Transcript Properties of Cipher Texts - Trinity College Computer

Expert System for
Analyzing Simple Ciphers:
Properties of Cipher Texts
Carolyn Rucci
Advisor: Ralph Morelli
1 year project
Overview


What are letter frequencies and index of coincidence.
What index of coincidence and patterns of letter
frequencies does each cipher follow?







Transposition
Caesar
Affine
Vigenère
Playfair
Summary
What next?
Review of Letter Frequencies and
Index of Coincidence

Letter Frequencies
abcdef ghijklmnopqrstuvwxyz
monographic frequency distribution of normal alphabet

Index of Coincidence
thisisatestoftheindexofcoincidenceinmessages
thisisatestoftheindexofcoincidenceinmessagesthi
5matches / 44letters ~ 11%
Transposition Cipher

Simply rearranges the letters  same letters
present in cipher text as plain text
 Reverse
text:
there once was a cat named fred
derf deman tac a saw ecno ereht

Conclusion: Frequency distribution will be the same.
Caesar

Each cipher letter corresponds to the plain
text letter three after it.


Plain Alphabet: 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
Caesar Alphabet: d e f g h i j k l m n o p q r s t u v w x y z a b c
the quick fox jumped
over the lazy dog

Shift
3
wkh txlfn ira mxpshg
ryhu wkh odcb grj
Conclusion: Frequency distribution will
match when shifted three spots.
Affine

Each cipher letter corresponds to exactly one plain text
letter.
C = (aP + b) mod 26
Ex: a=4 and b=5:
A = (4*1 + 5) mod 26
= 9 I
Conclusion:
Plain
remainder
Cipher
B
13
M
C
17
Q
D
21
U
E
25
Y
F
3
C
Same frequencies will be present but in a
random order.
Vigenère

Many cipher alphabets
created based on keyword.
 Conclusion: No pattern to
letter frequencies.
 Find identical sequences of
letters.
the frog jumping the fence…
dlc bffj tyklwej dlc bsefo…
 Calculate interval bt/w
sequences
 If interval between two
occurrences has common factor
 length of keyword
ABCDEF…XYZ
C
I
P
H
E
R
ABCDEF…XYZ
BCDEFG…YZA
C D E F GH … Z A B
:
Y Z A B C D ... V W X
ZABCDE…WXY
ABC DEF…XYZ
K
E
Y
W
O
R
D
KLMNOP …HIJ
EFGHIJK…BCD
YZABCD …VWX
WXYZAB …UVW
OPQRST …LMN
RSTUVW …OPQ
DEFGH I …ABC
Playfair

Mixed alphabetic sequence of 25 letters is written into
a 5x5 square (J normally omitted).
D
C
Q
Z
L
B
O
Y
A
U
M
X
R
K
H
Conclusion:
W
G
F
T
M
I
E
S
P
V
Case1: 2corners  replace
w/other corners
Case2: same row  replace
w/letters to right
Case3: same column  replace
w/letters below
No pattern of letter frequencies.
Summary of Findings
Index of
Coincidence
Frequency Distribution
(compared to normal)
Transposition
~6.6%
Same
Caesar
~6.6%
Will match if shifted 3 to right
Affine
~6.6%
Vigenère
~3.8%
Same frequencies present but in
different orders
Flat distribution
Playfair
~3.8%
Flat distribution
Review of Letter Frequencies and
Index of Coincidence

Letter Frequencies
abcdef ghijklmnopqrstuvwxyz
monographic frequency distribution of normal alphabet

Index of Coincidence
thisisatestoftheindexofcoincidenceinmessages
thisisatestoftheindexofcoincidenceinmessagesthi
5matches / 44letters ~ 11%
What Next?


Finalize criteria for distinguishing between
Vigenère and Playfair ciphers.
Create a Java program that:
1)
2)
Examines index of coincidence and patterns of
frequencies
Uses this information to determine which cipher
was used