Cryptanalysis - Polyalphabetic Ciphers

from  Senior Mathematics Thesis                                            
Hollins University

One of the world's most widely used methods of cryptanalysis is the polyalphabetic substitution cipher. The system behind the polyalphabetic cipher is that more than one alphabet is used to encipher a message and there is a particular order in which these alphabets are used.  The encipherer has 9 or 26 possible alphabets, depending on whether he uses a keydigit or a keyword.  To decipher the message, one must know the  keydigit or the keyword.

The following are "secret" messages about Hollins.  The first was enciphered with a keydigit and the second was enciphered with a keyword.   Can you figure out what they say?   (Need help?  Study example I and example II given below.) 

In her mathematics thesis, a Hollins senior designed and implemented several algorithms to decipher these and similar messages.

Message I (use a keydigit)
UWAEN TJTNT RUTYU ONFZF CBRPV XCPRM VSIUD TIJWI NTFLI GYSFW VJHED MRJXT
NFSUJ AGTUO IESXD BDTJS KFWDB DHVSD SJDUM NJLHU WIOLN JLHUF NEHOU NLMNO
OKOSR TIJTJ JSUMA UFIOI GFSES FTJTN TIFIT LMNNT XTVIE OYSUT EBHHP YHFWA OITPY 
HFHOM QEHJ

Message II (use a keyword)
MPVCM ELBVD YKBWA SWEHB QOWZZ VRNXF UMNBI JHZGP SIMPR ZQVTA HBIJX MXSRX
MPRSH CXIAN XYXXE YJCBO NDISN BFREC EFRCE TKMQD SKAMP EPKBD NDMFG WSCSL
GLYOE IGQAQ ZZKBH YYJYM RVMEZ ANXHZ HLRZI EWMAD XYHCT RXTAI EVIJE MJSWT
HKXO

 



Example I (keydigit)  

The following cipher has been coded (and so should be decoded) using the keydigit 346. 

KSROMTVMYYMXJMTLEYIMXVXIKEXWIXHHCRQKQWIRPRHKK

When decoding (see below), if a 3 appears above a cipher letter then that letter should be replaced according to the 3-alphabet (i.e. with the letter that appears in the alphabet 3 positions to the left).  Use the decipher chart below to finish decoding the following sentence about Hollins.

keynumber 3 4 6 3 4 6 3 4 6 3 4 6 3 4 6 3 4 6 3 4 6 3 4 6 3 4 6
cipher K S R O M T V M Y Y M X J M T L E Y I M X V X I K E X
message H O L L I N S I S
keynumber 3 4 6 3 4 6 3 4 6 3 4 6 3 4 6 3 4 6
cipher W I X H H C R Q K Q W I R P R H K K
message

Decipher Chart for Key Digits

cipher letter 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
                                                   
0 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
1 alphabet 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
2 alphabet Y 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
3 alphabet X Y Z A B C D E F G H I J K L M N O P Q R S T U V W
4 alphabet W X Y Z A B C D E F G H I J K L M N O P Q R S T U V
5 alphabet V W X Y Z A B C D E F G H I J K L M N O P Q R S T U
6 alphabet U V W X Y Z A B C D E F G H I J K L M N O P Q R S T
7 alphabet T U V W X Y Z A B C D E F G H I J K L M N O P Q R S
8 alphabet S T U V W X Y Z A B C D E F G H I J K L M N O P Q R
9 alphabet R S T U V W X Y Z A B C D E F G H I J K L M N O P Q

 



Example II (keyword)

The following cipher has been coded (and should be decoded) using the keyword "math."

OHTYXELSQWBZOOVRQILOANHYQDTZFHXMAUGKQRHMTOESUNL

When decoding (see below), if a "m" appears above a cipher letter then that letter should be replaced according to the m-alphabet.  Use the decipher chart below to finish decoding the following sentence about Hollins.

keyword m a t h m a t h m a t h m a t h m a t h m a t h

cipher

O H T Y X E L S Q W B Z O O V R Q I L O A N H Y
message c h a r l e s l e w I s c o c k e i
keyword m a t h m a t h m a t h m a t h m a t h m a t h
cipher Q D T Z F H X M A U G K Q R H M T O E S U N L
message

 

Decipher Chart for Key Letters A - Z

cipher letter 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 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
B alphabet 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
C alphabet 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 B
D 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
E alphabet 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 D
F alphabet F G H I J K L M N O P Q R S T U V W X Y Z A B C D E
G alphabet G H I J K L M N O P Q R S T U V W X Y Z A B C D E F
H alphabet H I J K L M N O P Q R S T U V W X Y Z A B C D E F G
I alphabet I J K L M N O P Q R S T U V W X Y Z A B C D E F G H
J alphabet J K L M N O P Q R S T U V W X Y Z A B C D E F G H I
K alphabet K L M N O P Q R S T U V W X Y Z A B C D E F G H I J
L alphabet L M N O P Q R S T U V W X Y Z A B C D E F G H I J K
M alphabet M N O P Q R S T U V W X Y Z A B C D E F G H I J K L
N alphabet N O P Q R S T U V W X Y Z A B C D E F G H I J K L M
O alphabet O P Q R S T U V W X Y Z A B C D E F G H I J K L M N
P alphabet P Q R S T U V W X Y Z A B C D E F G H I J K L M N O
Q alphabet Q R S T U V W X Y Z A B C D E F G H I J K L M N O P
R alphabet R S T U V W X Y Z A B C D E F G H I J K L M N O P Q
S alphabet S T U V W X Y Z A B C D E F G H I J K L M N O P Q R
T alphabet T U V W X Y Z A B C D E F G H I J K L M N O P Q R S
U alphabet U V W X Y Z A B C D E F G H I J K L M N O P Q R S T
V alphabet V W X Y Z A B C D E F G H I J K L M N O P Q R S T U
W alphabet W X Y Z A B C D E F G H I J K L M N O P Q R S T U V
X alphabet X Y Z A B C D E F G H I J K L M N O P Q R S T U V W
Y alphabet Y 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
Z alphabet 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