Links to Lanakis Classical Cryptography Course, Lectures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

 

By Randy Nichols (LANAKI)
President of the American Cryptogram Association from 1994-1996.
Executive Vice President from 1992-1994

 

 

CLASSICAL CRYPTOGRAPHY COURSE

 
BY LANAKI

 
March 10, 1996


 
Revision 1
COPYRIGHT 1996
ALL RIGHTS RESERVED
LECTURE 9
GERMAN REDUCTION CIPHERS

ENIGMA IN HISTORICAL AND MODERN TIMES

 


 

 

SUMMARY

 

In Lecture 9, we circumvent the schedule for another real treat - the ENIGMA cipher machine. Considering the focus of the 1995 ACA convention, several articles in CRYPTOLOGIA, a recent book by Robert Harris called Enigma, a Randomhouse challenge cipher contest based on the Enigma (won by several of the KREWE), many questions from my students, I thought we would address the subject of ENIGMA.

I have had the pleasure to work with ESSAYONS on a project in which we looked at the security of the original Enigma D machine in terms of 1995 technology improvements. ESSAYONS has brought to light some brilliant insights.

The ENIGMA 95 computer program cited in this lecture is available at the CDB. Contact NORTH DECODER for access, or click here: Enigma 95

Students have asked 1) what is Enigma and 2) where does Enigma fit into history of radio communications in WWII?

There are three pillars of radio-intelligence: direction finding, traffic analysis and deciphering. Direction finding equipment and technology is outside the scope of this course. Traffic analysis has been discussed in a previous lecture. We will quickly revisit its value and then follow Professor Jurgen Rohwer's analysis of the Atlantic Warfare to understand Enigma's position in cryptographic history. [ROHE]

The Enigma machine is actually a good starting point for my discussion on polygraphic and polyalphabetic cipher analysis (originally planned for Lecture 9). We start at the endpoint of a discussion and return to the beginning to build up the cryptanalytic tools to understand the cleverness of the ENIGMA. We will continue with the Friedman and MASTERTON in Lecture 10 and following. [MAST], [FR2], [FR3]

 

 

TRAFFIC ANALYSIS REVISITED

 

Recall that traffic analysis yields information via Crib messages, Isologs and Chatter. Crib messages assume a partial knowledge of the underlying plain text through recognition of the external characteristics. Command reports, up and down German channels, were especially easy for American crypees. The origin, serial number range, the cryptonet id, report type, the file date and time, message length and error messages in the clear, gave a clear picture of the German command process. German order of battle, troop dispositions and movements were deduced by traffic analysis.

An Isolog exists when the underlying plain text is encrypted in two different systems. They exist because of relay repetition requirements, book messages to multiple receivers or error by the code clerk. American crypees were particularly effective in obtaining intelligence from this method.

Traffic analysis boils down to finding the contact relationships among units, tracking their movements, building up the cryptonet authorities, capitalizing on lack of randomness in their structures, and exploiting book and relay cribs.

 

 

ENIGMA

 

ENIGMA was the generic term for the German machine ciphers. It was both the name of the first enciphering device and the many variations used during WWII. ULTRA was the British code-name for intelligence derived from cracking the Enigma machine ciphers by an organization of about 10,000 at Bletchley Park (BP). The extent of the penetration of the German command structure was so profound and so pervasive that it is clear that BP's work changed not only the conduct but the outcome of Allied European Operations in WWII. Most brilliant of ULTRA successes was against German Afrika Korps whereby the 8th Army HQ read Enigma telegrams before Rommel himself. [ASIR] [KAH2]

There now exists a fair amount of material on Enigma. The following annotated outline should give the reader some ideas how important Enigma was in WWII and sources of information:

 

ENIGMA CIPHER MACHINE(S)

 

 

A: HISTORY

A1: Historical Perspective - Atlantic Theater Warfare in Eight Phases 1939 - 1945.
Enigma was central to the Battle of the Atlantic in WWII. Primary sources for the historical perspective come from Germany, Canada, UK, and USA. Professor Jurgen Rohwer's Comparative Analysis of Allied and Axis Radio-Intelligence in the Battle of the Atlantic, [ROHE] presents the ENIGMA history in 8 phases:

 

     Phase 1 -  Single U-Boats vs Independent Ships
     9/39-6/40  Failure of BP on Schlussel M (Navy Machine)
     Phase 2 -  Wolf Pack vs Convoy
     7/40-5/41  Success of B-Dienst (German Naval decryption
                service)

     Phase 3 -  Evasive Routing, US Entry
     6/41-12/41 U-33 3 rotors recovered, U-110, Munchen
                Bombe limited success 336 settings
                German 4 rotor improvement

     Phase 4 -  BP Successes on Enigma D, US losses
     1/1-6/42

     Phase 5 -  Convoy Battles
     7/47-12/13 Triton Broken ; Rerouting; Milch runs

     Phase 6 -  Bay Offensive
     6/43-8/43

     Phase 7 -  Decreased Operations vs Convoys
     9/43-5/44  Increased use of Ultra

     Phase 8 -  Holding Campaign with Schnorkel U-boats
     6/44-end   New Enigma not released in time for Germany

Professor Rohwer presents 105 primary references. [ROHE]

A2. Discussion:
From September, 1939 to June 1940, German U-boats cruised west of the British Isles and Bay of Biscay to intercept Allied Merchant ships. U-boats found enough targets. Radio signals were as indispensable to the German Commander in Chief, U-boats (BdU = Befehlshaber der Unterseeboote - Commander in Chief of Submarines) for directing his U-boat groups or wolf packs as they were for Allied commanders directing the convoys of merchant ships and their escorts. The aim of the Axis powers was to sever the lines of communication by surface radars, aircraft and especially U-boats to attack ships in the convoys and thus sink more vessels and tonnage than the Allied shipbuilding yards could replace.

In the first two phases of the Battle of the Atlantic, there was a clear superiority with cryptanalytic success on the German side. Intelligence was of limited value to actual operations. The Germans introduced the short signal system, using a codebook to shorten communications to a few four letter groups which were superenciphered with daily settings of the Schlussel M [M Key] in the circuit of Heimische Gewasser (home waters). The Royal Navy used two crypto-systems - the first was the Naval Cypher which used 4 figure codebooks and the second was the 5 figure codebook Naval code. Both used subtractor tables of 5000 groups changed monthly. B-dienst was reading about 30 -50 % of the Naval Cypher, used by officers. The Merchant Navy Code was broken by the B-dienst in March 1940.

In the third phase BP mastered the Schlussel M-3 and saved about 400 ships by rerouting convoys. The Schlussel M-3 used three rotors out a stock of eight rotors. BP had limited no success against VI-VIII and limited success against rotors I-IV. The boarding of the Krebs gave the British a box of five rotors. A key to Enigma is its two inner settings, the Walzenlage, or rotor order, and the Ringstellung, the setting of the alphabet rings. In addition to these were the plugboard , the Steckerverbindungen, of ten pairs of letters and the Grundstellung, the starting positions of the rotors. The capture of U-110 gave BP a consistent set of settings and grid maps to reference. The British STR (Submarine Tracking Room) became key to rerouting ships valued at 1.5 mm GRT.

Phase 4 clearly went to the Germans because of their score of ships sunk off the Americas.

In Phase 5, near 1942, the BdU had many interceptions because the B-dienst decrypted the rerouting signals more effectively. Triton introduced and stumps BP. In March 1943, BP solves the Triton and Admiralty changes the operation patterns.

The six and seventh phases German cipher improvements broken by use of U. S. and British high speed Bombes.

Introduction of Kurier system for high speed transmissions to new U-boat type XXI was released to late to stop operation Overlord.

A3: Shipping Losses and Input Tonnage
Allied shipping losses were significant and import tonnage was reduced because of the U-boat success and communication. T. J. Runyan and Jan M. Copes "To Die Gallently" [RUNY] presents details.

A4. Enigma Chronology
David Kahn presents an Enigma chronology in terms of world events. A clearer picture of the effect of ULTRA can not be found. Timelines based on his and the honorable F. H. Hinsley books. [KAH2], [KAH3], [HINS] and [KAH3]

A5: British Perspective
The early history of the Enigma, the Polish attack and the beginnings of BP covered in [KAH3] ,[WINT] Winterbotham and Beesley give us special insights into the fray. [BEES] Other perspectives found in [ANTH] and [HYDE].

A6: Polish Perspective
The story of the Marian Rejewski, Jerzy Rozycki and Henryk Zygalski pioneering work in the Biuro Szyfrow (Cipher Bureau) and their escape to France is told in [ASIR].

 

B: SPECIFICATIONS

B1: Enigma Machine Classes A-E (Deavours)
Enigma was a class of machines. Cipher A. Deavours and Louis Kruh, in Chapter III of "Machine Cryptography and Modern Cryptanalysis", give detailed descriptions with pictures, rotor order, settings, plug-board and their influence on frequency distribution. [DEVO]

B2: Enigma - 3 rotor (Kahn)
David Kahn in his "Seizing the Enigma" ,pp 178 ff gives good detail. Also "Codebreakers" p422. , also various articles by Kahn in Cryptologia give pictorials. [KAH3] [KAHN]

B3: Army Enigma - 3 rotor (Hinsley)
F.H. Hinsley and Alan Strip in "Codebreakers - Story of Bletchley Park", [HINS] have pictures and supporting detail for the Army version 3 rotor device.

B4: Early Variations - (Friedman)
NSA's Friedman Legacy - A Tribute to William and Elizabeth Friedman, 1992, pp 201 ff discusses the early Enigma variants. [FL]

B5: Naval Variation - Air Ministry (3 of 8 rotors)
See Ref's [ASIR]

B6: Air Force Variation - 3 rotor of five (British Air Ministry)
See section B3.

B7: University of Hamburg - WWW : Enigma pictures
Dr. Klaus Brunnstein (University of Hamburg) has provided excellent GIF Enigma pictures in their Working Groups "museum":

     Address: http://www.informatik.uni-hamburg.de
     Select "international homepage"

     From 2nd entry "groups", select AGN
     (first of the working groups)

     There, select "Museum" (4th entry) where you get a
     list of about 40 pictures.   
     
     The CDB has these also.

C: PATENTS

C1: General - (Levine)
Jack Levine presents the most comprehensive treatment of U.S. Cryptographic Patents 1861-1981 in [LEVI].

C2: Scherbius #1,657,411 [LAUE] [Geheimschrijfmachine] 1919
Rudolph F Lauer discusses the original A. Scherbius Enigma patent # 1657411 in his "Computer Simulation of Classical Substitution Cryptographic Systems" in [LAUE]. This machine was used for diplomatic communications and had ten rotors. BP broke it late in the game using the Colossus machines.

C3: Herbern # 1,683,072 [Electric Code Machine], 1917
Reference [ASIR] gives an interesting account of Herbern's efforts.

 

D: ENCIPHERING PROCESS

D1: Naval Enigma (Kahn)
David Kahn in his "Seizing the Enigma" Appendix presents a detailed Enciphering procedure for the Naval Enigma. Approximately 20 pages of notes, biblio, interviews and diagrams. [KAH3]

D2: ESSAYONS and LANAKI present modern PC technology applied to encipherment process in [ENIG].

 

E: CRYPTANALYSIS

E1: BP Analysis (Turing)
Cryptanalysis of the various Enigma variants starts with Alan Turing "The Enigma", in [ALAN]

E2: Polish Attack (Rejewski)
Perhaps the earliest and best attack, Marian Rejewski wrote the brilliant "Mathematical Solution of the Enigma Cipher" published in [REJE].

E3: Double Encipherment Flaw (Bloch)
Gilbert Bloch and Ralph Erskine exploit the double encipherment flaw in article on Enigma, in Cryptologia. [BLOC]

E4: Lauer Analysis of Classical Systems & (Deavours)
Rudolph F. Lauer presents Cipher A Deavours simulation program p73 ff in reference [LAUE]. Deavour's program reveals the German Army cipher machine simulated consisted of three rotors (of eight), rings settings, plugboard (for key super - encipherment, rotor starting positions and a reflecting rotor. The program requires the user to set "prepare the machine" by setting the rotor wirings, rotor order, rotor starting position, ringsettings, plugboard pairs and no of plugs used and the current rotor positions. It calculates the patchpanel, dis- placements of cylinder coding and effects of reverse rotors, and reflecting rotor. There are no error checks for singularity.

Lauer also presents ten cryptographic systems and representative cipher machines in increasing order of difficulty. He presents 72 references (including the Cipher A. Deavours simulations) on disk. Each system is not only simulated but the principles for the entire class of machines are presented. Ignoring the programming language, BASIC ( I would choose FORTRAN, others would choose C, and others APL, and others ADA and..); the methods applicable to one machine apply equally well to others in the same class.

I have rearranged his classification methodology and added my own thoughts to show how ENIGMA fits into the progression of classical cryptographic / mechanical systems:

 


    E40: Mathematical Footholds
         a: Modulo 26 Arithmetic, Congruences, Matrices
         b: Statistical Phi values for small distributions
         c: Isomorphism - reference [CAND]
         d: Optimization Theory
         e: Advanced Calculus, Linear Transformations
         f: Probability Theory

    E41: Simple Substitution - Cipher Disk  {My Lectures 1-8 }
         Principles: monosubstitution, K1,K2,K3,K4, KM sequence
         keying, transpositional keys.

         Examples: Aristocrats, Patristocrats, Xenocrypts
         Caesar, sliding strips, rotating disks

         Attacks: Frequency analysis, word pattern, bigram,
         trigram, vowel spotting, letter distribution.

    E42: Periodic Polyalphabetic Substitution - Viggy Devices
    {My Lectures 10-13}

         Principles: poly-alpha-substitution, repeat key
          sequence

         Examples: Vigenere, Variant, Beaufort, Porta, Gronsfeld

         Attack: Periodicity, Kasiski, trigraphic, traffic
         analysis, Kerckhoff's method.

    E43: Running Key and Autokey - Kammel and Weller Devices

         Principles: polyalphasubstitution, non-repeat key
         sequence, PT autokey, CT autokey and running key

         Examples: Running key and autokey ciphers

         Attack: Friedman attack - "Solution of Running Key
         Ciphers, probable word, known plain text.

