EnigmaMeghan Emilio

Advisor: Professor Ralph Morelli

April 2004

Objective

There are two main objectives of this project First, to create a working simulation of an

Engima machine that is as faithful as possible. Second, to create a program which will “break”

Engima. That is, decrypt messages even if little or no information about the original settings is known.

What is Enigma?

Electrical enciphering machine widely used by the German Military during WWII.

Three rotating rotors. Breaking Enigma a

turning point of the war.

Rotors First rotor rotates

each time a character is input.

The second rotor rotates once each time the first rotor makes one full turn.

The third rotor rotates once each time the second rotor has rotated completely.

Plug Board

Swaps pairs of letters, automatically, both before and after each character passes through the rotors.

Major difference between commercial and military Enigma.

Putting It All Together

Swap

Swap

Swap

Swap

Input Output

Swap

Accomplished

Created an Enigma Simulation Input English/Encrypted text and

output Encrypted text/English Java Applet Faithful to rotor wirings and

reflectors used during WWII

Accomplished

Created an Analyzer Input encrypted text and output original English text No other input information is needed Assumes possession of an Enigma machine Assumes text was encrypted without a plug board Searches through possible decryptions and choosing

the best one Uses Index of Coincidence (IC) as a scoring function

What is Index of Coincidence?

Index of Coincidence (IC) is defined to be the probability that two randomly selected letters will be identical.

It was introduced by William Friedman in The Index of Coincidence and its Applications in Cryptography (1920).

IC is a statistical measure which distinguishes text encrypted with a polyalphabetic substitution cipher from text encrypted with a monoalphabetic substitution cipher.

Calculating the IC

The formula used to calculate IC:

Σ(fi * (fi-1))

N(N-1) where 0 > i > 25, fi is the frequency in the sample of the ith letter of

the alphabet, and N is the total number of letters in the sample Every language has such an IC, for example:

English: 0.0667 German: 0.0762 Spanish: 0.0775

The IC for random text (even distribution of letters) is 0.0385

Why IC?

Text encrypted by Enigma is polyalphabetic, so IC can distinguish easily between encrypted text and English.

Allows for a heuristic algorithm Instead of searching all possible decryptions, take

the first one that comes close to 0.0667 Effective on larger sample sizes (comparable to

exhaustive search) More efficient (comparable to rotor setting)

Problems with IC The effectiveness of IC depends on the

size of the sample:

50 Characters

0.03

0.04

0.05

0.06

0.07

300 Characters

0.03

0.04

0.05

0.06

0.07

Actual Distribution

0.03

0.04

0.05

0.06

0.07

Results

Effectiveness

0

20

40

60

80

100

120

50 100 200 300

Sample Size (Characters)

Per

cent

age

Cor

rect

Iterative Search

Heuristic Search

Efficiency

0

5

10

15

20

25

30

50 chars 100 chars 200 chars 300 chars

Sample Size (Characters)

Tim

e (H

ours

) Iterative Search

Heuristic Search 1

Heuristic Serach 2

Future Work

Plug BoardSimple Substitution Analyzer

ImprovementsDistributed Computing Better Heuristic Algorithm

References History of the Enigma Machine. <http://

www.ugrad.cs.jhu.edu/~russell/classes/enigma/history.html>. Cryptography -- Enigma Cipher. <http://www.trincoll.edu/depts/cpsc/cryptography/enigma.html>. The German Enigma Cipher Machine – History of Solving. <http://

home.us.net/~encore/Enigma/text.html>. Hodges, Andrew. Alan Turing the Enigma. New York: Simon & Schuster,

Inc., 1983. Carlson, Andy. Simulating the Engima.

<http://homepages.tesco.net/~andycarlson/enigma/simulating_enigma.html>.

Pictures © 1995, Morton Swimming, <http://www.swimmer.org/morton/enigma.html>.

Questions?