•
Rather than just shifting the alphabet
•
Could shuffle (jumble) the letters arbitrarily
•
Each plaintext letter maps to a different random cipher text letter
• hence key is 26 letters long
Plain: abcdefghijklmnopqrstuvwxyz
Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN
Plaintext: ifwewishtoreplaceletters
Cipher text: WIRFRWAJUHYFTSDVFSFUUFYA

•
Now have a total of 26! keys
•
With so many keys, might think the system is secure
•
But would be !!!WRONG!!!
•
Problem is the regularities of the language

•
Human languages are redundant
•
Letters are not equally commonly used
•
The English letter e is by far the most common letter
•
Then T,R,N,I,O,A,S
•
Other letters are fairly rare
•
Z,J,K,Q,X

•
Key concept - monoalphabetic substitution ciphers do not change relative letter frequencies
•
Discovered by Arabian scientists in 9 th century
•
Calculate letter frequencies for ciphertext
• compare counts against known values

•
Given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
•
Count relative letter frequencies (see text)
•
The most common letters are P & Z and are equivalent to e and t
•
The most common Digram are ZW is equivalent to th and hence ZWP is the
•
Proceeding with trial and error finally get: it was disclosed yesterday that several informal but direct contacts have been made with political representatives of the viet cong in moscow

•
Not even the large number of keys in a monoalphabetic cipher provides security
•
One approach to improving security was to encrypt multiple letters
•
The Playfair Cipher is an example
•
Invented by Charles Wheatstone in 1854, but named after his friend Baron Playfair

•
A 5X5 matrix of letters based on a keyword
M O N A R
•
Fill in letters of keyword
C H Y B D
•
Fill rest of matrix with other letters
E F G I/J K
L P Q S T
• eg. using the keyword
MONARCHY
U V W X Z

• plaintext encrypted two letters at a time:
– if a pair is a repeated letter, insert a filler like 'X', eg. "balloon" encrypts as "ba lx lo on"
– if both letters fall in the same row, replace each with letter to right (wrapping back to start from end), eg. “ar" encrypts as "RM"
– if both letters fall in the same column, replace each with the letter below it (again wrapping to top from bottom), eg. “mu" encrypts to "CM"
– otherwise each letter is replaced by the one in its row in the column of the other letter of the pair, eg. “hs" encrypts to
"BP", and “ea" to "IM" or "JM"

• security much improved over monoalphabetic
• since have 26 x 26 = 676 digrams
• would need a 676 entry frequency table to analyse
(verses 26 for a monoalphabetic)
• and correspondingly more ciphertext
• was widely used for many years (eg. US & British military in WW1)
• it can be broken, given a few hundred letters
• since still has much of plaintext structure

Hill Cipher
•
Developed by the mathematician Lester Hill in 1929.
•
The encryption algorithm takes m successive plain text and substitute for them m cipher text letters.
•
Each character is assigned a numerical value
(a=0,…z=25).
C
1


C
2
C
3



K
11
K
12
K
13


K
21
K
22
K
23
K
31
K
32
K
33





P
1
P
2
P
3

 mod 26
C

KP mod 26
P

K

1
C mod 26

KK

1
P

P