    E44: Simple Progressive

         Principles: constant shift interval to employ all
         secondary alphabets (period = 26)

         Examples: Progressive Cipher

         Attacks: Friedman attacks, periodicity at 26,13,2,1
         same as E42, Chi test, matching frequency
         distributions, decimation intervals, coherent key

    E45: Irregular - KRYHA

         Principles: irregular shifting of primary components
         non coherent key, non recognizable key, long key
         derived from two or more short keys, pseudo-random
         different interval shifts on progressive; sum of shifts
         be relatively prime to N in alphabet

         Examples: One time pad, Vernam Key Tape

         Attacks: Sacco's solution, Isomorphism, Friedmans
         technique

    E46: Wheatstone Cryptograph

         Principles: Aperiodic cipher, extra sequence shift,
         error control

         Examples: Jefferson, Hebern machine, Vernam

         Attack: Friedmans techniques [FR4] probable phrase

    E47: Multiplex Systems

         Principles: Wheel ciphers

         Examples: Jefferson, M-138, M-94

         Attack: Friedman techniques, De Viaris examination,
         synoptic tables, G. Mellen attack, Rohrbach method
         coincidences - generatrices group

    E48: HAGELIN M-209

         Principles: pin lug mechanism, cylindrical cage, guide
         arm - print wheel rotates number of positions = sum of
         the lugs on those key wheels which were affected by
         active pins.  ==> key value with period of 3,120,180
         letters.

         Examples: C-36, M-209

         Attack: Wayne Barker analysis one wheel to six wheels,
         statistical analysis on settings, probable word

    E49: ENIGMA

         Principles: electrical rotor or transfer wheel,
         stepping gears, maze between keyboard and indicating
         device  producing 26 ** N different enciphering
         alphabets, re-entrance phenomenon, excess contacts.
         superencipherment

         Examples: ENIGMA A-E

         Attacks: Polish, BP, Turing, Deavours, Friedman IC,
         E1-E8 previously cited, Chi test on diagonals,
         isomorphs, Pohlig w/ PT, Konheim analysis, Lisicki
         Grille 1000x1000 rearrangements

         Modern Experiments: Remove reflecting rotor.
                             Use re-entrance type rotor
         [ ACA and           Install bi-directional Rotors
           University of     Increase entropy
           Hamburg ]         Expand character sets


    E410: HILL SYSTEM  {NORTH DECODER in Lecture 8}

         Principles: Polygraphic encipherment, non - linear
         encipherment == forerunner of "S" boxes in DES

         Examples: Playfair, Hill Device

         Attacks: Konheim technique, Rhee analysis, Mapping,

E5: Polish attacks (Kozaczuk)
Dr. Wladyslaw Kozaczuk discusses the Polish attacks on Enigma in [KOZA]

E6: Involution Principle (Konheim)
Involution principles are presented by Alan G. Konheim, "Cryptography -A Primer" , in [KONH]

E7: Related Machines (Barker)
Wayne G. Barker presents a related analysis in "Cryptanalysis of the Hagelin Cryptograph, in [BARK].

E8: Enigma 3 (Sassoons )
A clever treatment of the Enigma 3 wheel device can be found in George Sassoons, "Radio Hackers Code Book", [SASS]

E9: Tieman C (Schneier)
Bruce Schneier, in his "Applied Cryptography', presents Tieman's C program. [SCH1]

 

F: ROTOR SYSTEMS

F1: Theory (Konheim)
The general theory of rotor systems is well presented in chapter 5 of Konheim's primer. [KONH]

F2: Polish Solution
The brilliance of Marian Rejewski solution is presented in "The Mathematical Solution of the Enigma Cipher " in [REJE]

F3: Computer Crypto and Probability Analysis [A German View]
Norbert Ryska and Siegfried Herda give a fresh look at computer techniques required for Cryptography. From a German point of view, it gives the reader a look at security risks, and crypto- methodology. [RYSK]

 

G: ENIGMA IMPROVEMENTS

G1: Code Changes (Sassoon)
Sassoon suggests improvements to Enigma by using full ASCII set of 256. Sequence length 256 x x 256. Rotor settings in blocks of 256 8-bit bytes one to define the position of each rotor. Sassoon's Basic Enigma3 simulation 4 rotors and a reflector rotor. It simulates the movement towards the reflector or away from it. Rotor cross connections are well defined. Subroutines to test the encryption and decryption are included. Clear rotor advancement routines. Error checking subs as well. No plugboard. [SASS]

G2: Improved Security (ESSAYONS and LANAKI)
Clarence Tyner Jr. has spent significant time since 1944 on German cipher production and reduction efforts. Starting with a Model D (circa 1920's) Tyner simulated the original Enigma with wartime enhancements (plugboard, expanded rotor sets, etc.) and then improved it while staying within the original concepts of the original machine (keyboard input, data path through a plugboard, rotating rotors, reflecting rotors, and output display. Presented in detail later in this lecture.

 

H: ORGANIZATIONS (Kahn) (ASI)

 

   H1:BP
   H2:OSS
   H3:German Navy - U Boat Command
   H4:B-Dienst
   H5:Bureau De Chiffer
   H6:Polish Biuro Szyfrow
   H7:French Service Renseignements
   H8:AVA Telecomunications
   H9:German Army Command
   H10:SOE
   H11:RAF-SLU
   H12:Siemans und Halske Aktiengesellschaft
   H13:AC Bridge Laboratory
David Kahn in his books "Seizing Enigma", "Codebreakers" , "Kahn on Codes" and "Hitlers Spies" presents the various people and organizations surrounding Enigma. Also the British Air Scientific Institute, chap 6 describes the relevance of each organization in the cracking of Enigma. [ASIR] [KAH1] [KAH2] [KAHN]

 

 

ENIGMA 95

 

A simulation of an enhanced Enigma Cipher Machine on a standard personal computer:
 

          Clarence E. Tyner Jr. and Randall K. Nichols
          ADDRESS : 11322 Carrollwood Drive, Tampa, Florida, 33618, USA.
          5953 Long Creek Drive, Corpus Christi, Texas, 78414, USA

ABSTRACT:

An exploration into the possibilities of what can be done with the operating methods of the Enigma on the personal computer. The same concept of employing keyboard input, a plugboard, rotors ( both normal and reflecting ), Uhr box and visual output are used, but are expanded by using 100-position rotors that intermittently rotate a prime amount after each input, allowing the number of rotors to vary from 1 to 12, in front or backwards orientation, top permit any keyboard character ( including spaces ) to be encrypted, and to simultaneously display cipher and clear text for editing. A rotating Character Set converts single-character input into 2-digit numbers for processing and superencipherment of numeric output into alpha bigrams is possible. Regular rotors, Reversing rotors, Character Sets and Superencipherment Tables are provided in sets of 100 for extensive variety. Visual monitor display and paper printout are employed and other controls are provided. It is a "what if" speculation that shows what could have been possible if the technology had been available.

 

KEYWORDS:

Enigma, prime numbers, rotors, intermittent rotation, superencipherment, personal computer, QBasic, interval method, character set, random numbers, checksum, plugboard, orientation, internal settings, external settings.

Everyone is familiar with the Enigma Cipher Machine and the way it operates.

However, the more you learn about it and read about the cryptanalysis that overcame it in World War II, the more you wonder if it could be improved without becoming impossibly complicated. The personal computer provides a means to improve the concepts that made the original Enigma work, and it can make it work much better.

This project started as a simulation of the original Enigma. The pathway of the electric circuit caused by pressing a key is easy to understand. It goes from the keyboard through the plugboard to the rotors, is reflected from the reversing rotor, back through the rotors, through the plugboard and finally to a lamp that lights under a round window with an alphabet on it. At least one rotor will rotate during the pressing of the key and the pathway through the rotors will change from what it was previously. The internal wiring of the rotors is random and the cumulative circuit offset combinations produce an extensive number of substitution alphabets. The plugboard adds to this, as did the Uhr box.

Aside from administrative and operator errors, the weaknesses of the enigma were as follows:
 

   1.  The internal wiring of the rotors was fixed.  It never changed except for
       a few specialized purposes.   While the mathematical possibilities were
       astronomical, only a small portion of them were utilized probably because of
       manufacturing, cost and logistics considerations.

   2.  There were only eight rotors in a set and only 3 or 4 could be used at a
       time.

   3.  The rotors rotated only very restricted basis.  One moved one position
       each time.  The second moved only after the first had moved 1 to 26 positions.
       The 3rd moved only after the 2nd had moved 1 to 26 positions.  There were
       notches on the rotors to accomplish this and the rotors could be set so that 
       the movements occurred at different times, but movement of two rotors was 
       infrequent, and movement of all rotors was limited and somewhat predictable.

   4.  The reversing ( reflecting ) rotor did not move, nor could it be moved (
       except on the earlier models ).

   5.  A subtle weakness was that a given letter could never be encrypted as
       itself.

   6.  It was expensive and labor-intensive both to manufacture and to operate.
       Once it had been determined how to simulate the rotation of rotors and to
       simulate the transfer of the electrical current between rotors correctly,
       a major problem was solved.  Then it was necessary to determine how to 
       keep the internal wiring connections unchanged during rotation.  This 
       was followed by developing a method of selecting and installing the 
       rotors at a given position and then how to rotate them to an initial 
       setting.   Having an old Model D Enigma ( 3 rotor ) so that it was 
       possible to determine what the outcome should be was helpful.
Creation of rotors presented a challenge in establishing the internal wiring and in making a set from which to choose three. Edward H. Hebern used the Interval Method of wiring his rotors, so it was decided to use that approach. For those who are not familiar with it, it involves determining the positional difference (interval ) between points connected on opposite faces of the rotor. For a 26 ( A - Z ) position rotor, the intervals range from 0 to 25, with each interval being used only once. But the geometry of the problem prevents one interval from being used and requires one interval to be used twice. All intervals are measured in the same direction. For example, a connection from point A on one face to point C on the other has an interval of 2 ( assuming opposite positions are identified with the same letter ).

I don't know how Mr. Hebern did it, but it is a job perfectly suited for a computer. At any rate, "wiring" a rotor using the Interval Method can be very tedious because it involves a lot of trial and error if done manually (or, as it turned out, by computer ). It would be interesting to know if there is a simple algorithm. It is supposed to produce a more secure encryption. After trying to do it manually ( by diagramming on paper ), programs were written to do it for both regular and reversing rotors. The programs also produce a file on a floppy disk to simulate a set of rotors and print the results for record purposes. Each rotor had to be unique from all others so use of random numbers was involved.

The plugboard was programmed so that it was possible to enter the 2-point (from -to ) sets that were to be connected. Multiple sets could be created, just as it is possible to have multiple cable connections on a mechanical Enigma. A file of plugboards is not needed because the variance within fixed fields is derived from the connections, and to allow numbers of connections to be varied. It was necessary though to provide for editing to insure that each position was used only once ( as in real life ).

At this point, the idea of expanding the Enigma came into being in the form of introducing variability between the keyboard and the plugboard such as the Uhr Box does. It was decided to make the Enigma process the data in numerical form and expand it from a 26 to a 100 character format. This numerical format (00 -99) has the disadvantage of doubling the length of a message, but it has certain advantages. In addition to handling alphabetic letters, it can also:

   1.  Allow upper/lower cases, numbers, symbols, punctuations, and spaces to be
       encrypted.
   2.  Better conceal the language and individual characters being transmitted.
   3.  Eliminate the problem of a letter not being encrypted as itself.
   4.  Allow a longer period between repetitions.
   5.  Permit superencipherment.
   6.  Provide 100-position rotors and plugboard which are more difficult to
       analyze.
   7.  Facilitate masking control elements in messages. ( e.g., rotor settings,
       etc. )
This format required a method of converting input into 2-digit form. It was done by creating what are called "Character Sets". These are randomly organized sets of 100 characters ( upper and lowercase ) that appear on the keyboard. The entire 100 positions are not used and the unused are filled with a seldom-used accent mark. One hundred sets are available in a file on floppy disk. The sets are used in both encryption and decryption to convert from and back to cleartext.

Using 100 as a common feature, brought into use the digits 00 - 99 to identify rotors, sets, tables and plugboard positions. Sets of these components have 100 of each ( "00" means "100" ).

The next feature was to provide for the unique rotation or non-rotation (movement of each rotor is randomly intermittent ) of each regular and the reversing rotor after each input. The Character Set also rotates so that doubles (like "oo" in book ) are converted differently. Rotation is by a prime amount to 100 (2 and 5 are not used ). Editing prevents using other numbers. An additional feature was to provide a Rotor Display similar to the windows on the Enigma. This is primarily informational but has proven to be helpful in de-bugging the program...and it does provide a sense of rotor movement.

Another idea was borrowed from Mr. Hebern. That was the ability to "insert" rotors into the machine either forwards or backwards which doubles the number of rotors in a given set. It was also possible to provide for a variable number of rotors. An arbitrary limit of 12 was chosen but it would be possible to have more (though that might be considered overkill ). The important thing here is that it would be possible to employ from 1 to 12 rotors ( from a set of 100 ), depending on the security desired. The rotor display automatically adjusts to the selected number.

The next feature that was added was the ability to optionally superencipher the resulting numeric ciphertext. This involves replacing a 2-digit numeric cipher with a 2-character alphabetic bigram (e.g., 36 to HK ). It also permits each numeric cipher to be represented by one of 6 or 7 bigrams (e.g., 36 could be HK, UM, RY, AU, ZM or BI ). The 7th bigram appears only for selected numerics because the 676 (26 x 26) possible bigrams are evenly distributed amongst the 100 numerics. In addition, the use of a given bigram in a set for each numeric is incremented sequentially so using this example, the numeric "36" would be converted to HK the first time it appears, to UM the second time, etc. The first selection can start at any of the first 6 positions and it cycles around to position 1 when position 6 or 7 is used. A SuperEnciphering Table (Figure 18) accomplishes this and there is a matching SuperDeciphering Table ( Figure 19 ) to reverse it.

Text input requires no use of the key and the computer buffer handles rapid input so that the entry of clear or cipher text is faster than that of the original Enigma. Input is displayed on the monitor and the resulting cipher/clear text is displayed immediately below so that it is possible to visually check it. If an error occurs, a simple procedure allows you to correct it without having to re-type everything. A screenful of data consists of 6 sets of double lines ( one input, one output ) double spaced with the sets separated by a dotted line for clarity. There are 27 inputs per line for a total of 162. When the 159th - 161st are entered, a beep sounds to alert you to the approaching end of a screen. This allows you to make a final check of the input for errors (and easily correct them) before entering the 162nd which triggers printing that screenful to paper. During the printing you can start entering the next screenful. A limit of 1943 inputs ( 12 screenfuls less 1 ) was arbitrarily chosen for demonstration purposes (more would be possible, depending on memory available). This limit can be easily set to a shorter value to control message length to make cryptanalysis more difficult.

