CX 103: Introduction to Computers

Lecture 28
 
 

Today's Agenda

Cryptology and Computer Security II
 
 




 

CIPHERS

MONALPHABETIC SUBSTITUTION

POLYALPHABETIC SUBSTITUTION

POLYGRAPHIC SYSTEMS
 
 

MONALPHABETIC SUBSTITUTION

Caesar Cipher: Replace each letter of the message by the letter x places beyond it in the normal alphabet.

Numerical Implementation

of Caesar Cipher

1) Replace each letter by its position in the alphabet

2) Add 3 % 26 to the position (treat 0 as 26)

3) Replace resulting number by its letter equivalent
 
 

M --> 13 --> 16 --> P
 
 

In JavaScript

Phrase is variable name; it contains a character string.

The first character in Phrase is Phrase.charAt(0);

Its ASCII value is ascii = Phrase.charCodeAt(0);

Its position in the alphabet is position = ascii - 64

To add 3 mod 26: cipherPosition =(position + 3) % 26

Now cipherPosition is the position of new letter in the alphabet.

Its ASCII value is x = cipherPosition + 64.

The corresponding letter is String.fromCharCode(x)
 
 

Summarizing:

ascii = Phrase.CharCodeAt(0);

position = ascii - 64;

cipherPosition =(position + 3) % 26

NewAscii = cipherPosition + 64

CipherCharacter = String.fromCharCode(NewAscii)

Caesar.html
 

Any rearrangement of the alphabet produces another substitution scheme.

Here is another way to get a rearrangement;

Pick a key word: VERMONT

Make the letters the heads of columns in a table.

Fill in the rest of the alphabet into the table from left to right.
 
V E R M O N T
A B C D F G H
I J K L P Q S
U W X Y Z    

 

Then read the letters out of the table, column by column

going from left to right, reading each column from top to bottom:

VAIU EBJW RCKX MDLY OFPZ NGQ THS
 
 


Implementing Monoalphabetic Substitution

Encrypt:

(1) Find position of plaintext letter in straight

(2) Replace it with ciphertext in same position in mixed

Example: plaintext character is stored in PlainChar

position = straight.IndexOf(PlainChar)

CipherChar = mixed.charAt( position );

straight = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";

mixed = "VAIUEBJWRCKXMDLYOFPZNGQTHS";
 
 
 
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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
V A I U E B J W R C K X M D L Y O F P Z N G Q T H S

 

Decrypt: Reverse the roles of straight and mixed.

keyword.html

How would you Break a Ciphered Message?

Use the Cryptoanalyst's most powerful tool!

Frequency Analysis:

Frequency.html
 
 

Standard Written English


E the highest frequency
T A O I N S H R high frequency group
D L medium frequency
C U M W F G Y P B low frequency
V K J X Q Z rare

 

With a Caesar Cipher, we only need to know where one letter goes to find the key (since all other letters are shifted the same amount)

How to Use Frequency Analysis

For Caesar Cipher: Do a frequency analysis of the ciphertext. Guess that E was shifted to the most frequent letter and try this shift as the key. Your guess should also be consistent with the following observations about standard written English:

Among High Frequency Letters:

A, E, I are 4 apart (equally spaced)

R, S, T from a consecutive triple

Among Low Frequency Letters;

V, W, X, Y, Z are 5 consecutive lows.

What happens to these patterns under a shift?


Aside: The frequency of individual letters is known as a "first order statistic." Pairs of letters that occur together are called digrams or digraphs while triples are called trigrams or trigraphs. The frequencies of these higher order statistics are also useful:

The Federalist Papers

Shakespeare

Hemingway

Deep Throat

Primary Colors
 


 

Part 2