A GENERALIZATION OF THE KNAPSACK ALGORITHM USING GALOIS FIELDS

We prove a generalization of a theorem of Rejewski. This theorem shows how one can solve an equation of the form XY=α in a symmetric group, where α is a given permutation and X and Y are each of order two with a specified number of disjoint transpositions. The number of solutions is also part of the theorem. Using this theorem we outline what we believe was the Polish solution (or very close to it) to the Enigma assuming that one had no data from daily keys. With some assumptions on independence of events, we show that the Polish Cipher Bureau would probably have broken the Enigma in just over four years.     

EXTRAORDINARY CODEBREAKERS,OUTSTANDING FAMILY: A REVIEW

The effectiveness of Alan Turing's original bombe design is discussed in this article along with organizational methods of implementing it via a microcomputer. To illustrate the material presented, a three part German Werhmacht message is solved.     

Resurrecting Bomba Kryptologiczna: Archaeology of Algorithmic Artefacts,I

Abstract

The procedure executed on the Polish Bomba Kryptologiczna is reconstructed on the basis of Marian Rejewski's accounts and simulative experiment. An original Wehrmacht message from the period in question is broken to illustrate the effectiveness of the hardware and the routines employed. The authenticity of the indicators given in Rejewski's first and later reports is investigated and the circuitry of a simplified version of the bomba presented.     

RECOVERING THE WIRING OF ENIGMA'S UMKEHRWALZE A

Umkehrwalze A was the original reflector used in the version of the Enigma machine employed by the German armed services. Its wiring was originally deduced by the Polish cryptanalyst Marian Rejewski in December 1932 or January 1933, but details of the wiring have not previously been published. Sufficient information to recover the wiring analytically is provided in a wartime document by Alan Turing, and other sources have been found to confirm the solution. This paper presents the wiring, along with alternative methods of recovering it from Turing's data.     

KRIEGSMARINE SIGNAL INDICATORS

Indicators used by the Kriegsmarine in its signals traffic in World War II are explained.     

UMKEHRWALZE D: ENIGMA'S REWIRABLE REFLECTOR - PART II

Umkehrwalze D was a field-rewirable reflector for the German service Enigma machine, introduced primarily on German Air Force cipher networks late in the Second World War. The three parts of this article discuss the history of the device and the various techniques and machines developed by the British and American signals intelligence agencies to deal with it.     

UMKEHRWALZE D: ENIGMA'S REWIRABLE REFLECTOR - PART III

Umkehrwalze D was a field-rewirable reflector for the German service Enigma machine, introduced primarily on German Air Force cipher networks late in the Second World War. This article discusses the history of the device and the various techniques and machines developed by the British and American signals intelligence agencies to deal with it.     

History and Modern Cryptanalysis of Enigma's Pluggable Reflector

The development history of Umkehrwalze Dora, Enigma's pluggable reflector, is presented from the first ideas in the mid-1920s to the last development plans and its actual usage in 1945. An Enigma message in three parts, enciphered with Umkehrwalze Dora and intercepted by the British on 11 March 1945, is shown. The successful recovery of the key of this message is described. Modern computer-based cryptanalysis is used to recover the wiring of the unknown “Uncle Dick,” which the British called this field-rewirable reflector. The attack is based on the known ciphertext and plaintext pair from the first part of the intercept. After recovery of the unknown reflector wiring and the daily key, the plaintext of the second part of the message is revealed.     

UMKEHRWALZE D: ENIGMA'S REWIRABLE REFLECTOR - PART I

Umkehrwalze D was a field-rewirable reflector for the German service Enigma machine, introduced primarily on German Air Force cipher networks late in the Second World War. The three parts of this article discuss the history of the device and the various techniques and machines developed by the wartime British and American signals intelligence agencies to deal with it.     

Rejewski's Test Message as a Crib

After Marian Rejewski had determined the Enigma wiring, he used a test message to help resolve the turnover and correct twist of the rotors [7 Kozaczuk, W. 1984. Enigma-How the German Machine Cipher was Broken, and How it was Read by the Allies in World War Two, ed. and trans. C. Kasparek. see Appendix D. Frederick, MD: University Publications of America, Inc. [Google Scholar], p. 258]. However, it is of historical interest to note that this message could have been used as a crib in its own right. It is shown that using only hand methods and Rejewski's guess that the entry permutation was alphabetic, the message could have revealed the wiring of rotors I and III despite its short length of 90 letters.     