Printing is considered essential for the purpose of having a record of what was sent and how it was encrypted or decrypted ( e.g., was the cleartext entered correctly and was the machine correctly set ? ). It also eliminates the need for a second person to transcribe the output. Attached are four exhibits that are examples of the printouts that can be produced:
 

         Exhibit A : Encryption into numeric form
         Exhibit B : Decryption of Exhibit A
         Exhibit C : Encryption in Superenciphered Form
         Exhibit D : Decryption of Exhibit C
Each exhibit is divided into the following parts:
         1.  The Heading:  This indicates whether it is encryption or
             decryption,
             and the date and time that the settings were entered .  
             This does not change for repeated use of the settings 
             for two or more consecutive messages.  To enter a
             new date/time group or change the internal settings, 
             the program must be completely restarted.  
             (See A1, B1, C1 or D1 )

         2.  The Internal Control Settings:  This indicates the number
             of plugboard connections used, the specific plugboard 
             connections, the number of rotors used, the specific rotor
             numbers in the position sequence and then each rotors 
             orientation (frontwards or backwards).  The reversing 
             rotor number is indicated.  Next, the unique rotation 
             value for each rotor and the reversing rotor are shown, 
             followed by the character set number and its rotation value.
             These constitute the internal settings that would be 
             specified by the Signal Operating Instructions ( SOI ).  
             All of these settings generate an Internal Checksum which
             is used to verify that the settings have been correctly
             entered.

             This checksum is printed.  If it does not agree with that
             provided in the SOI, then all the settings must be 
             re-entered by restarting the program. Intermittent
             rotation of each rotor is a function of the installed 
             rotors and previous entries and does not have to be 
             specified.

         3.  The External Control Settings:  This lists the settings 
             that the operator selects and enters for the specific 
             message.  They consist of the Initial Settings of each
             rotor and optionally the Superencipherment Table number 
             if it is used.  These settings add to the Internal Checksum 
             and produce an External Checksum in the form of a 2-digit
             number ( mod-100 of the total sum ) that is sent with 
             the message.  The superencipherment table counter setting
             is NOT included and is NOT sent because the recipient 
             does not have to know it. 
             (See A1, B1, C1, D1)

        4.  The Input / Output Message Text:  This duplicates that 
            which appears on the monitor screen and is provided 
            primarily for a message audit ( to insure that the message
            was entered correctly ).  Each "line" has 27 inputs with 
            the 27 outputs below.  Twenty-seven was used to provide
            legibility on an 80-column screen. Six such "lines" 
            are possible for each screenful.  
            (See A1, B1, C1 or D1)

        5.  The Message Control Data:  A count of the input characters
            (message length ) is provided for both superenciphered and
            non-superenciphered messages.
However, only non-superenciphered (numeric ciphertext) messages have the following additional data provided:

 

             a.   A Hash Total which is a Mod-100 sum of the numeric 
                  cipher text.
                  ( See A1, B1)

             b.   A set of Column Check Totals which is the Mod-100
                  sum of each of the 27 columns of cipher text.  
                  This is followed by a non-mod total of the columns. 
                  (See A2, A3, B2)

             c.   A total of Row Check Totals which is the Mod-100
                  sum of each row of cipher text. This is followed 
                  by a non-mod total of the rows.  (See A2,A3,B2)
The purpose of providing column and row totals is to be able to locate transmission garbles. They would be sent only if requested. Variances in any given column and row would locate the error by intersection.
       6.  The Message in Transmission Form:  This is what would be sent 
           and would contain only the External Control Settings (rotor 
           settings, superencipherment table number and external checksum), 
           the date and time group, the message ciphertext and the character
           count.  The External Control Settings would be disguised by a 
           simple manual superencipherment that would be administrative and
           outside the operation of the Enigma 95 ( i.e., prescribed by 
           the SOI ).  (See A3, C2 )  If it is decryption, the cleartext
           message is presented with normal
           horizontal spacing and vertically double spaced for convenient 
           reading.  
           (See B3, D2)

       7.  Following this is an optional message analysis which is simply a
           count of input and output characters.  This can be skipped and 
           was provided only to assist any system analysis.
           (See A4 and C3)
This completes the printing.

Next displayed on the monitor is an option to re-use the Internal Control Settings for another message ( it was assumed that these would remain in effect for a period of time as was the case for the Enigma ). If this is not selected, the program ends.

 

 

HARDWARE AND SOFTWARE REQUIREMENTS

 

The Enigma 95 is a program written in Microsoft QBasic. This was done so that it could be run on any standard MS DOS computer using MS DOS 5 or higher ( QBasic is bundled with MS DOS ) thereby eliminating the need for a specialized computer. It fits onto a 3.5 inch floppy disc, together with the necessary data files that constitute the Regular Rotors Set, Reversing Rotors Set, Character Sets and Superencipherment Tables. It is possible to also have on the same disk, the programs that create these files and the necessary documentation ( .DOC ) text files for each one. This makes the Enigma 95 very portable, very inexpensive and very easy to replicate.

Any computer that will run MS DOS QBasic is suitable for the Enigma 95. A color monitor is preferred but not essential. A printer is very useful, but could be eliminated if one is willing to copy output manually from the monitor screen ( as the original Enigma required ).

There is provided a program that produces a graphic representation of the circuit path through the Enigma 95 and a program to produce pseudo-random numbers to use in programs that produce the rotor disks. Also included are programs to analyze the Enigma 95.

 

 

OPERATIONAL OVERVIEW OF THE ENIGMA 95

 

The following is a run-through of the operating procedure, with the appropriate illustrations of the monitor screen at each meaningful step.

 

1.  The computer is turned on, QBasic is selected and the Enigma95 program is
    loaded and run.

2.  You are asked to place the data files disk in the Drive B so that they will
    be available.

3.  You are then asked to enter the Internal Control Settings:
        a.  Number of Plugboard Settings (1 to 50).  45 is optimum.
        b.  The plugboard settings (from and to)         (Figure 1)

SOI : ENTER THE NUMBER OF PLUGBOARD CONNECTIONS TO SET : 21 SET 1 : 1735 SET 11 : 2653 SET 21 : SET 2 : 2356 SET 12 : 4899 SET 3 : 4581 SET 13 : 6250 SET 4 : 9852 SET 14 : 4069 SET 5 : 3377 SET 15 : 3180 SET 6 : 5544 SET 16 : 9402 SET 7 : 6612 SET 17 : 8437 SET 8 : 5987 SET 18 : 9307 SET 9 : 3254 SET 19 : 8843 SET 10 : 6791 SET 20 : 8514
Plugboard Positions not yet selected 01 03 04 05 06 08 09 10 11 13 15 16 18 19 20 21 22 24 25 27 28 29 30 34 36 38 39 41 42 46 47 49 51 57 58 60 61 63 64 65 68 70 71 72 73 74 75 76 78 79 82 83 86 89 90 92 95 96 97 00 Figure 1 c. Number of rotors to be used ( 1 to 12 ) d. The rotor number ( 1 to 100 ) for each position and its orientation ( 1=Fwd,2 = Bkwd ) e. The reversing rotor number ( 1 to 100 ) Figure 2 12 ROTORS ARE TO BE SELECTED FROM THE S.O.I. Select Rotor ( 1 to 100 ) and Orientation ( 1 or 2 ) IN THE SAME ENTRY For example : < RO > or < RRO > or < RRRO > < 71 > < 232 > < 1001 > ROTOR ORIENTATION Position No. 1 32 1 - Forward Position No. 2 49 2 - Backward Position No. 3 42 1 - Forward Position No. 4 98 1 - Forward Position No. 5 63 2 - Backward Position No. 6 94 2 - Backward Position No. 7 62 1 - Forward Position No. 9 4 1 - Forward Position No. 10 33 2 - Backward Position No. 11 25 1 - Forward Position No. 12 11 1 - Forward ENTER REVERSING ROTOR NUMBER (1 TO 100): 53 Figure 2 f. The rotational shift value for each rotor ( a prime number between 0 and 97 inclusive less 2 and 5 ) Figure 3 (See the current S.O.I. for the values to use) SET ROTATIONAL SHIFT VALUES FOR EACH ROTOR POSITION USING THE FOLLOWING PRIME NUMBERS (EACH ONLY ONCE) 0,1,3,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 FOR ROTOR POSITION 1 : 07 FOR ROTOR POSITION 2 : 29 FOR ROTOR POSITION 3 : 01 FOR ROTOR POSITION 4 : 71 FOR ROTOR POSITION 5 : 17 FOR ROTOR POSITION 6 : 13 FOR ROTOR POSITION 7 : 11 FOR ROTOR POSITION 8 : 47 FOR ROTOR POSITION 9 : 03 FOR ROTOR POSITION 10 : 61 FOR ROTOR POSITION 11 : 23 FOR ROTOR POSITION 12 : 19 FOR REVERSING ROTOR : 31 Figure 3 g. The Character Set number ( 1 to 100 ) ( Figure 4 ) ( See S.O.I. ) ENTER CHARACTER SET NUMBER : 44 Figure 4 h. The rotational value for the character set ( the same range as f. above ). (Figure 5 ) ( See the current S.O.I. for the values to use ) SET ROTATIONAL SHIFT VALUE FOR THE CHARACTER SET USING ONE OF THE FOLLOWING PRIME NUMBERS NOT USED FOR THE ROTORS 0,1,3,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 ROTATIONAL VALUE : 89 Figure 5 4. You are then asked: DO YOU WANT TO (1) ENCIPHER OR (2) DECIPHER? a. Assuming that ( 1 ) is selected, a "random number" generator is presented to select numbers for use as Internal Settings. b. This is a sort of "spin the arrow" device to prevent bad selection of settings but any source of random numbers may be used. It is optional. It is skipped if (2) is selected. 5. The Internal Checksum is displayed and then you are asked for the External Control Settings: a. Initial settings for the regular rotors ( 1 to 100 ). b. Initial setting for the reversing rotor ( 1 to 100 ). ( Figure 6 ) Internal Checksum = 60354 ( See your list ) SET INITIAL ROTOR SETTINGS ( 1 TO 100 ) ROTOR 1 : 15 ROTOR 2 : 22 ROTOR 3 : 09 ROTOR 4 : 41 ROTOR 5 : 87 ROTOR 6 : 36 ROTOR 7 : 08 ROTOR 8 : 01 ROTOR 9 : 57 ROTOR 10 : 91 ROTOR 11 : 03 ROTOR 12 : 49 REVERSING ROTOR : 77 Figure 6 c. The Superencipherment Table number ( 1 to 100 ) if used, and d. The initial setting of the superencipherment table counter (1 to 6). Figure 7 (See your list) ENTER SUPERENCIPHERMENT TABLE NUMBER : 35 SET INITIAL COUNT ( 1 TO 6 ) : 4 Figure 7 6. The opening screen for beginning the message entry appears with: ( Figure 8 ) a. The External Checksum. b. Instructions for starting and stopping text entry and making corrections. ENTERNAL CHECKSUM = 99 To stop operations and : 1. Print text : Press \ 2. Correct input : Press Shift & | Press ENTER key to start - or - to make the next screen Figure 8 7. After pressing , a blank screen will appear with the initial Rotor Display at the bottom and START ENTERING MESSAGE will appear in the middle of the screen. Figure 9 START ENTERING MESSAGE Rotor Display 15 22 09 41 87 36 08 01 57 91 03 49 77 Figure 9 8. At this point you can start entering text and see it appear on the monitor,starting at the upper left corner, and filling left to right. The input and its related output will appear simultaneously. At the bottom of the screen,above the rotor display, are instructions for ending the input and for making corrections to the input. There is also a count of input at the right corner. Figure 10 F O U R S C O R E A N D S E V E N Y E A R S A FM VQ ND OU UF OF EN MX FE ZR DO YD BS YW VO RB BB HC QI UR ZD BW BZ TQ EO WD RF G O , O U R F FW DP JA XW QN ZX OT DA WX Enter '\' to end message. Press 'Shift |' to make correction. Input No. 36 Rotor Display 41 73 31 61 44 79 62 00 11 72 25 67 04 Figure 10
 
Below is a listing ( in columns 4 through 16 ) of the 13 Rotor Display windows of the above 36 inputs, to show the intermittent movement of the rotors. See Figures 11and 12.
      Col. 1 is the Input No.
      Col. 2 is the cleartext input.
      Col. 3 is the Character Set conversion of the cleartext.
      Cols. 4 - 15 are the Regular Rotor displays.
      Col. 16 is the Reversing Rotor display.
      Col. 17 is the numeric cipher output.
      Col. 18 is the superenciphered output.
When numbers are repeated in a rotor column, this indicates that the rotor did not rotate after that specific input. When rotation does occur, it rotates the amount previously set for that rotor. This illustration is not part of the regular operating display. It was used only as a test and to illustrate intermittent movement.

 

         Start       15  22  09  41  87  36  08  01  57  91  03  49   77
                     --  --  --  --  --  --  --  --  --  --  --  --   --
         1  F  87    15  51  10  12  87  49  19  48  60  52  03  68   08    52
 FM
         2  O  26    15  51  11  83  87  49  19  48  63  52  03  68   39    18
 VQ
         3  U  64    15  51  12  54  04  62  19  48  66  52  03  68   70    06
 ND
         4  R  57    15  51  13  54  21  62  30  48  69  13  26  87   01    15
 OU
         5  S  79    22  80  14  25  21  62  30  95  69  13  26  06   32    03
 UF
         6  C  10    29  09  15  96  21  75  41  42  69  74  49  06   32    64
 OF
         7  O  81    29  09  15  96  38  75  41  42  69  35  49  06   32    69
 EN
         8  R  01    36  38  15  67  38  75  52  42  69  35  72  25   32    03
 MX
         9  E  65    36  38  15  38  38  75  63  42  72  96  72  44   32    92
 FE
        10     06    43  67  16  09  55  88  74  89  75  96  72  63   32    37
 ZR
        11  A  20    50  67  16  80  72  88  74  89  78  57  72  82   63    53
 DO
        12  N  12    50  96  16  80  89  88  85  89  81  18  95  01   94    34
 YD
        13  D  61    57  25  17  80  89  88  85  89  81  79  18  01   94    46
 BS
        14     50    57  25  18  51  06  88  96  89  81  79  18  20   94    93
 YW
        15  S  89    64  25  18  51  06  01  96  36  84  79  18  39   25    42
 VO
        16  E  42    64  54  19  22  23  14  96  36  84  40  18  39   25    65
 RB
        17  V  71    64  83  20  22  23  27  96  36  84  01  41  58   25    13
 BB
        18  E  64    64  83  21  93  40  40  96  83  84  62  64  77   56    66
 HC
        19  N  89    64  83  21  93  57  40  96  83  87  62  87  77   56    53
 QI
        20     16    71  12  22  64  57  53  07  30  87  62  10  96   56    20
 UR
        21  Y  84    71  12  22  64  74  53  07  30  90  23  10  15   56    60
 ZD
        22  E   8    78  12  22  35  91  66  07  77  93  23  10  34   56    93
 BW
        23  A  52    78  12  23  06  08  66  07  77  96  84  10  53   56    80
 BZ
        24  R  77    85  41  24  06  25  66  07  24  96  84  10  72   87    39
 TQ
        25  S  99    92  41  25  06  42  66  18  71  96  84  10  91   18    55
 EO
        26     82    92  70  25  06  59  66  29  18  96  84  33  10   18    20
 WD
        27  A  96    92  99  25  77  59  66  29  18  96  45  33  10   49    92
 RF
        28  G  65    99  99  26  77  76  66  29  65  99  06  33  29   49    01
 FW
        29  O  23    99  28  26  77  76  66  40  12  02  67  33  48   49    01
 DP
        30  '  36    06  57  27  77  93  66  40  59  05  28  56  67   80    65
 JA
        31     37    13  86  27  48  10  66  40  59  05  89  79  67   11    59
 XW
        32  O  56    20  15  28  19  10  66  40  06  08  50  79  67   11    18
 QN
        33  U  94    27  15  28  19  27  66  40  06  08  50  02  67   11    38
 ZX
        34  R  87    34  44  29  90  27  79  40  53  11  50  02  67   42    34
 OT
        35     81    34  44  30  61  27  79  51  53  11  11  02  67   73    28
 DA
        36  F  72    41  73  31  61  44  79  62  00  11  72  25  67   04    17
 WX 
								
Figure 11 - 13 - Figure 12 is the same as Figure 11 except that the repeated numbers in each column have been replaced by a [] to indicate no movement to emphasize the irregular movement of each rotor.

