Lesson 9: German Reduction Ciphers: Enigma In Historical And Modern Times
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.
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 11
and 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 the
offset 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.
-------------------
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written, clear to understand but as authoritative as
they come! ]
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[LYNC] Lynch, Frederick D., "Pattern Word List, Vol 1.,"
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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.]
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[CAREFUL! Lots of Errors - Basic research efforts may
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[SHAN] Shannon, C. E., "The Communication Theory of Secrecy
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