the development of an independent American attack on Naval Enigma. That belief lasted Colin Burke 1-2001 © throughout the war and caused friction between the two nations. Other consequences of OP-20-G‘s mid-1941 decision were to delay the adoption of the British Bombe and its allied methods and to waste perhaps six months of the vital time of the new team of cryptanalysts and engineers assigned, in early 1942, to develop an American Bombe. KEYWORDS: OP-20-G, Enigma, Driscoll, Denniston, GC&CS, Bombe, Safford, Wenger, Weeks, Currier, Engstrom, catalog, Banburismus, hot-point, cold-point, Tiltman. Introduction: A Fragile British-American Crypto-Alliance By the end of World War II Great Britain and the United States had forged uniquely close relationships--even among their intelligence agencies.1 Much had to be overcome to achieve the long-lasting 1 Robert Louis Benson, A History of U.S. -
The Enigma Cipher Machine
MTAT.07.006 Research Seminar in Cryptography The Enigma Cipher Machine Kadri Hendla University of Tartu kadri [email protected] Research Seminar in Cryptography, 05.12.2005 The Enigma Cipher Machine, Kadri Hendla 1 Overview • Description of Enigma • Enigma in Use • Cryptanalysis of Enigma Research Seminar in Cryptography, 05.12.2005 The Enigma Cipher Machine, Kadri Hendla 2 History of Enigma • Enigma is most known for its part in World War II. • In 1918 Arthur Scherbius applied for a patent for Enigma. • German military adopted Enigma in 1926. • There were many different versions of Enigma. Research Seminar in Cryptography, 05.12.2005 The Enigma Cipher Machine, Kadri Hendla 3 The Enigma Machine Research Seminar in Cryptography, 05.12.2005 The Enigma Cipher Machine, Kadri Hendla 4 Description of Enigma: Working Principle • Scrambler (3 rotors and a reflector) • Lamps • Keyboard • Plugboard Research Seminar in Cryptography, 05.12.2005 The Enigma Cipher Machine, Kadri Hendla 5 Description of Enigma: Rotors • 1. notched ring • 2. marking dot for ”A” contact • 3. alphabet ring • 4. plate contacts • 5. wire connections • 6. pin contacts • 7. spring-loaded ring adjusting lever • 8. hub • 9. finger wheel • 10. ratchet wheel Research Seminar in Cryptography, 05.12.2005 The Enigma Cipher Machine, Kadri Hendla 6 Description of Enigma: Reflector The reflector gave two important properties to Enigma: • Encryption was the same as decryption. • No letter could be encrypted to itself. Research Seminar in Cryptography, 05.12.2005 The Enigma Cipher Machine, Kadri Hendla -
Non-Associative Algebraic System in Cryptology. Protection Against "Meet in the Middle" Attack
Quasigroups and Related Systems 8 (2001), 7 14 Non-associative algebraic system in cryptology. Protection against "meet in the middle" attack József Dénes and Tamás Dénes Abstract In this paper we shall mention an algorithm of zero knowledge proof based on Latin squares. We shall dene the DLm(n) type Latin squares, which have a further property that is stronger than the pan-Hamiltonian squares: Every pair of DLm(n) rows and columns is a cycle of length n, if n is prime. 1. Basic notions In general the cryptology is based on elds which are commutative and asso- ciative. There is a method which studies the evolution of dierences during encryption of pairs of plaintexts, and derives the most likely keys from a pool of many pairs. It is called dierential cryptanalysis. Dierential crypt- analysis can also be used to nd collisions in "hash" functions. For DES (Data Encryption Standard) like cryptosystems the dierences are usually in terms of exclusive or of the intermediate data in the pair. Dierential cryptanalysis might apply "meet in the middle attack" (introduced in [2]). Denition 1.1. Meet in the Middle Attack: An attack in which the evolu- tion of the data is studied from both directions: from the plaintext forwards towards an intermediate round and from the ciphertext backwards towards the same intermediate round. If the results at the intermediate round are not the same in both directions, then the tested value of the key is not the real value. If both results are the same in several encryptions, then the tested value of the key is the real value with high probability.