 

         Rotor No.   01  02  03  04  05  06  07  08  09  10  11  12   RR
Rotation     7  29   1  71  17  13  11  47   3  61  23  19   31

Start Posn  15  22  09  41  87  36  08  01  57  91  03  49   77

                     --  --  --  --  --  --  --  --  --  --  --  --   --
         1  F  87    []  51  10  12  []  49  19  48  60  52  []  68   08    52
 FM
         2  O  26    []  []  11  83  []  []  []  []  63  []  []  []   39    18
 VQ
         3  U  64    []  []  12  54  04  62  []  []  66  []  []  []   70    06
 ND
         4  R  57    []  []  13  []  21  []  30  []  69  13  26  87   01    15
 OU
         5  S  79    22  80  14  25  []  []  []  95  []  []  []  06   32    03
 UF
         6  C  10    29  09  15  96  []  75  41  42  []  74  49  []   []    64
 OF
         7  O  81    []  []  []  []  38  []  []  []  []  35  []  []   []    69
 EN
         8  R  01    36  38  []  67  []  []  52  []  []  []  72  25   []    03
 MX
         9  E  65    []  []  []  38  []  []  63  []  72  96  []  44   []    92
 FE
        10     06    43  67  16  09  55  88  74  89  75  []  []  63   []    37
 ZR
        11  A  20    50  []  []  80  72  []  []  []  78  57  []  82   63    53
 DO
        12  N  12    []  96  []  []  89  []  85  []  81  18  95  01   94    34
 YD
        13  D  61    57  25  17  []  []  []  []  []  []  79  18  []   []    46
 BS
        14     50    []  []  18  51  06  []  96  []  []  []  []  20   []    93
 YW
        15  S  89    64  []  []  []  []  01  []  36  84  []  []  39   25    42
 VO
        16  E  42    []  54  19  22  23  14  []  []  []  40  []  []   []    65
 RB
        17  V  71    []  83  20  []  []  27  []  []  []  01  41  58   []    13
 BB
        18  E  64    []  []  21  93  40  40  []  83  []  62  64  77   56    66
 HC
        19  N  89    []  []  []  []  57  []  []  []  87  []  87  []   []    53
 QI
        20     16    71  12  22  64  []  53  07  30  []  []  10  96   []    20
 UR
        21  Y  84    []  []  []  []  74  []  []  []  90  23  []  15   []    60
 ZD
        22  E   8    78  []  []  35  91  66  []  77  93  []  []  34   []    93
 BW
        23  A  52    []  []  23  06  08  []  []  []  96  84  []  53   []    80
 BZ
        24  R  77    85  41  24  []  25  []  []  24  []  []  []  72   87    39
 TQ
        25  S  99    92  []  25  []  42  []  18  71  []  []  []  91   18    55
 EO
        26     82    []  70  []  []  59  []  29  18  []  []  33  10   []    20
 WD
        27  A  96    []  99  []  77  []  []  []  []  []  45  []  []   49    92
 RF
        28  G  65    99  []  26  []  76  []  []  65  99  06  []  29   []    01
 FW
        29  O  23    []  28  []  []  []  []  40  12  02  67  []  48   []    01
 DP
        30  '  36    06  57  27  []  93  []  []  59  05  28  56  67   80    65
 JA
        31     37    13  86  []  48  10  []  []  []  []  89  79  []   11    59
 XW
        32  O  56    20  15  28  19  []  []  []  06  08  50  []  []   []    18
 QN
        33  U  94    27  []  []  []  27  []  []  []  []  []  02  []   []    38
 ZX
        34  R  87    34  44  29  90  []  79  []  53  11  []  []  []   42    34
 OT
        35     81    []  []  30  61  []  []  51  []  []  11  []  []   73    28
 DA
        36  F  72    41  73  31  []  44  []  62  00  []  72  25  []   04    17
 WX

[] = no movement (repeated numbers)
Figure 12
9.  Corrections are made by pressing the " shift and | " keys
    simultaneously. Light magenta numbers appear between the 
    lines of input and output so that you can identify where
    the error is.  This position number ( note 37 below ) is
    entered (Figure 13 ).



F  O  U  R  S  C  O  R  E     A  N  D     S  E  V  E  N     Y  E  A  R  S
    A
     01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
26 27
     FM VQ ND OU UF OF EN MX FE ZR DO YD BS YW VO RB BB HC QI UR ZD BW BZ TQ EO
WD RF

    
      G  O  ,     O  U  R     F  U  R  F  A  Y  T  H  E  R  S
     28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
53 54
     FW DP JA XW QN ZX OT DA WX MG LY QW KM WQ EL WM DG XB HY


     55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
80 81


     82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
07 08


     09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
34 35


     36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
61 62

Enter '\' to end message.   Press 'Shift |' to make correction. Input No.
 46
     ENTER THE (FIRST) POSITION TO CORRECT 37

Figure 13

10. The  key is pressed twice.  The screen will blank and then
    automatically refill with "good" text up to that number and stop.
    CONTINUE ENTERING MESSAGE will appear in the middle of the screen.
    Entry of correct text is then continued from that
    point onwards (Figure 14).

F  O  U  R  S  C  O  R  E     A  N  D     S  E  V  E  N     Y  E  A  R  S
    A

     FM VQ ND OU UF OF EN MX FE ZR DO YD BS YW VO RB BB HC QI UR ZD BW BZ TQ EO
WD RF

      G  O  ,     O  U  R     F

     FW DP JA XW QN ZX OT DA WX


CONTINUE ENTERING MESSAGE


     Enter '\' to end message.   Press 'Shift |' to make correction.  Input No. 36

Rotor Display   41   73   31   61   44   79   62   00   11   72   25   67
                     04

Figure 14

11.  When the first screen is filled ( 162 characters input ) or is ended
     with a backslash ( \ ), the above control settings, etc. are printed, followed by
     the text screen.  As each subsequent screenful is completed it will be printed.
     This continues until the end of the message is reached and the backslash ( \ )
     key is pressed. This causes any partial screen to be printed before the message
     control data, message form and other output is printed.

     If Decipherment ( 2 ) is selected, the process is essentially the same
     (entering control settings, etc.) except the input is ciphertext and the output is
     cleartext. Message Control Data is available but message analysis is not.
								
								

 

ROTORS, SETS AND TABLES

 

The term "data files" encompasses the files that constitute the 100 each groupings of Regular Rotors, Reversing Rotors, Character Sets and Superencipherment Tables that are used by Enigma 95. They have been described earlier and now they are presented for inspection. They were used in the examples discussed earlier.

									

A  From  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25
          -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
-- --
  B  To   58 28 56 40 80 78 05 92 49 31 14 93 30 77 62 64 79 25 13 22 41 65 29
43 39

  A  From 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
49 50
          -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
-- --
  B  To   51 19 73 02 01 42 83 94 08 69 04 07 66 57 84 26 54 44 09 68 85 52 34
03 46

  A  From 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73
74 75
          -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
-- --
  B  To   27 10 17 70 37 23 06 38 59 97 91 71 95 88 96 32 45 18 82 53 61 99 81
12 16

  A  From 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98
99 00
          -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
-- --
  B  To   36 60 24 48 67 33 11 72 63 76 21 75 87 86 00 50 47 35 98 90 89 74 20
55 15

Figure 15 - Regular Rotor No.  32
      The "To" position indicates the position on the rotor's opposite face to
achieve theoffset effect.
      (For example, position 1 on face A is connected to position 58 on face B)


From  01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23
24 25
           -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
-- --
     To    48 65 34 39 86 95 82 51 12 71 17 09 90 26 43 42 11 91 67 60 59 89 87
25 24

     From  26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
49 50
           -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
-- --
     To    14 83 78 99 72 77 61 35 03 33 53 57 97 04 50 96 16 15 93 49 62 54 01
45 40

     From  51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73
74 75
           -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
-- --
     To    08 70 36 47 63 69 37 73 21 20 32 46 55 85 02 00 19 92 56 52 10 30 58
79 84

     From  76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98
99 00
           -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
-- --
     To    98 31 28 74 94 88 07 27 75 64 05 23 81 22 13 18 68 44 80 06 41 38 76
29 66

Figure 16 - Reversing Rotor No.  53
      The "To" position indicates the connecting position on the same face to
      achieve the offset effect.(For example, Positions 1 and 48 are connected,
      2 and 65 are connected, etc.)


Posn  01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20
               -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
         Char  #  q  .  c  j  t     +  9  A  *  4  f  r  O  ~  ,  {  8  d

         Posn  21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
               -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
         Char  y  o  5  R  n  h  w  X  D  p  g  M  ~  3  S  e  m  l  T  -

         Posn  41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
               -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
         Char  [  U  1  &  @  /  z  ~  ~  Q  a  =  P  !  C  7  ~  0  K  u

         Posn  61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
               -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
         Char  B  '  ~  Y  s  b  <  G  W  v  ?  I  ~  H  (  >  E  :  ~  x

         Posn  81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00
               -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
         Char  }  L  J  ~  k  Z  F  ~  _  )  N  ~  2  ;  V  i  6  ]  %  $

Figure 17 - Character Set No. 44
      "Posn" is the position value the Character is converted to when it is
      input. The characters "rotate" afterwards so that character position 
      values change.This figure shows the set before the first input.

      Letter "A" = 10 initially.  After the first input, "A" = "99", then "88" (
      For a rotation values of 89 ), etc.

01  02  03  04  05  06  07               01  02  03  04  05  06  07
         --  --  --  --  --  --  --               --  --  --  --  --  --  --
    01   HO  HI  BV  FW  DP  PX  BK          51   AO  YC  JI  VC  CT  ET  IX
    02   EF  DS  SJ  QJ  MK  BH  GS          52   DD  NO  NL  FM  XA  EM
    03   BG  HD  EP  UF  MX  YB  WV          53   NT  PJ  CJ  DO  QI  AN  FC
    04   JG  OO  TI  QW  UJ  IQ              54   TD  VR  TV  QG  EE  JU  RK
    05   VW  ZL  BX  LD  KF  TL  CM          55   QD  GE  MD  EO  OX  JW  IH
    06   DQ  XZ  CK  ND  AM  MH  LE          56   XP  BL  UN  FQ  KR  MV
    07   WO  FH  PT  FY  WN  GN  SI          57   OL  CH  SU  NI  GX  HZ  DU
    08   UW  FN  RA  YU  YR  ZZ              58   MS  MJ  FA  EW  TY  YX  WJ
    09   WB  DZ  OJ  LU  QL  WZ  SK          59   VA  TO  OI  XW  ZQ  ZA  WG
    10   XG  KL  OB  RE  QP  UQ  JH          60   RJ  IK  YH  ZD  SR  HJ
    11   FU  WI  QS  MP  UX  ZH  IF          61   M0  AA  NZ  AP  IV  JB  VS
    12   KP  OA  SF  IG  SO  FS              62   DE  LF  FO  UP  EV  CB  GB
    13   CY  BJ  TJ  BB  KQ  WE  PA          63   GH  UV  IM  OE  XL  ST  QF
    14   NK  BQ  HA  HU  FG  XS  CN          64   GF  TX  NS  OF  NU  VY
    15   VU  FI  UB  OU  YV  GT  PH          65   SG  KC  MN  RB  JA  KE  TE
    16   UH  PI  RU  LC  HB  NJ              66   VX  CW  QO  HC  BM  SC  ES
    17   LQ  NM  UD  WX  WM  EH  PQ          67   VJ  PF  QQ  QR  LS  XI  BE
    18   CF  HM  DY  VQ  QN  HW  AS          68   LJ  LV  ZT  LY  DM  WC
    19   JV  CX  ED  XC  OG  ID  KS          69   JN  YG  XV  EN  FL  AB  TT
    20   HH  AX  AJ  UR  WD  MY              70   VP  AT  GL  PO  KI  IY  WK
    21   YY  KA  NF  AI  VT  ZO  TM          71   ME  UU  SX  XN  RN  HE  KD
    22   ER  DX  JF  QK  TF  MA  FT          72   YI  QA  GA  EL  KO  QH
    23   HF  OH  DC  VM  VD  VG  RR          73   LX  CS  FK  PE  JO  YN  VK
    24   JX  FZ  SD  UZ  DN  FX              74   WU  LT  DR  ZC  IE  BC  XK
    25   RG  PG  HX  RM  IJ  RQ  LZ          75   XR  US  KG  EQ  JZ  QT  MB
    26   KX  YA  GO  XQ  OM  FD  NC          76   CP  IU  PK  ZN  IZ  AW
    27   IA  BP  PZ  II  KH  PP  IO          77   GU  QB  EY  ZV  LM  XF  TG
    28   MM  UL  IT  DA  GQ  IB              78   EC  SS  VH  NP  PS  ZI  ON
    29   IW  CU  IC  GI  KY  BR  CL          79   MR  TU  NW  AY  QM  ZY  BY
    30   KJ  PL  JE  DJ  RT  XU  PU          80   QC  OD  RW  BZ  CZ  SW
    31   CE  JK  WS  UT  AD  AK  JJ          81   ZP  SA  XO  YZ  NG  EU  QE
    32   UK  XJ  PR  JY  XY  SQ              82   GJ  ZW  RX  RH  EK  AC  JC
    33   WL  KV  LG  YM  NR  BA  EB          83   TA  OS  KZ  CQ  UA  WP  AV
    34   IP  CR  LB  YD  OT  XB  GC          84   TK  OW  AH  UY  HP  DW
    35   QU  YP  JT  VB  KT  AR  VI          85   FR  WW  PY  KM  WQ  MQ  LN
    36   HK  UM  RY  AU  ZM  BI              86   SY  GZ  TR  RC  BO  UC  EI
    37   MZ  PD  YK  ZR  UE  JL  NA          87   AQ  DV  RD  YL  RO  PM  KK
    38   OC  TZ  DF  ZX  CC  NB  IS          88   KU  CA  CQ  MG  QV  YS
    39   BF  XE  NH  TQ  HN  SE  JM          89   NV  BU  GK  EJ  GR  LW  MW
    40   SL  LI  WF  NQ  NN  XT              90   PB  OR  TB  RV  VN  CV  VL
    41   MF  MC  WH  OZ  VE  ZG  AG          91   DL  TN  DB  LP  YO  LH  LL
    42   HG  GD  GG  VO  OQ  UO  HS          92   QZ  DI  XM  FE  RF  WA
    43   HL  SM  VF  SZ  PW  HV  RL          93   YQ  MI  NX  YW  BW  PN  GY
    44   KW  JQ  SN  ZB  BD  VZ              94   LO  JS  GV  YE  ML  YT  FP
    45   WY  EZ  SB  AZ  GW  ZS  ZF          95   OV  JD  DT  DG  QX  PV  JR
    46   OP  NE  GP  BS  RS  CO  HQ          96   NY  EA  MU  AL  FJ  CD
    47   LK  YJ  IN  ZJ  XH  CI  PC          97   OY  KB  ZU  HY  GM  QY  TW
    48   RI  WT  FF  RP  SH  EX              98   FB  TS  HR  UG  TH  BN  IL
    49   MT  XD  ZE  WR  AF  DH  RZ          99   EG  YF  IR  LR  SP  TC  LA
    50   DK  ZK  UI  JP  VV  HT  TP          00   AE  KN  SV  FV  XX  BT  OK

