1. Basic Cryptology

2. 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)

3. Parts of a Cipher Alphabet Position Key
The number of the letter from 1-26 (i.e. A=1 B=2…etc.)
Key
The operation used to encipher or decipher a code 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 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

4. 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”

5. 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”

6. 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

7. 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)

8. 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

9. Vigenere Square

10. 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

11. English Alphabet Frequency Table
Letter Relative Frequency E % 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%

12. 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

13. Frequency Table 1- Q 7- R 1- S 13- T 12- U 3- V 0- W 8- X 11- Y 14- Z
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

14. 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

15. 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

16. 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.

17. References
Cryptology. (n.d.). Retrieved September 24, 2009, from
Knight, J. (2004). Cryptology, History. Retrieved September 24, 2009, from
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 graphy/cryptography.htm