CIPHERTEXT-ONLY CRYPTANALYSIS OF ENIGMA

Enigma messages can be solved by recovering the message key settings, the ring settings, and the plug settings individually. Recovery of the message key setting is sensitive enough to distinguish the correct rotor order. The method is demonstrated on a 647-letter message, and its performance is estimated for different message lengths and numbers of plugs used.     

SEIZING THE ENIGMA TWO REVIEWS OF ONE BOOK

A list of important events in the making and breaking of the German Enigma cipher machine of World War II is given in the order of their occurrences.     

NAVAL ENIGMA: M4 AND ITS ROTORS

The wiring of rotors in the naval version of Enigma is given (including that of beta and gamma) and events leading to the introduction of Triton, a cipher for Atlantic U-boats, are described. It is shown that an alpha rotor did not enter service, and that Triton became operational in October 1941.     

Spanish Enigma: A History of the Enigma in Spain

Abstract

The presentation of a brief study of the use of Enigma Machines in Spain, during the Spanish Civil War (1936–1939) and later, until their final replacement.     

18TH CENTURY SHORTHAND EXPERT NEEDED (RE-RUN)

Abstract

Fialka M-125 (sometimes called the “Russian Enigma”) is an electro-mechanical rotor cipher machine used during the Cold War. The designers of this cipher eliminated the known weaknesses of Enigma. In this article, the authors summarize the main principle of the Fialka algorithm from public sources. Moreover, they introduce a mathematical model of the Fialka cipher, and they analyse the effect of blocking pin settings on the cipher's period.     

THE MARKET FOR ENCRYPTION

Abstract

In 1942, the United States Navy recognized that in the ranks of newly-enlisted WAVES lay the potential for much-needed assistance in processing German Navy Enigma messages that had been intercepted and deciphered. This is the improbable story of one of those WAVES.     

The Turing Bombe Victory and the first naval Enigma decrypts

Victory was the name of the first prototype Bombe that was developed for breaking the German Enigma messages of World War II. It lacked the diagonal board and simultaneous scanning that was provided for all the later models, but these disadvantages were overcome by the ingenious use of a column menu (a special Bombe menu where the Enigma fast rotors are all in the same position) to break six days of naval traffic, 22–27 April 1940, following the pinch of material from an armed trawler Schiff 26 (Polares). These were the first naval decrypts of the War, and their solution took several months to complete. No further naval breaks occurred until November. This article examines the decryption process in some detail in order to explain the difficulties, highlight the role of Victory in this process, and provide detailed workings of the processes. It also sheds some light on the early development of the British Bombe.     

Recovering the military Enigma using permutations—filling in the details of Rejewski's solution

During the last few months of 1932, the Polish mathematician Marian Rejewski solved the problem of finding the internal connections of the rotors and reflector of the Enigma cipher machine used by the German army at that time. This allowed the Polish Cipher Bureau to construct an analogue of the machine, and subsequently to find effective methods for deciphering secret messages. Rejewski performed this feat virtually alone using cryptographic material provided by the Polish secret services. His knowledge of the theory of permutation groups was essential in solving this problem.

This article describes in detail how to find the complete wiring of the rotors and reflector of Enigma, as well as other specifics, using data that Rejewski had at his disposal, by systematically presenting the resolution of all cases that could have been encountered. Similarly, we complete those stages of the procedure that were only outlined by Rejewski.     

DEVICES AND MACHINES

The third Britisher who, in addition to Alastair Denniston and Dillwyn Knox, met the Poles near Pyry in 1939 to to receive a copy of the Enigma machine has been wrongly identified as Stewart Menzies, head of the British foreign Intelligence service. In fact he was Humphrey Sandwith, head of the Admiralty's interception and direction-finding service.     

THE VERSATILITY OF REJEWSKI'S METHOD: SOLVING FOR THE WIRING OF THE SECOND ROTOR

We show that the recovery of the wiring of the second rotor of the Enigma does not depend on the rotors being reordered.