Figure 18 - Superencipherment  Table No. 35
      The left column is the numeric cipher.  The other  7 columns are the
      possible super encipherments. 36 can be converted to HK , UM , RY , AU , ZM , BI in
      turn, depending on where the counter starts. A blank causes the counter to 
      be reset to 1.
     A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y
 Z
    -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
--
A  61 69 82 31 00 49 41 84 21 20 31 96 06 53 51 61 87 35 18 70 36 83 76 20 79
45  A
 B  33 13 74 44 67 39 03 02 36 13 01 56 66 98 86 27 14 29 46 00 89 01 93 05 79
80  B
 C  88 62 38 96 31 18 88 57 47 53 06 29 05 14 46 76 83 34 73 51 29 90 66 19 13
80  C
 D  28 91 23 52 62 38 95 49 92 30 50 91 68 24 53 01 06 74 02 95 57 87 84 22 18
09  D
 E  96 33 78 19 54 02 99 17 86 89 82 72 52 69 55 03 75 22 66 51 81 62 58 48 77
45  E
 F  58 98 53 26 92 48 14 07 15 96 73 69 52 08 62 94 56 85 12 22 11 00 01 24 07
24  F
 G  72 62 34 42 55 64 42 63 29 82 89 70 97 07 26 46 28 89 02 15 77 94 45 57 93
86  G
 H  14 16 66 03 71 23 42 20 01 60 36 43 18 39 01 84 46 98 42 50 14 43 18 25 97
57  H
 I  27 28 29 19 74 11 12 55 27 25 60 98 63 47 27 34 04 99 38 28 76 61 29 51 70
76  I
 J  65 61 82 95 30 22 04 10 51 31 31 37 39 69 73 50 44 95 94 35 54 19 55 24 32
75  J
 K  21 97 65 71 65 05 75 27 70 30 87 10 85 00 72 12 13 56 19 35 88 33 44 26 29
83  K
 L  99 34 16 05 06 62 33 91 40 68 47 91 77 85 94 91 17 99 67 74 09 68 89 73 68
25  L
 M  22 75 41 55 71 41 88 06 93 58 02 94 28 65 61 11 85 79 58 49 96 56 89 03 20
37  M
 N  37 38 26 06 46 21 81 39 57 16 14 52 17 40 52 78 40 33 64 53 64 89 79 93 96
61  N
 O  12 10 38 80 63 64 19 23 59 09 00 57 26 78 04 46 42 90 83 34 15 95 84 55 97
41  O
 P  13 90 47 37 73 67 25 15 16 53 76 30 87 93 70 27 17 32 78 07 30 95 43 01 85
27  P
 Q  72 77 80 55 81 63 54 72 53 02 22 09 79 18 66 10 67 67 11 75 35 88 04 95 97
92  Q
 R  08 65 86 87 10 92 25 82 48 60 54 43 25 71 87 48 25 23 46 30 16 90 80 82 36
49  R
 S  81 45 66 24 39 12 65 48 07 02 09 40 43 44 12 99 32 60 78 63 57 00 80 71 86
43  S
 T  83 90 99 54 65 22 77 98 04 13 84 05 21 91 59 50 39 86 98 69 79 54 97 64 58
38  T
 U  83 15 86 17 37 03 98 16 50 04 32 28 36 56 42 62 10 20 75 31 71 63 08 11 84
24  U
 V  59 35 51 23 41 43 23 78 35 67 73 90 23 90 42 70 18 54 61 21 15 50 05 66 64
44  V
 W  92 09 68 20 13 40 59 41 11 58 70 33 17 07 07 83 85 49 31 48 74 03 85 17 45
09  W
 X  52 34 19 49 39 77 10 47 67 32 74 63 92 71 81 56 26 75 14 40 30 69 59 00 32
06  X
 Y  26 03 51 34 94 99 69 60 72 47 37 87 33 73 91 35 93 08 88 94 08 15 93 58 21
81  Y
 Z  59 44 74 60 49 45 41 11 78 47 50 05 36 76 21 81 59 37 45 68 97 77 82 38 79
08  Z
    -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
--
A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y
 Z

Figure 19 - Superdecipherment Table 35 First letter at left. Second letter at top. Numeric cipher at intersection ( HK, UM, RY, etc. = 36 ) The Enigma rotor operation principle has probably been long superseded by much more sophisticated methods of encryption that are faster and more secure, but it will remain interesting for a long time to amateurs such as myself. It is something that is understandable and before the advent of the computer, resulted in some beautiful machines. The Enigma 95 is not one now, but I believe that it could be "translated" into a handsome electro-mechanical device. It is something to dream about. The only absolutely secure cipher is the One Time Pad and it has the disadvantage of requiring copies to be destroyed after one use. The Enigma 95 is an attempt to approach this holy Grail of cryptography by providing an almost unlimited supply of enhanced (both in size and method of rotation) Rotors, Character Sets, Superencipherment Tables and a lengthened Plugboard. While I cannot prove it mathematically or otherwise, I suspect that the ability to use almost unlimited expendable sets of all possible combinations of these for very limited periods (throw away feature) such as is possible in the Enigma 95, would strengthen any cipher considerably by preventing the accumulation of sufficient material on which to base an in-depth cryptanalysis. Any comments would appreciated.
 

 

AT THE CRYPTO DROP BOX IS

 

The disk accompanying this article contains ENIGMA 95 and the necessary supporting files needed in its operation. Also included are program files to create them and to analyze and test its operation. DOC files are included for each file to explain them. Start with CRYPTO.1ST, then read ENIGMA95.DOC and study ENIGMA95.FLO to gain an understanding of Enigma 95 before running it. The list of files is:

 

CRYPTO.1ST             :  An outline of the files that constitute Enigma 95
system
ENIGMA95.DOC           :  Detailed documentation pertaining to ENIGMA95
ENIGMA95.FLO           :  A flowchart of the ENIGMA95 operation
ENIGMA95.BAS  *        :  ENIGMA95

ROTORS.DAT             :  Set of 100 Regular Rotors
REVROTRS.DAT           :  Set of 100 Reversing Rotors
CHARS.DAT              :  Set of 100 Character Sets
CODE.DAT               :  Set of 100 Super Encipherment Tables

CRYPTO05.BAS  *  :  Random Numbers Generator for CRYPTO27 & CRYPTO34
CRYPTO27.BAS  *  :  Regular Rotor Creation using the Interval Method
CRYPTO28.BAS  *  :  Super Encipherment Tables Creation
CRYPTO30.BAS  *  :  Character Set Creation
CRYPTO34.BAS  *  :  Reversing Rotor Creation

CRYPTO43.BAS  *  :  ENIGMA95 Cipher Machine Data Paths Demonstrator
CRYPTO45.BAS  *  :  Rotors Matching Analysis
CRYPTO47.BAS  *  :  Check of Rotor Files for Errors
CRYPTO48.BAS  *  :  Analysis of Cleartext vs. Ciphertext
CRYPTO49.BAS  *  :  Rotor Intermittent Movement Test
CRYPTO51.BAS     :  Plugboard Combinations

ENIGMA95.WRI      :  The article about Enigma 95.  ( Created using Windows 3.1
Write )

               * = Has a matching .DOC file

      The .1st , .DOC and .FLO files are DOS files
            The .BAS and .DAT files are QBASIC or QUICKBASIC  files
            The .WRI file is a WINDOWS 3.1 Write file

