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]
[ACA] ACA and You, "Handbook For Members of the American
Cryptogram Association," ACA publications, 1995.
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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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