CRYPTOGRAPHY
Digital Diva
March 2012
Eastern Michigan University
Professor S. Haynes, shaynes@emich.edu
URL for this material: http://people.emich.edu/shaynes/DigitalDiva2012
Shift
Substitution
Permutation
Tap Code
Steganography
Book Cipher
Playfair
No hay tarea
:-(
Definitions
Plaintext:
Ciphertext:
an unencrypted message
an encrypted message
Cipher: encrypt, ciphertext, encryption algorithm
Encryption: transforming plaintext into ciphertext so that the plaintext is kept a secret; this usually
requires use of a key.
Decryption: transforming ciphertext into plaintext; this usually requires use of a key.
Encode: transform something into something else. For example, English  Spanish, letters to
numbers (a, b, c, … z)  (1, 2, 3, … 26).
Decode: undo an encoding (Spanish  English; (1, 2, 3, … 26)  (a, b, c, … z) ).
Algorithm: A sequence of instructions to accomplish something.
Key: Something that is known to the sender and the receiver of a message and is used to encrypt and
decrypt messages.
Secret key (aka private key, symmetric key, shared key): the sender and the receiver have exactly the
same key. The sender encrypts with the secret key, the receiver decrypts with the same secret key.
Public key (aka asymmetric key): a key that comes in two parts: (1) public and (2) private.
Shift cipher: To encrypt plaintext, shift each plaintext letter to the right by key steps. To decrypt
ciphertext, shift each ciphertext letter to the left by key steps.
Substitution cipher: Each plaintext letter is converted to a specific cipher text letter; each cipher text
letter is decrypted to the original plaintext letter.
Steganography: the secret message is hidden in another message.
Alice: the sender of a message
Bob: the receiver of a message
Shift cipher
1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
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
The shared key, k, is the size of the shift
Encryption algorithm: Each plaintext letter is encrypted as the letter k positions to the right with
wrap-around.
Decryption algorithm: Each ciphertext letter is encrypted as the letter k positions to the left with
wrap-around.
Example Encryption, key = 3 (Caesar cipher)
Plaintext:
lazy one
Ciphertext:
odcb rqh
Example Decryption
Ciphertext:
tzlc
Plaintext:
quiz
Substitution cipher
Each plaintext letter is matched to a unique ciphertext letter.
Example
Plaintext: 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
Ciphertext: Z A B Y C D X E F W G H V I J U K L T M N S O P R Q
The key for a substitution cipher is a permuted alphabet.
Simple ways to form a key:
- a shift cipher is a substitution cipher
- reverse the alphabet
- pick a word or phrase, e.g., “go green beat toledo”. Write down each letter in order from the
phrase under the alphabet, without repetition. Then complete the alphabet by copying the
unused letters in order. You’ll see the same idea in Playfair cipher later.
Example:
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
G O R E N B A T L D C F H I J K M P Q S U V W X Y Z
Permutation
The key is the permutation order.
Break the plain text message into blocks of size k. Number the letters in each block in order 0, 1, 2, …
k-1.
Encrypt each block separately following the permutation order given by the key.
To decrypt, find the permutation that will undo the encryption permutation. Then follow the same
steps as encryption with the new (inverse) permutation.
Example
Block size = 8
key = 0 7 1 2 6 5 3 4
to undo permutation: 0 2 3 6 7 5 4 1
Labelled blocks:
0 1 2 3 4 5 6 7
n o w i s t h e
0 1 2 3 4 5 6 7
t i m e f o r a
0 1 2 3 4 5 6 7
l l g o o d m e
0 1 2 3…
n x q x…
Permute according to the key. This is the ciphertext.
N E O W H T I S
T A I M R O E F
L E L G M D O O
N X X…
To decrypt:
0 1 2 3 4 5 6 7
N E O W H T I S
0 1 2 3 4 5 6 7
T A I M R O E F
0 1 2 3 4 5 6 7
L E L G M D O O
0 1 2
N X X…
n o w i s t h e
t i m e f o r a
l l g o o d m e
n x q …
Tap Code
The plain text is given inside the grid, the cipher text is the corresponding row and column numbers.
So for the letter ‘i’, you would tap two times for the row, then four times for the column: ..
1
2
3
4
5
1
A
F
L
Q
V
2
B
G
M
R
W
3
C
H
N
S
X
4
D
I
O
T
Y
....
5
E
J
P
U
Z
The space between letters is a little longer than the space between row and column. End of sentence
is marked with ‘x’ (..... ... )
Use the letter ‘C’ if you need a ‘K’.
Steganography
Hidden writing has many possibilities:
Invisible ink
“Subliminal advertising”
“Meaningful” stitches in quilts (e.g., 3 french knots to indicate a ‘c’, 4 to indicate a ‘d’)
Pin pricks in letters
For our example, we’re using differences in style to mark significant letters or words.
“Book cipher”
To my memory, Sherlock Holmes broke two ciphers. One was a simple substitution cipher. The other
was a book cipher.
To use a book cipher, sender and receiver must agree on exactly the same edition and printing of a
particular book.
The key is how the address of a word is specified, for example: page#, line#, word#
Each word of the plaintext is encrypted by finding the word in the common text, then producing that
word’s address as the ciphertext.
Playfair cipher
This cipher uses a 5 X 5 grid, where the letters of the alphabet are laid out (I and J occupy the same
cell). The key is a word or phrase.
To fill in the grid, copy the key, without any duplication of the letters (left to right, top to bottom),
then fill in the rest of the grid with any unused letters in order.
Example grid: key = “crypto rocks”
C
O
D
I/J
U
R
K
E
L
V
Y
S
F
M
W
P
A
G
N
X
T
B
H
Q
Z
To encrypt:
Divide the plain text into two letter blocks with the following “fix”: no block can have two identical
letters. To avoid that, insert an ‘x’ after the first letter.
Example:
calling gramma
ca lx li ng gr am ma
^
Find the two letters of a single block on the grid.
There are three possibilities:
(1) The two letters form two of the four corners of a rectangle (e.g., ‘ca’)
output the other two corners, row first ca  PO
pk  RA
(2) The two letters are on the same row (e.g., ‘ks’)
Output the two letters found by moving one space right of each letter: ks  SA
If you run out of room on the right, then do wrap-around: eh -> FD
(3) The two letters are on the same column (e.g., ‘ag’)
Output the two letters found by moving one space down from each letter:
ag  GN, Rl  KV.
If you run out of room on the bottom, then do wrap-around:
rv  KR, gx  NP
Decryption:
Case (1), same as for encryption.
Case (2), move left
Case (3), move up