ENCRYPTION                                           10-31-1995  16:36:57  Hours

No. of PB Connections 21 Plugboard Connections (1735) (2356) (4581) (9852) (3377) (5544) (6612) (5987) (3254) (6791) (2653) (4899) (6250) (4069) (3180) (9402) (8437) (9307) (8843) (8514) (2176) No. of Rotors 12 Rotors Sequence 32 49 42 98 63 94 62 60 04 33 25 11 Rotors Orientation 1 2 1 1 2 2 1 1 2 2 1 1 Reversing Rotor No. 53 Rotors Rotation Values 07 29 01 71 17 13 11 47 03 61 23 19 Rev Rotor Rotation Value 31 Character Set (CS) No. 44 CS Rotation Value 89 Internal Checksum 60354
Rotors Initial Settings 15 22 09 41 87 36 08 01 57 91 03 49 Rev Rotor Initial Setting 77 External Checksum 64
F O U R S C O R E A N D S E V E N Y E A R S A 52 18 06 15 03 64 69 03 92 37 53 34 46 93 42 65 13 66 53 20 60 93 80 39 55 20 92
G O , O U R F O R E F A T H E R S B R O U G H T 01 01 65 59 18 38 34 28 17 43 63 98 60 64 41 31 11 13 56 20 34 65 57 72 73 95 10
F O R T H U P O N T H I S C O N T I N E N T 53 19 21 23 57 21 59 32 96 45 50 23 79 29 01 92 30 12 30 42 04 58 82 66 86 40 28
A N E W N A T I O N . 1 2 3 4 5 6 7 8 9 0 ( * ) 27 86 23 88 28 11 26 30 91 76 90 06 96 83 85 74 48 64 96 82 80 53 00 59 25 74 73
TOTAL INPUT CHARACTERS IS 108 HASH TOTAL OF CODE IS 02 EXHIBIT A-1 COL CHECK TOTALS 33 24 15 85 06 34 88 93 96 01 56 61 81 69 69 62 02 55 35 64 78 69 19 36 39 29 03 TOTAL COLUMNS = 5202 ROW CHECK TOTALS 83 67 78 74 TOTAL ROWS = 5202 EXHIBIT A-2 ================================= SEPARATE PAGE ================================ FOR TRANSMISSION AS MESSAGE No. -------------------------------------------------------------------------------- 15 22 09 41 87 36 08 01 57 91 03 49 77 64 10 31 95 16 36 57 -------------------------------------------------------------------------------- 52 18 06 15 03 64 69 03 92 37 53 34 46 93 42 65 13 66 53 20 60 93 80 39 55 20 92 01 01 65 59 18 38 34 28 17 43 63 98 60 64 41 31 11 13 56 20 34 65 57 72 73 95 10 53 19 21 23 57 21 59 32 96 45 50 23 79 29 01 92 30 12 30 42 04 58 82 66 86 40 28 27 86 23 88 28 11 26 30 91 76 91 06 96 83 85 74 48 64 96 82 80 53 00 59 25 74 73 108 02 -------------------------------------------------------------------------------- Column and row totals. Do not transmit unless requested. 33 24 15 85 06 34 88 93 96 01 56 61 81 69 69 62 02 55 35 64 78 69 19 36 39 29 03 83 67 78 74 EXHIBIT A-3 INPUT FREQUENCY ANALYSIS | Char Freq | Char Freq | Char Freq | Char Freq | Char Freq | | ---- ---- | ---- ---- | ---- ---- | ---- ---- | ---- ---- | | A 6 | U 4 | ; | k | ? | | B 1 | V 1 | ' | l | ( 1 | | C 2 | W 1 | = | m | ) 1 | | D 1 | X | ! | n | { | | E 8 | Y 1 | @ | o | } | | F 4 | Z | # | p | < | | G 2 | 0 1 | $ | q | > | | H 4 | 1 1 | % | r | [ | | I 3 | 2 1 | & | s | ] | | J | 3 1 | * 1 | t | ~ | | K | 4 1 | a | u | ~ | | L | 5 1 | b | v | ~ | | M | 6 1 | c | w | ~ | | N 9 | 7 1 | d | x | ~ | | O 10 | 8 1 | e | y | ~ | | P 1 | 9 1 | f | z | ~ | | Q | space 15 | g | _ | ~ | | R 8 | . 1 | h | - | ~ | | S 5 | , 1 | i | + | ~ | | T 7 | : | j | / | ~ | Total = 108 OUTPUT FREQUENCY ANALYSIS Code Count Code Count Code Count Code Count Code Count |---------------|----------------|----------------|----------------|------------ ----| | 1 = 3 | 21 = 2 | 41 = 1 | 61 = | 81 = | | 2 = | 22 = | 42 = 2 | 62 = | 82 = 2 | | 3 = 2 | 23 = 3 | 43 = 1 | 63 = 1 | 83 = 1 | | 4 = 1 | 24 = | 44 = | 64 = 3 | 84 = | | 5 = | 25 = 1 | 45 = 1 | 65 = 3 | 85 = 1 | | 6 = 2 | 26 = 1 | 46 = 1 | 66 = 2 | 86 = 2 | | 7 = | 27 = 1 | 47 = | 67 = | 87 = | | 8 = | 28 = 3 | 48 = 1 | 68 = | 88 = 1 | | 9 = | 29 = 1 | 49 = | 69 = 1 | 89 = | | 10 = 1 | 30 = 3 | 50 = 1 | 70 = | 90 = 1 | | 11 = 2 | 31 = 1 | 51 = | 71 = | 91 = 1 | | 12 = 1 | 32 = 1 | 52 = 1 | 72 = 1 | 92 = 3 | | 13 = 2 | 33 = | 53 = 4 | 73 = 2 | 93 = 2 | | 14 = | 34 = 3 | 54 = | 74 = 2 | 94 = | | 15 = 1 | 35 = | 55 = 1 | 75 = | 95 = 1 | | 16 = | 36 = | 56 = 1 | 76 = 1 | 96 = 3 | | 17 = 1 | 37 = 1 | 57 = 2 | 77 = | 97 = | | 18 = 2 | 38 = 1 | 58 = 1 | 78 = | 98 = 1 | | 19 = 1 | 39 = 1 | 59 = 3 | 79 = 1 | 99 = | | 20 = 3 | 40 = 1 | 60 = 2 | 80 = 2 | 00 = 1 | Total = 108 EXHIBIT A-4 DECRYPTION 10-31-1995 17:00:58 Hours -------------------------------------------------------------------------------- No. of PB Connections 21 Plugboard Connections (1735) (2356) (4581) (9852) (3377) (5544) (6612) (5987) (3254) (6791) (2653) (4899) (6250) (4069) (3180) (9402) (8437) (9307) (8843) (8514) (2176) No. of Rotors 12 Rotors Sequence 32 49 42 98 63 94 62 60 04 33 25 11 Rotors Orientation 1 2 1 1 2 2 1 1 2 2 1 1 Reversing Rotor No. 53 Rotors Rotation Values 07 29 01 71 17 13 11 47 03 61 23 19 Rev Rotor Rotation Value 31 Character Set (CS) No. 44 CS Rotation Value 89 Internal Checksum 60354 -------------------------------------------------------------------------------- Rotors Initial Settings 15 22 09 41 87 36 08 01 57 91 03 49 Rev Rotor Initial Setting 77 External Checksum 64 -------------------------------------------------------------------------------- 52 18 06 15 03 64 69 03 92 37 53 34 46 93 42 65 13 66 53 20 60 93 80 39 55 20 92 F O U R S C O R E A N D S E V E N Y E A R S A -------------------------------------------------------------------------------- 01 01 65 59 18 38 34 28 17 43 63 98 60 64 41 31 11 13 56 20 34 65 57 72 73 95 10 G O , O U R F O R E F A T H E R S B R O U G H T -------------------------------------------------------------------------------- 53 19 21 23 57 21 59 32 96 45 50 23 79 29 01 92 30 12 30 42 04 58 82 66 86 40 28 F O R T H U P O N T H I S C O N T I N E N T -------------------------------------------------------------------------------- 27 86 23 88 28 11 26 30 91 76 90 06 96 83 85 74 48 64 96 82 80 53 00 59 25 74 73 A N E W N A T I O N . 1 2 3 4 5 6 7 8 9 0 ( * ) -------------------------------------------------------------------------------- TOTAL INPUT CHARACTERS IS 108 HASH TOTAL OF CODE IS 02 EXHIBIT B-1 COL CHECK TOTALS 33 24 15 85 06 34 88 93 96 01 56 61 81 69 69 62 02 55 35 64 78 69 19 36 39 29 03 TOTAL COLUMNS = 5202 ROW CHECK TOTALS 83 67 78 74 TOTAL ROWS = 5202 EXHIBIT B-2 ================================= SEPARATE PAGE ================================ Messsage No.--------------------From----------------------------------Date/Time of Receipt : : : / : : : : / : -------------------------------------------------------------------------------- ---------- FOURSCORE AND SEVEN YEARS AGO, OUR FOREFATHERS BROUGHT FORTH UPON THIS CONTINENT A NEW NAT ION. 1234567890(*) EX HIBIT B-3 ENCRYPTION 10-31-1995 16:36:57 Hours -------------------------------------------------------------------------------- No. of PB Connections 21 Plugboard Connections (1735) (2356) (4581) (9852) (3377) (5544) (6612) (5987) (3254) (6791) (2653) (4899) (6250) (4069) (3180) (9402) (8437) (9307) (8843) (8514) (2176) No. of Rotors 12 Rotors Sequence 32 49 42 98 63 94 62 60 04 33 25 11 Rotors Orientation 1 2 1 1 2 2 1 1 2 2 1 1 Reversing Rotor No. 53 Rotors Rotation Values 07 29 01 71 17 13 11 47 03 61 23 19 Rev Rotor Rotation Value 31 Character Set (CS) No. 44 CS Rotation Value 89 Internal Checksum 60354 -------------------------------------------------------------------------------- Rotors Initial Settings 15 22 09 41 87 36 08 01 57 91 03 49 Rev Rotor Initial Setting 77 Super Encipher Table No. 35 External Checksum 99 -------------------------------------------------------------------------------- F O U R S C O R E A N D S E V E N Y E A R S A FM VQ ND OU UF OF EN MX FE ZR DO YD BS YW VO RB BB HC QI UR ZD BW BZ TQ EO WD RF -------------------------------------------------------------------------------- G O , O U R F O R E F A T H E R S B R O U G H T FW DP JA XW QN ZX OT DA WX SZ OE UG SR NU OZ UT MP KQ FQ MY XB KE NI EL PE DG RE -------------------------------------------------------------------------------- F O R T H U P O N T H I S C O N T I N E N T AN XC AI VM GX VT ZQ JY AL AZ JP VD AY GI PX WA DJ IG RT OQ QW EW RH BM RC NQ GQ -------------------------------------------------------------------------------- A N E W N A T I O N . 1 2 3 4 5 6 7 8 9 0 ( * ) II BO VG MG IB UX XQ XU LP ZN RV AM FJ CQ KM ZC RP VY CD EK CZ FC FV ZA RM IE JO -------------------------------------------------------------------------------- TOTAL INPUT CHARACTERS IS 108 EXHIBIT C-1 FOR TRANSMISSION AS MESSAGE No. -------------------------------------------------------------------------------- 15 22 09 41 87 36 08 01 57 91 03 49 77 35 99 10 31 95 17 00 58 -------------------------------------------------------------------------------- FM VQ ND OU UF OF EN MX FE ZR DO YD BS YW VO RB BB HC QI UR ZD BW BZ TQ EO WD RF FW DP JA XW QN ZX OT DA WX SZ OE UG SR NU OZ UT MP KQ FQ MY XB KE NI EL PE DG RE AN XC AI VM GX VT ZQ JY AL AZ JP VD AY GI PX WA DJ IG RT OQ QW EW RH BM RC NQ GQ II BO VG MG IB UX XQ XU LP ZN RV AM FJ CQ KM ZC RP VY CD EK CZ FC FV ZA RM IE JO 108 EXHIBIT C-2 INPUT FREQUENCY ANALYSIS | Char Freq | Char Freq | Char Freq | Char Freq | Char Freq | | ---- ---- | ---- ---- | ---- ---- | ---- ---- | ---- ---- | | A 6 | U 4 | ; | k | ? | | B 1 | V 1 | ' | l | ( 1 | | C 2 | W 1 | = | m | ) 1 | | D 1 | X | ! | n | { | | E 8 | Y 1 | @ | o | } | | F 4 | Z | # | p | < | | G 2 | 0 1 | $ | q | > | | H 4 | 1 1 | % | r | [ | | I 3 | 2 1 | & | s | ] | | J | 3 1 | * 1 | t | ~ | | K | 4 1 | a | u | ~ | | L | 5 1 | b | v | ~ | | M | 6 1 | c | w | ~ | | N 9 | 7 1 | d | x | ~ | | O 10 | 8 1 | e | y | ~ | | P 1 | 9 1 | f | z | ~ | | Q | space 15 | g | _ | ~ | | R 8 | . 1 | h | - | ~ | | S 5 | , 1 | i | + | ~ | | T 7 | : | j | / | ~ | Total = 108 OUTPUT FREQUENCY ANALYSIS \2 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Total 1\ -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ----- A 1 1 1 1 1 1 6 B 1 1 1 1 1 1 6 C 1 1 1 3 D 1 1 1 1 1 5 E 1 1 1 1 1 5 F 1 1 1 1 1 1 1 7 G 1 1 1 3 H 1 1 I 1 1 1 1 4 J 1 1 1 1 4 K 1 1 1 3 L 1 1 M 1 1 1 1 4 N 1 1 1 1 4 O 1 1 1 1 1 1 6 P 1 1 2 Q 1 1 1 3 R 1 1 1 1 1 1 1 1 1 9 S 1 1 2 T 1 1 U 1 1 1 1 1 5 V 1 1 1 1 1 1 1 7 W 1 1 1 3 X 1 1 1 1 1 5 Y 1 1 2 Z 1 1 1 1 1 1 1 7 -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ----- A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Total -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ----- 4 4 5 6 6 3 5 1 5 2 1 2 6 4 5 5 10 3 1 4 3 2 6 6 4 5 108 EXHIB IT C-3 DECRYPTION 10-31-1995 17:36:57 Hours -------------------------------------------------------------------------------- No. of PB Connections 21 Plugboard Connections (1735) (2356) (4581) (9852) (3377) (5544) (6612) (5987) (3254) (6791) (2653) (4899) (6250) (4069) (3180) (9402) (8437) (9307) (8843) (8514) (2176) No. of Rotors 12 Rotors Sequence 32 49 42 98 63 94 62 60 04 33 25 11 Rotors Orientation 1 2 1 1 2 2 1 1 2 2 1 1 Reversing Rotor No. 53 Rotors Rotation Values 07 29 01 71 17 13 11 47 03 61 23 19 Rev Rotor Rotation Value 31 Character Set (CS) No. 44 CS Rotation Value 89 Internal Checksum 60354 -------------------------------------------------------------------------------- Rotors Initial Settings 15 22 09 41 87 36 08 01 57 91 03 49 Rev Rotor Initial Setting 77 Super Encipher Table No. 35 External Checksum 99 -------------------------------------------------------------------------------- FM VQ ND OU UF OF EN MX FE ZR DO YD BS YW VO RB BB HC QI UR ZD BW BZ TQ EO WD RF F O U R S C O R E A N D S E V E N Y E A R S A -------------------------------------------------------------------------------- FW DP JA XW QN ZX OT DA WX SZ OE UG SR NU OZ UT MP KQ FQ MY XB KE NI EL PE DG RE G O , O U R F O R E F A T H E R S B R O U G H T -------------------------------------------------------------------------------- AN XC AI VM GX VT ZQ JY AL AZ JP VD AY GI PX WA DJ IG RT OQ QW EW RH BM RC NQ GQ F O R T H U P O N T H I S C O N T I N E N T -------------------------------------------------------------------------------- A N E W N A T I O N . 1 2 3 4 5 6 7 8 9 0 ( * ) II BO VG MG IB UX XQ XU LP ZN RV AM FJ CQ KM ZC RP VY CD EK CZ FC FV ZA RM IE JO -------------------------------------------------------------------------------- TOTAL INPUT CHARACTERS IS 108 EXHIBIT D-1 Messsage No.--------------------From----------------------------------Date/Time of Receipt : : : / : : : : / : -------------------------------------------------------------------------------- FOURSCORE AND SEVEN YEARS AGO, OUR FOREFATHERS BROUGHT FORTH UPON THIS CONTINENT A NEW NAT ION. 1234567890(*)

 

SOLUTIONS TO LECTURE 8 PROBLEMS

 

Thanks to GRAPE JUICE for the quick and clear reply: C-1 Give two solutions to: (BE)**2 = ARE A>0 , B= 1...3, E>0, R>0 (16) ** 2 = 256 and (31) ** 2 = 961 C-2 Square root: [OKLA] [OKLI] R, A, T, S A= E+1 +4,9 ----------- B |Q UA RT ET E -A I > A ----- O=0 T UA Q >A, T -T SI R =2,3 ----- S U RT T -A UT U =S+1 > A, E ----- T E AO ET U -E ES UB --------- R AR 2 4 1 7 4=4,9 + ------------ 9> 1 | 5 84 21 31 3 -4 6 ---------------- 0=0 1 84 5>4,1 -1 76 2=2,3 ---------------- 7 1 8 21 8=7+1 >4,3 =7,8 -4 81 1 ---------------- 8 3 40 31 -3 37 89 ---------------- 2 42 A B E I O Q R S T U 1 2 3 4 5 6 7 8 9 0 T R E A Q I S U B O A B E I O Q R S T U 0 1 2 3 4 5 6 7 8 9 O T R E A Q I S U B A B E I O Q R S T U 0 9 8 7 6 5 4 3 2 1 O B U S I Q A E R T A B E I O Q R S T U 9 8 7 6 5 4 3 2 1 0 B U S I Q A E R T O From Sinkov [SINK] two Hill system problems: Hill-1 Decipher the message: YITJP GWJOW FAQTQ XCSMA ETSQU SQAPU SQGKC PQTYJ Use the deciphering matrix | 5 1 | | 2 7 | Let A =1, B=2... Z=26 P1 = 5(C1) + 1(C2) P2 = 2(C1) + 7(C2) 5(Y) + 1(I) = 5(25) + 1(9) = 125 + 9 =134 MOD 26 = 4 = D 2(Y) + 7(I) = 2(25) + 7(9) = 50 + 63 =113 MOD 26 = 9 = I 5(T) + 1(J) = 5(20) + 1(10) = 100 + 10=110 MOD 26 = 6 = F 2(T) + 7(J) = 2(20) + 7(10) = 40 + 70 =110 MOD 26 = 6 = F Difficulties are things that show what men are. Hill-2 Decipher the message: MWALO LIAIW WTGBH JNTAK QZJKA ADAWS SKQKU AYARN CSODN IIAES OQKJY B Use the deciphering matrix | 2 23 | use A=1, B=2, ...Z=26 P1 = 2(C1) +23(C2) P2 = 21(C1) +7(C2) 2(M) + 23(W) =2(13) + 23(23) =26 + 529 = 555 MOD 26 = 9 = I 21(M) +7(W) =21(13) + 7(23) =273 + 161 = 434 MOD 26 =18 = R 2(A) + 23(L) = 2(1) + 23(12) = 2 + 276 = 278 MOD 26 = 18= R 21(A) +7(L) = 21(1) + 7(12) = 21 + 84 = 105 MOD 26 = 1 = A Irrationally held truths may be more harmful than reasoned errors.

 

REFERENCES / RESOURCES

 

 

 

[updated 10 March 1996]

 

 

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       of Bletchley Park", Oxford University Press, 1994.

[HIN3] Hinsley, F. H., et. al., "British Intilligence in The
       Second World War: Its Influence on Strategy and
       Operations," London, HMSO vol I, 1979, vol II 1981, vol
       III, 1984 and 1988.

[HISA] Hisashi Takahashi, "Military Friction, Diplomatic
       Suasion in China, 1937 - 1938," The Journal of
       International Studies, Sophia Univ, Vol 19, July, 1987.

[HIS1] Barker, Wayne G., "History of Codes and Ciphers in the
       U.S. Prior to World War I," Aegean Park Press, Laguna
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[HITT] Hitt, Parker, Col. " Manual for the Solution of Military
       Ciphers,"  Aegean Park Press, Laguna Hills, CA, 1976.

[HODG] Hodges, Andrew, "Alan Turing: The Enigma," New York,
       Simon and Schuster, 1983.

