Information Science
Comap
Chapter 17
Sections 17.3 and 17.4
Micheal Kim
Objectives
Understand what cryptology is
Understand the basic logic behind cryptosystems
Learn what Boolean logic is and how it can be used in
web searches
Cryptography
What is Cryptography?
Encryption
: the process of disguising data
Cryptology
: the study of methods to make and break
codes
Cryptography
Some examples:
Military and diplomatic transmissions
Internet credit

card transactions
A quick history lesson: September 1998
President Bill Clinton and Ireland’s Prime Minister Bertie
Ahern used digital signatures to sign an intergovernmental
document
Cryptography: The
Caesar Cipher
The earliest known cryptosystem
Used by Julius
Caeser
to send messages to his troops
How it works :
There is a message and a shift value of three
Translate the letters into numbers, according to A = 0
… Z = 25
Add the shift value to the letter and then rewrite the
corresponding letter of the new number
Cryptography: The
Caesar Cipher
Example:
ATTACK AT DAWN
Answer: DWWDFN DW GDZQ
Example 2:
ZLOOLDP & PDUB
Answer: William & Mary
Cryptography: Modular
Arithmetic
For more sophisticated cryptosystems it is
convenient to use a special kind of arithmetic known
as modular arithmetic.
For any positive integers
a
and
n
, we define
a
mod
n
to
be the remainder when
a
is divided by
n
.
Ex:
3 mod 2 =
37 mod 10 =
342 mod 85 =
Cryptography: Modular
Arithmetic
For more sophisticated cryptosystems it is
convenient to use a special kind of arithmetic known
as modular arithmetic.
For any positive integers
a
and
n
, we define
a
mod
n
to
be the remainder when
a
is divided by
n
.
Ex:
3 mod 2 = 1
37 mod 10 = 7
342 mod 85 = 2
Cryptography: Modular
Arithmetic
We often unconsciously use this concept.
Example: If I say it is September what month will it
be 25 months from now
Obviously October
How did you get to this?
25 = 2 * 12 + 1
Cryptography: Modular
Arithmetic
So back to the Caesar cipher, how does modular
arithmetic apply?
A = 0, B = 1, C = 2, … Z = 25
The cipher then replaces the letter in position
i
with
the letter in position (
i
+ 3)
mod
26
Cryptography: The
Vigenere
Cipher
Using modular arithmetic as a base we can use this
more sophisticated cryptosystem.
How it works:
Select a key word
The letters of the key word are then used to determine
the amount of shifting for each letter of the message
Cryptography: The
Vigenere
Cipher
Example:
We will use the same message, ATTACK AT DAWN
Let the key word be MATH
The formula here is (
i
+ j
)
mod
26
Answer: MTMHOK TA PAPU
Explanation: shift the first letter of the message by 12
because M = 12, the
seccond
is shifted by 0 because A = 0,
so on and so on. When you use all of the letters in the key
repeat
Web Searches and
Mathematical Logic
To understand any of this we must first understand
Boolean logic
What is it?
Web Searches and Mathematical
Logic: Boolean Logic
Boolean logic was created by George Boole.
It consists of expressions which are simply
statements that are either true or false
Web Searches and Mathematical
Logic: Boolean Logic
We can combine individual expressions into complex
expressions with things known as connectives
The three basic ones are AND, OR, NOT
So when we put this into the idea of a search engine:
Ex. Search for “Florida election”, this is interpreted as
an expression and when a web page contains the
phrase “Florida election” the result is true and is put in
the list of web pages.
Web Searches and Mathematical
Logic: Boolean Logic
Boolean logic can be quickly shown with truth tables.
Lets look at a basic truth table expressing p and q
P Q  P
∧
Q
T T  T
T F  F
F T  F
F
F 
F
HW 1
Using the Caesar’s Cipher, decode
KRPHZRUN
HW 2
Show the truth table for p and not q and not r
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