Transcript Cryptology - Mu Alpha Theta

BASIC CRYPTOLOGY
What is Cryptology?

Cryptology is the umbrella word that represents the
art of enciphering words so as to protect their
original meaning (cryptography) and also
represents the science of breaking these enciphered
codes (cryptanalysis)
Parts of a Cipher

Alphabet Position
 The
number of the letter from 1-26 (i.e. A=1
B=2…etc.)
A B C
D E F G H I
0 0 0
1 2 3
0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2
4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6

J
K L
M N O P Q R S T U V W X Y Z
Key
 The
operation used to encipher or decipher a code
The Key


Used to change cipher-text to plain-text or vice versa
Always in the form of N=Ax+B
N being the resulting alphabet position number
 A being the multiplicative number
 B being the additive number
 X being the original alphabet position


Example: N=3x+2 for letter “b”

N=3(2)+2

N=6+2

N=8

“h”
Wraparound

Wraparound is the term used to define the act of
restarting a series when the end is reached

e.g. Assigning 4 blocks 3 different colors in order; the colors
being red, green, and blue.

Block 1-red, Block 2-green, Block 3-blue, Block 4-red


Wraparound caused the sequence of colors to restart in order to
complete the task
In cryptology, wraparound is used when N>26

e.g. N=6(3)+10

N=28

28-26=2
 “b”
The Modulus Function

The denotation of the “wraparound formula” is
donated by the inclusion of a “mod”
 From
the previous example:
 28-26=2


28mod26=2
The modulus function also works in multiples
 54mod26
also equals 2
 54-26=28

28-26=2
Types of Basic Cryptography

Additive
 Cipher
involving the shift of letters by a set number of
places

Multiplicative
 Cipher
involving the multiplication of a letter’s position
by a set amount

Affine
 Combination

of multiplicative and additive
Vigenere
 Use
of a system of alphabets shifted additively 26
times over (Vigenere Square)
Multiplicative Complications

Occasionally when two numbers are decoded using
a multiplicative cipher, they come out to equal the
same number
 To
deter this, only numbers that are relatively prime to
26 may be used
 1,
3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25
Vigenere Square
Cryptanalysis


The most important part of Cryptanalysis is the
Frequency Table
When a message is enciphered, every letter
corresponds to a plain-text letter, so the frequency
should be the same


Ergo, the frequency for an enciphered ‘e’ will be the same
as the plain-text ‘e’ in the original message
Generally, an enciphered message is placed into blocks
of 4 or 5 letters, making it harder for the cryptanalyst
to decode the message
English Alphabet Frequency Table
Letter Relative Frequency
E
11.1607%
M
3.0129%
A
8.4966%
H
3.0034%
R
7.5809%
G
2.4705%
I
7.5448%
B
2.0720%
O
7.1635%
F
1.8121%
T
6.9509%
Y
1.7779%
N
6.6544%
W
1.2899%
S
5.7351%
K
1.1016%
L
5.4893%
V
1.0074%
C
4.5388%
X
0.2902%
U
3.6308%
Z
0.2722%
D
3.3844%
J
0.1965%
P
3.1671%
Q
0.1962%
Additive Cipher

ROLKY HAZGC GRQOT MYNGJ UCGVU UXVRG
EKXZN GZYZX AZYGT JLXKZ
YNOYN UAXAV UTZNK YZGMK GTJZN KTOYN
KGXJT USUXK OZOYG ZGRKZ
URJHE GTOJO UZLAR RULYU ATJGT JLAXE YOMTO
LEOTM TUZNO TMGHI
Frequency Table
7- A
0 -B
2- C
0- D
4- E
0 -F
15- G
3- H
1- I
8- J
9- K
6- L
5- M
8- N
12- O
0- P
1- Q
7- R
1- S
13- T
12- U
3- V
0- W
8- X
11- Y
14- Z
G to E

PMJIW FYXEA EPOMR KWLEH SAETS SVTPE CIVXL
EXWXV YXWER HJVIX
WLMWL SYVYT SRXLI WXEKI ERHXL IRMWL IEVHR
SQSVI MXMWE XEPIX
SPHFC ERMHM SXJYP PSJWS YRHER HJYVC
WMKRM JCMRK RSXLM RKEFG
G to A

LIFES BUTAW ALKIN GSHAD OWAPO ORPLA
YERTH ATSTR UTSAN DFRET SHISH OURUP ONTHE
STAGE ANDTH ENISH EARDN OMORE ITISA TALET
OLDBY ANIDI OTFUL LOFSO UNDAN DFURY SIGNI
FYING NOTHI NGABC
Text Manipulated

LIFE'S BUT A WALKING SHADOW, A POOR PLAYER
THAT STRUTS AND FRETS HIS HOUR UPON THE
STAGE AND THEN IS HEARD NO MORE: IT IS A
TALE TOLD BY AN IDIOT, FULL OF SOUND AND
FURY, SIGNIFYING NOTHING.
References





Cryptology. (n.d.). Retrieved September 24, 2009, from
http://www.resonancepub.com/homecrypto.htm
Knight, J. (2004). Cryptology, History. Retrieved September 24, 2009, from
http://www.encyclopedia.com/doc/1G2-3403300200.html
Lewand, R. E. (2000). Cryptological Mathematics (Classroom Resource Materials).
Washington: The Mathematical Association Of America.
Singh, S. (2000). The Code Book: The Science of Secrecy from Ancient Egypt to
Quantum Cryptography. New York: Anchor.
Waggener, J. (1998, June 11). CRYPTOGRAPHY. Retrieved September 24, 2009,
from
http://jwilson.coe.uga.edu/emt668/EMT668.Folders.F97/Waggener/Units/Crypto
graphy/cryptography.htm