[HOFF] Hoffman, Lance J., editor,  "Building In Big Brother:
       The Cryptographic Policy Debate," Springer-Verlag,
       N.Y.C., 1995. ( A useful and well balanced book of
       cryptographic resource materials. )

[HOF1] Hoffman, Lance. J., et. al.," Cryptography Policy,"
       Communications of the ACM 37, 1994, pp. 109-17.

[HOLM  Holmes, W. J., "Double-Edged Secrets: U.S. Naval
       Intelligence Operations in the Pacific During WWII",
       Annapolis, MD: Naval Institute Press, 1979.

[HOM1] Homophonic: A Multiple Substitution Number Cipher", S-
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       Association, 1945.

[HOM2] Homophonic: Bilinear Substitution Cipher, Straddling,"
       ISHCABIBEL, The Cryptogram, AS48, American Cryptogram
       Association, 1948.

[HOM3] Homophonic: Computer Column:"Homophonic Solving,"
       PHOENIX, The Cryptogram, MA84, American Cryptogram
       Association, 1984.

[HOM4] Homophonic: Hocheck Cipher,", SI SI, The Cryptogram,
       JA90, American Cryptogram Association, 1990.

[HOM5] Homophonic: "Homophonic Checkerboard," GEMINATOR, The
       Cryptogram, MA90, American Cryptogram Association, 1990.

[HOM6] Homophonic: "Homophonic Number Cipher," (Novice Notes)
       LEDGE, The Cryptogram, SO71, American Cryptogram
       Association, 1971.

[HUNG] Rip Van Winkel, "Hungarian," The Cryptogram, March -
       April,  American Cryptogram Association, 1956.

[HYDE] H. Montgomery Hyde, "Room 3603, The Story of British
       Intelligence Center in New York During World War II",
       New York, Farrar, Straus, 1963.

[IBM1] IBM Research Reports, Vol 7., No 4, IBM Research,
       Yorktown Heights, N.Y., 1971.

[INDE] PHOENIX, Index to the Cryptogram: 1932-1993, ACA, 1994.

[ITAL] Italian - English Dictionary, compiled by Vittore E.
       Bocchetta, Fawcett Premier, New York, 1965.

[JAPA] Martin, S.E., "Basic Japanese Coversation Dictionary,"
       Charles E. Tuttle Co., Toyko, 1981.

[JOHN] Johnson, Brian, 'The Secret War', Arrow Books,
       London 1979.

[KADI] al-Kadi, Ibrahim A., Cryptography and Data Security:
       Cryptographic Properties of Arabic, Proceedings of the
       Third Saudi Engineering Conference. Riyadh, Saudi
       Arabia: Nov 24-27, Vol 2:910-921., 1991.

[KAHN] Kahn, David, "The Codebreakers", Macmillian Publishing
       Co. , 1967.

[KAH1] Kahn, David, "Kahn On Codes - Secrets of the New
       Cryptology," MacMillan Co., New York, 1983.

[KAH2] Kahn, David, "An Enigma Chronology", Cryptologia Vol
       XVII,Number 3, July 1993.

[KAH3] Kahn, David, "Seizing The Enigma: The Race to Break the
       German U-Boat Codes 1939-1943 ", Houghton Mifflin, New
       York, 1991.

[KERC] Kerckhoffs, "la Cryptographie Militaire, " Journel des
       Sciences militaires, 9th series, IX, (January and
       February, 1883, Libraire Militaire de L. Baudoin &Co.,
       Paris.  English trans. by Warren T, McCready of the
       University of Toronto, 1964

[KOBL] Koblitz, Neal, " A Course in Number Theory and
       Cryptography, 2nd Ed, Springer-Verlag, New York, 1994.

[KONH] Konheim, Alan G., "Cryptography -A Primer" , John Wiley,
       1981, pp 212 ff.

[KORD] Kordemsky, B., "The Moscow Puzzles," Schribners, 1972.

[KOTT] Kottack, Phillip Conrad, "Anthropology: The Exploration
       Of Human Diversity," 6th ed., McGraw-Hill, Inc., New
       York, N.Y.  1994.

[KOZA] Kozaczuk, Dr. Wladyslaw,  "Enigma: How the German
       Machine Cipher was Broken and How it Was Read by the
       Allies in WWI", University Pub, 1984.

[KRAI] Kraitchek, "Mathematical Recreations," Norton, 1942, and
       Dover, 1963.

[KULL] Kullback, Solomon, Statistical Methods in Cryptanalysis,
       Aegean Park Press, Laguna Hills, Ca. 1976

[LAFF] Laffin, John, "Codes and Ciphers: Secret Writing Through
       The Ages," Abelard-Schuman, London, 1973.

[LAI]  Lai, Xuejia, "On the Design and Security of Block
       Ciphers," ETH Series in Information Processing 1, 1992.
       (Article defines the IDEA Cipher)

[LAIM] Lai, Xuejia, and James L. Massey, "A Proposal for a New
       Block Encryption Standard," Advances in Cryptology -
       Eurocrypt 90 Proceedings, 1992, pp. 55-70.

[LAKE] Lakoff, R., "Language and the Women's Place," Harper &
       Row, New York, 1975.

[LANG] Langie, Andre, "Cryptography," translated from French
       by J.C.H. Macbeth, Constable and Co., London, 1922.

[LATI] BRASSPOUNDER, "Latin Language Data, "The Cryptogram,"
       July-August 1993.

[LAUE] Lauer, Rudolph F.,  "Computer Simulation of Classical
       Substitution Cryptographic Systems" Aegean Park Press,
       1981, p72 ff.

[LEAR] Leary, Penn, " The Second Cryptographic Shakespeare,"
       Omaha, NE [from author]  1994.

[LEA1] Leary, Penn, " Supplement to The Second Cryptographic
       Shakespeare," Omaha, NE [from author]  1994.

[LEAU] Leaute, H., "Sur les Mecanismes Cryptographiques de M.
       de Viaris,"  Le Genie Civil, XIII, Sept 1, 1888.

[LEDG] LEDGE, "NOVICE NOTES," American Cryptogram Association,
       1994.  [ One of the best introductory texts on ciphers
       written by an expert in the field.  Not only well
       written, clear to understand but as authoritative as
       they come! ]

[LENS] Lenstra, A.K. et. al. "The Number Field Sieve,"
       Proceedings of the 22 ACM Symposium on the Theory of
       Computing," Baltimore, ACM Press, 1990, pp 564-72.

[LEN1] Lenstra, A.K. et. al. "The Factorization of the Ninth
       Fermat Number," Mathematics of Computation 61 1993,
       pp. 319-50.

[LEWI] Lewin, Ronald, 'Ultra goes to War', Hutchinson,
       London 1978.

[LEWY] Lewy, Guenter, "America In Vietnam", Oxford University
       Press, New York, 1978.

[LEVI] Levine, J.,  U.S. Cryptographic Patents 1861-1981,
       Cryptologia, Terre Haute, In 1983.

[LEV1] Levine, J.  1961.  Some Elementary Cryptanalysis
       of Algebraic Cryptography.  American Mathematical
       Monthly.  68:411-418

[LEV2] Levine, J.  1961.  Some Applications of High-
       Speed Computers to the Case n =2 of Algebraic
       Cryptography.  Mathematics of Computation.  15:254-260

[LEV3] Levine, J. 1963.  Analysis of the Case n =3 in Algebraic
       Cryptography With Involuntary Key Matrix With Known
       Alphabet.  Journal fuer die Reine und Angewante
       Mathematik.  213:1-30.

[LISI] Lisicki, Tadeusz, 'Dzialania Enigmy', Orzet Biaty,
       London July-August, 1975; 'Enigma i Lacida',
       Przeglad lacznosci, London 1974- 4; 'Pogromcy
       Enigmy we Francji', Orzet Biaty, London, Sept.
       1975.'

[LYNC] Lynch, Frederick D., "Pattern Word List, Vol 1.,"
       Aegean Park Press, Laguna Hills, CA, 1977.

[LYSI] Lysing, Henry, aka John Leonard Nanovic, "Secret
       Writing," David Kemp Co., NY 1936.

[MACI] Macintyre, D., "The Battle of the Atlantic," New York,
       Macmillan, 1961.

[MADA] Madachy, J. S., "Mathematics on Vacation," Scribners,
       1972.

[MAGN] Magne, Emile, Le plaisant Abbe de Boisrobert, Paris,
       Mecure de France, 1909.

[MANN] Mann, B.,"Cryptography with Matrices," The Pentagon, Vol
       21, Fall 1961.

[MANS] Mansfield, Louis C. S., "The Solution of Codes and
       Ciphers", Alexander Maclehose & Co., London, 1936.

[MARO] Marotta, Michael, E.  "The Code Book - All About
       Unbreakable Codes and How To Use Them," Loompanics
       Unlimited, 1979.  [This is a terrible book.  Badly
       written, without proper authority, unprofessional, and
       prejudicial to boot.  And, it has one of the better
       illustrations of the Soviet one-time pad with example,
       with three errors in cipher text, that I have corrected
       for the author.]

[MARS] Marshall, Alan, "Intelligence and Espionage in the Reign
       of Charles II," 1660-1665, Cambridge University, New
       York, N.Y., 1994.

[MART] Martin, James,  "Security, Accuracy and Privacy in
       Computer Systems," Prentice Hall, Englewood Cliffs,
       N.J., 1973.

[MAVE] Mavenel, Denis L.,  Lettres, Instructions Diplomatiques
       et Papiers d' Etat du Cardinal Richelieu, Historie
       Politique, Paris 1853-1877 Collection.

[MAYA] Coe, M. D., "Breaking The Maya Code," Thames and Hudson,
       New York, 1992.

[MAZU] Mazur, Barry, "Questions On Decidability and
       Undecidability in Number Theory," Journal of Symbolic
       Logic, Volume 54, Number 9, June, 1994.

[MELL] Mellen G.  1981. Graphic Solution of a Linear
       Transformation Cipher. Cryptologia. 5:1-19.

[MEND] Mendelsohn, Capt. C. J.,  Studies in German Diplomatic
       Codes Employed During World War, GPO, 1937.

[MERK] Merkle, Ralph, "Secrecy, Authentication and Public Key
       Systems," Ann Arbor, UMI Research Press, 1982.

[MER1] Merkle, Ralph, "Secure Communications Over Insecure
       Channels," Communications of the ACM 21, 1978, pp. 294-
       99.

[MER2] Merkle, Ralph and Martin E. Hellman, "On the Security of
       Multiple Encryption ," Communications of the ACM 24,
       1981, pp. 465-67.

[MER3] Merkle, Ralph and Martin E. Hellman, "Hiding
       Information and Signatures in Trap Door Knapsacks,"
       IEEE Transactions on Information Theory 24, 1978, pp.
       525-30.

[MILL] Millikin, Donald, " Elementary Cryptography ", NYU
       Bookstore, NY, 1943.

[MM]   Meyer, C. H., and Matyas, S. M., " CRYPTOGRAPHY - A New
       Dimension in Computer Data Security, " Wiley
       Interscience, New York, 1982.

[MODE] Modelski, Tadeusz, 'The Polish Contribution to the
       Ultimate Allied Victory in the Second World War',
       Worthing (Sussex) 1986.

[MRAY] Mrayati, Mohammad, Yahya Meer Alam and Hassan al-
       Tayyan., Ilm at-Ta'miyah wa Istikhraj al-Mu,amma Ind
       al-Arab. Vol 1. Damascus: The Arab Academy of Damascus.,
       1987.

[MULL] Mulligan, Timothy," The German Navy Examines its
       Cryptographic Security, Oct. 1941, Military affairs, vol
       49, no 2, April 1985.

[MYER] Myer, Albert, "Manual of Signals," Washington, D.C.,
       USGPO, 1879.


[NBS]  National Bureau of Standards, "Data Encryption
       Standard," FIPS PUB 46-1, 1987.

[NIBL] Niblack, A. P., "Proposed Day, Night and Fog Signals for
       the Navy with Brief Description of the Ardois Hight
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[NIC1] Nichols, Randall K., "Xeno Data on 10 Different
       Languages," ACA-L, August 18, 1995.

[NIC2] Nichols, Randall K., "Chinese Cryptography Parts 1-3,"
       ACA-L, August 24, 1995.


[NIC3] Nichols, Randall K., "German Reduction Ciphers Parts
       1-4," ACA-L, September 15, 1995.

[NIC4] Nichols, Randall K., "Russian Cryptography Parts 1-3,"
       ACA-L, September 05, 1995.

[NIC5] Nichols, Randall K., "A Tribute to William F. Friedman",
       NCSA FORUM, August 20, 1995.

[NIC6] Nichols, Randall K., "Wallis and Rossignol,"  NCSA
       FORUM, September 25, 1995.

[NIC7] Nichols, Randall K., "Arabic Contributions to
       Cryptography,", in The Cryptogram, ND95, ACA, 1995.

[NIC8] Nichols, Randall K., "U.S. Coast Guard Shuts Down Morse
       Code System," The Cryptogram, SO95, ACA publications,
       1995.

[NIC9] Nichols, Randall K., "PCP Cipher," NCSA FORUM, March 10,
       1995.

[NICX] Nichols, R. K., Keynote Speech to A.C.A. Convention,
       "Breaking Ciphers in Other Languages.," New Orleans,
       La., 1993.

[NICK] Nickels, Hamilton, "Codemaster: Secrets of Making and
       Breaking Codes," Paladin Press, Boulder, CO., 1990.

[NORM] Norman, Bruce, 'Secret Warfare', David & Charles,
       Newton Abbot (Devon) 1973.

[NORW] Marm, Ingvald and Sommerfelt, Alf, "Norwegian," Teach
       Yourself Books, Hodder and Stoughton, London, 1967.

[NSA]  NSA's Friedman Legacy - A Tribute to William and
       Elizabeth Friedman, NSA Center for Cryptological
       History, 1992, pp 201 ff.

[OKLA] Andre, Josephine and Richard V. Andree, "Cryptarithms,"
       Unit One, Problem Solving and Logical Thinking,
       University of Oklahoma, Norman, Ok.  Copy No: 486, 1976.

[OKLI] Andre, Josephine and Richard V. Andree, " Instructors
       Manual For Cryptarithms," Unit One, Problem Solving and
       Logical Thinking, University of Oklahoma, Norman, Ok.
       Copy No: 486, 1976.

[OP20] "Course in Cryptanalysis," OP-20-G', Navy Department,
       Office of Chief of Naval Operations, Washington, 1941.

[PERR] Perrault, Charles, Tallement des Reaux, Les
       Historiettes, Bibliotheque del La Pleiade, Paris 1960,
       pp 256-258.

[PGP]  Garfinkel, Simson, "PGP: Pretty Good Privacy," O'reilly
       and Associates, Inc. Sebastopol, CA. 1995.

[PHIL] Phillips, H., "My Best Puzzles in Logic and Reasoning,"
       Dover, 1961.

[PIER] Pierce, Clayton C., "Cryptoprivacy", 325 Carol Drive,
       Ventura, Ca. 93003.

[POLY] Polya, G., "Mathematics and Plausible Reasoning,"
       Princeton Press, 1954.

[POL1] Polya, G., "How To Solve It.," Princeton Press, 1948.

[POPE] Pope, Maurice, "The Story of Decipherment: From Egyptian
       Hieroglyphic to Linear B., Thames and Hudson Ltd., 1975.

[PORT] Barker, Wayne G. "Cryptograms in Portuguese," Aegean
       Park Press, Laguna Hills, CA., 1986.

[POR1] Aliandro, Hygino, "The Portuguese-English Dictionary,"
       Pocket Books, New York, N.Y., 1960.

[PRIC] Price, A.,"Instruments of Darkness: the History of
       Electronic Warfare, London, Macdonalds and Janes, 1977.

[RAJ1] "Pattern and Non Pattern Words of 2 to 6 Letters," G &
       C.  Merriam Co., Norman, OK. 1977.

[RAJ2] "Pattern and Non Pattern Words of 7 to 8 Letters," G &
       C.  Merriam Co., Norman, OK. 1980.

[RAJ3] "Pattern and Non Pattern Words of 9 to 10 Letters," G &
       C.  Merriam Co., Norman, OK. 1981.

[RAJ4] "Non Pattern Words of 3 to 14 Letters," RAJA Books,
       Norman, OK. 1982.

[RAJ5] "Pattern and Non Pattern Words of 10 Letters," G & C.
       Merriam Co., Norman, OK. 1982.

[REJE] Rejewski, Marian, "Mathematical Solution of the Enigma
       Cipher" published in vol 6, #1, Jan 1982 Cryptologia pp
       1-37.

[RENA] Renauld, P. "La Machine a' chiffrer 'Enigma'", Bulletin
       Trimestriel de l'association des Amis de L'Ecole
       superieure de guerre no 78, 1978.

[RHEE] Rhee, Man Young, "Cryptography and Secure Commun-
       ications,"  McGraw Hill Co, 1994

[RIVE] Rivest, Ron, "Ciphertext: The RSA Newsletter 1, 1993.

[RIV1] Rivest, Ron, Shamir, A and L. Adleman, "A Method for
       Obtaining Digital Signatures and Public Key
       Cryptosystems," Communications of the ACM 21, 1978.

[ROAC] Roach, T., "Hobbyist's Guide To COMINT Collection and
       Analysis," 1330 Copper Peak Lane, San Jose, Ca. 95120-
       4271, 1994.

[ROBO] NYPHO, The Cryptogram, Dec 1940, Feb, 1941.

[ROHE] Jurgen Rohwer's Comparative Analysis of Allied and Axis
       Radio-Intelligence in the Battle of the Atlantic,
       Proceedings of the 13th Military History Symposium, USAF
       Academy, 1988, pp 77-109.

[ROHW] Rohwer Jurgen,  "Critical Convoy Battles of March 1943,"
       London, Ian Allan, 1977.

[ROH1] Rohwer Jurgen, "Nachwort: Die Schlacht im Atlantik in
       der Historischen Forschung, Munchen: Bernard and Graefe,
       1980.

[ROH2] Rohwer Jurgen, et. al. , "Chronology of the War at Sea,
       Vol I, 1939-1942, London, Ian Allan, 1972.

[ROH3] Rohwer Jurgen, "U-Boote, Eine Chronik in Bildern,
       Oldenburs, Stalling, 1962. Skizzen der 8 Phasen.

[ROOM] Hyde, H. Montgomery, "Room 3603, The Story of British
       Intelligence Center in New York During World War II",
       New York, Farrar, Straus, 1963.

[ROSE] Budge, E. A. Wallis, "The Rosetta Stone," British Museum
       Press, London, 1927.

[RSA]  RSA Data Security, Inc., "Mailsafe: Public Key
       Encryption Software Users Manual, Version 5.0, Redwood
       City, CA, 1994

[RUNY] Runyan, T. J. and Jan M. Copes "To Die Gallently",
       Westview Press 1994, p85-86 ff.

[RYSK] Norbert Ryska and Siegfried Herda, "Kryptographische
       Verfahren in der Datenverarbeitung," Gesellschaft fur
       Informatik, Berlin, Springer-Verlag1980.

[SADL] Sadler, A. L., "The Code of the Samurai," Rutland and
       Tokyo: Charles E. Tuttle Co., 1969.

[SACC] Sacco, Generale Luigi, " Manuale di Crittografia",
       3rd ed., Rome, 1947.

[SALE] Salewski, Michael, "Die Deutscher Seekriegsleitung,
       1938- 1945, Frankfurt/Main: Bernard and Graefe, 1970-
       1974.  3 volumes.

[SANB] Sanbohonbu, ed., "Sanbohonbu kotokan shokuinhyo." NIDS
       Archives.

[SAPR] Sapir, E., "Conceptual Categories in Primitive
       Language," Science: 74: 578-584., 1931.

[SASS] Sassoons, George, "Radio Hackers Code Book", Duckworth,
       London, 1986.

[SCHN] Schneier, Bruce, "Applied Cryptography: Protocols,
       Algorithms, and Source Code C," John Wiley and Sons,
       1994.

[SCH2] Schneier, Bruce, "Applied Cryptography: Protocols,
       Algorithms, and Source Code C," 2nd ed., John Wiley and
       Sons, 1995.

[SCHU] Schuh, fred, "Master Book of Mathematical Recreation,"
       Dover, 1968.

[SCHW] Schwab, Charles, "The Equalizer," Charles Schwab, San
       Francisco, 1994.

[SEBE] Seberry, Jennifer and Joseph Pieprzyk, "Cryptography: An
       Introduction to Computer Security," Prentice Hall, 1989.
       [CAREFUL!  Lots of Errors - Basic research efforts may
       be flawed - see Appendix A pg 307 for example.]

[SHAN] Shannon, C. E., "The Communication Theory of Secrecy
       Systems," Bell System Technical Journal, Vol 28 (October
       1949).

[SHIN] Shinsaku Tamura, "Myohin kosaku," San'ei Shuppansha,
       Toyko, 1953.

[SIG1] "International Code Of Signals For Visual, Sound, and
       Radio Communications,"  Defense Mapping Agency,
       Hydrographic/Topographic Center, United States Ed.
       Revised 1981

[SIG2] "International Code Of Signals For Visual, Sound, and
       Radio Communications,"  U. S. Naval Oceanographic
       Office, United States Ed., Pub. 102,  1969.

[SIMM] Simmons, G. J., "How To Insure that Data Acquired to
       Verify Treaty Compliance are Trustworthy, " in
       "Authentication without secrecy: A secure communications
       problem uniquely solvable by asymmetric encryption
       techniques.", IEEE EASCON 79, Washington, 1979, pp. 661-
       62.

[SINK] Sinkov, Abraham, "Elementary Cryptanalysis", The
       Mathematical Association of America, NYU, 1966.

[SISI] Pierce, C.C., "Cryptoprivacy," Author/Publisher, Ventura
       Ca., 1995. (XOR Logic and SIGTOT teleprinters)

[SMIH] Smith, David E., "John Wallis as Cryptographer",
       Bulletin of American Mathematical Society, XXIV, 1917.

[SMIT] Smith, Laurence D., "Cryptography, the Science of Secret
       Writing," Dover, NY, 1943.

[SOLZ] Solzhenitsyn, Aleksandr I. , "The Gulag Archipelago I-
       III, " Harper and Row, New York, N.Y., 1975.


[SPAN] Barker, Wayne G. "Cryptograms in Spanish," Aegean Park
       Press, Laguna Hills, CA., 1986.

[STEV] Stevenson, William, 'A Man Called INTREPID',
       Macmillan, London 1976.

[STIN] Stinson, D. R., "Cryptography, Theory and Practice,"
       CRC Press, London, 1995.

[STIX] Stix, F., Zur Geschicte und Organisation  der Wiener
       Geheimen Ziffernkanzlei, Mitteilungen des
       Osterreichischen Instituts fir Geschichtsforschung,
       LI 1937.

[STUR] Sturtevant, E. H. and Bechtel, G., "A Hittite
       Chrestomathy," Linguistic Society of American and
       University of Pennsylvania, Philadelphia, 1935.

[SUVO] Suvorov, Viktor "Inside Soviet Military Intelligence,"
       Berkley Press, New York, 1985.

[TERR] Terrett, D., "The Signal Corps: The Emergency (to
       December 1941); G. R. Thompson, et. al, The Test(
       December 1941 -  July 1943); D. Harris and G. Thompson,
       The Outcome;(Mid 1943 to 1945), Department of the Army,
       Office of the Chief of Military History, USGPO,
       Washington,1956 -1966.

[THEO] Theodore White and Annalee Jacoby, "Thunder Out Of
       China," William Sloane Assoc., New York, 1946.

[THOM] Thompson, Ken, "Reflections on Trusting Trust,"
       Communications of the ACM 27, 1984.

[TILD] Glover, D. Beaird, Secret Ciphers of The 1876
       Presidential Election, Aegean Park Press, Laguna Hills,
       Ca. 1991.

[TM32] TM 32-250, Fundamentals of Traffic Analysis (Radio
       Telegraph) Department of the Army, 1948.

[TRAD] U. S. Army Military History Institute, "Traditions of
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[TRAI] Lange, Andre and Soudart, E. A., "Treatise On
       Cryptography," Aegean Park Press, Laguna Hills, Ca.
       1981.

[TRIB] Anonymous, New York Tribune, Extra No. 44, "The Cipher
       Dispatches, New York, 1879.

[TRIT] Trithemius:Paul Chacornac, "Grandeur et Adversite de
       Jean Tritheme ,Paris: Editions Traditionelles, 1963.

[TUCK] Harris, Frances A., "Solving Simple Substitution
       Ciphers," ACA, 1959.


[TUKK] Tuckerman, B.,  "A Study of The Vigenere-Vernam Single
       and Multiple Loop Enciphering Systems," IBM Report
       RC2879, Thomas J. Watson Research Center, Yorktown
       Heights, N.Y.  1970.

[TUCM] Tuckerman, B., "A Study of The Vigenere-Vernam Single
       and Multiple Loop Enciphering Systems," IBM Report
       RC2879, Thomas J. Watson Research Center, Yorktown
       Heights, N.Y.  1970.

[UBAL] Ubaldino Mori Ubaldini, "I Sommergibili begli Oceani: La
       Marina Italian nella Seconda Guerra Mondiale," vol XII,
       Roma, Ufficio Storico della Marina Militare, 1963.

[USAA] U. S. Army, Office of Chief Signal Officer,
       "Instructions for Using the Cipher Device Type M-94,
       February, 1922," USGPO, Washington, 1922.

[VAIL] Vaille, Euggene, Le Cabinet Noir, Paris Presses
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[VALE] Valerio, "De La Cryptographie," Journal des Scienses
       militares, 9th series, Dec 1892 - May 1895, Paris.

[VAND] Van de Rhoer, E., "Deadly Magic: A personal Account of
       Communications Intilligence in WWII in the Pacific, New
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       Secret Wire and Radio Telegraphic Communications," J.
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[VIAR] de Viaris in Genie Civil: "Cryptographie", Publications
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[VIA1] de Viaris, "L'art de chiffre et dechiffre les depeches
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[VOGE] Vogel, Donald S., "Inside a KGB Cipher," Cryptologia,
       Vol XIV, Number 1, January 1990.

[WALL] Wallis, John, "A Collection of Letters and other Papers
       in Cipher" , Oxford University, Bodleian Library, 1653.

[WAL1] Wallace, Robert W. Pattern Words: Ten Letters and Eleven
       Letters in Length, Aegean Park Press, Laguna Hills, CA
       92654, 1993.

[WAL2] Wallace, Robert W. Pattern Words: Twelve Letters and
       Greater in Length, Aegean Park Press, Laguna Hills, CA
       92654, 1993.

[WATS] Watson, R. W. Seton-, ed, "The Abbot Trithemius," in
       Tudor Studies, Longmans and Green, London, 1924.

[WEBE] Weber, Ralph Edward, "United States Diplomatic Codes and
       Ciphers, 1175-1938, Chicago, Precedent Publishing, 1979.

[WEL]  Welsh, Dominic, "Codes and Cryptography," Oxford Science
       Publications, New York, 1993.

[WELC] Welchman, Gordon, 'The Hut Six Story', McGraw-Hill,
       New York 1982.

[WHOR] Whorf, B. L., "A Linguistic Consideration of Thinking In
       Primitive Communities,"  In Language, Thought, and
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       B.  Carroll, Cambridge, MA: MIT Press, pp. 65-86., 1956.

[WINT] Winton, J., " Ultra at Sea: How Breaking the Nazi Code
       Affected Allied Naval Strategy During WWII," New Uork,
       William Morror, 1988.

[WINK] Winkle, Rip Van, "Hungarian: The Cryptogram,", March -
       April 1956.

[WINT] Winterbotham, F.W., 'The Ultra Secret', Weidenfeld
       and Nicolson, London 1974.

[WOLE] Wolfe, Ramond W., "Secret Writing," McGraw Hill Books,
       NY, 1970.

[WOLF] Wolfe, Jack M., " A First Course in Cryptanalysis,"
       Brooklin College Press, NY, 1943.

[WRIX] Wrixon, Fred B. "Codes, Ciphers and Secret Languages,"
       Crown Publishers, New York, 1990.

[XEN1] PHOENIX, "Xenocrypt Handbook," American Cryptogram
       Association, 1 Pidgeon Dr., Wilbraham, MA., 01095-2603,
       for publication March, 1996.

[YARD] Yardley, Herbert, O., "The American Black Chamber,"
       Bobbs-Merrill, NY, 1931.

[YAR1] Yardley, H. O., "The Chinese Black Chamber," Houghton
       Mifflin, Boston, 1983.

[YOKO] Yukio Yokoyama, "Tokushu joho kaisoka," unpublished
       handwritten manuscript.

[YOUS] Youshkevitch, A. P., Geschichte der Mathematik im
       Mittelatter, Liepzig, Germany: Teubner, 1964.

[YUKI] Yukio Nishihara, "Kantogan tai-So Sakusenshi," Vol 17.,
       unpublished manuscript, National Institute for Defense
       Studies Military Archives, Tokyo.,(hereafter NIDS
       Archives)

[ZIM]  Zim, Herbert S., "Codes and Secret Writing." William
       Morrow Co., New York, 1948.

[ZEND] Callimahos, L. D.,  Traffic Analysis and the Zendian
       Problem, Agean Park Press, 1984.  (also available
       through NSA Center for Cryptologic History)
 

 

Links to Lanakis Classical Cryptography Course, Lectures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

 

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