1. Playfair, Transpositions, and ADFGVX
The Ultimate Classical Cryptosystems
April 18, 2005
copyright Kevin O'Bryant

2. Playfair’s CryptosystemN K E Y L V A B C D F G H
I/J P Q R S T U W X Z
Key is a 5x5 box of the alphabet, with I/J in the same box.
Break plaintext into 2-grams:
“pl ai nt ex tx ta ke st im eq”
using “x” to break up repeated letters
Encrypt plaintext using key
If in same column, shift each down
If in same row, shift each right
If at opposite corners of a rectangle, replace each with the “other” corner on the same row
April 18, 2005
copyright Kevin O'Bryant

3. Playfair’s Cryptosystem
“me is smart too!”
becomes
“me is sm ar tx to oq”
me  OM
is  PI
sm  IE
ar  GX
tx  UZ
to  UM
oq  NP
ciphertext is
“OM PI IE GX UZ UM NP” M O N K E Y L V A B C D F G H
I/J P Q R S T U W X Z
April 18, 2005
copyright Kevin O'Bryant

4. Playfair’s Cryptosystem
Exercise: Decrypt
BQZRX SQWTW VSGSV XLUNQ XAPKP SABEM ZSNDF CVXGT AXSBX GDYBS BGLCC BTMEM XZHI
using the key at right R P M L D S A X
I/J C H K Q U Y E W O Z G B F T V N
April 18, 2005
copyright Kevin O'Bryant

5. copyright Kevin O'Bryant
Transpositions
Part of an actual telegram from Union Army General Halleck to General Buell (quoted from Battle Cry of Freedom: The Civil War Era)
YOU MARCHED THE IS THE ELSEWHERE MOVE OF SURPRISING TWO TIMES HALLECK AS SLOWLY ARMY IN HAS DISTANCE HAVE FOUR LAST MOST IMMOBILITY YOU HERE TOO YOUR BRAGG MONTHS THE
HERE AS
ELSEWHERE
YOU
MOVE
TOO
SLOWLY
THE
IMMOBILITY OF
YOUR
ARMY IS
MOST
SURPRISING
BRAGG IN
LAST
TWO
MONTHS
HAS
MARCHED
FOUR
TIMES
DISTANCE
HAVE
HALLECK
April 18, 2005
copyright Kevin O'Bryant

6. copyright Kevin O'Bryant
From Lincoln
1863 WOULD RELIEVED MEADE SINCE HAVE THE WITHOUT ME WAS WHO THE SATURDAY HEVY A WAR FIGHTING CORPS KNOW PLEASE THE TO OF AND IMPRESSION TO CAMERON 15 I BE THAT ALL GETTYSBURG GET RIVER TELL WHO COMMANDER IN ON LINCOLN SIGNED OF FOR ONE YOU FIGHT OVER ONLY BATTLE SMITH THE MUCH SIMON WASHINGTON FOR GIVE OF COUCH THE STRIVEN ENEMY ANOTHER IF THE WAS COUNCIL NIGHT
Image from
April 18, 2005
copyright Kevin O'Bryant

7. Rectangular Transposition
Let’s encrypt
“Out of life’s school of war: What does not destroy me, makes me stronger.”
with keyword Nietzsche
Step 1: Convert keyword to permutation. The lexicographically first letter in our keyword is c, followed by e, e, h, i, n, s, t, z:
April 18, 2005
copyright Kevin O'Bryant

8. Rectangular Transposition
Step 2: Write the plaintext under the permutation row-wise 6 5 2 8 9 7 1 4 3 o u t f l i e s c h w a r d n y m k g
April 18, 2005
copyright Kevin O'Bryant

9. Rectangular Transposition6 5 2 8 9 7 1 4 3 o u t f l i e s c h w a r d n y m k g
Step 3: Write down the columns according to the numbers at the top:
ILTEAO TCRNYE EFOTEG FODSKN USASOMR
OSWERSE LOADMR OHWOMS FOHTET
April 18, 2005
copyright Kevin O'Bryant

10. Rectangular Transposition
Step 4: Break into 5-grams:
ILTEAO TCRNYE EFOTEG FODSKN USASOMR
OSWERSE LOADMR OHWOMS FOHTET
becomes
ILTEA OTCRN YEEFO TEGFO DSKNU SASOM
ROSWE RSELO ADMRO HWOMS FOHTE T
April 18, 2005
copyright Kevin O'Bryant

11. copyright Kevin O'Bryant
ADFGVX Cryptosystem
Key consists of a 6x6 grid of the letters and digits, and a permutation of
1, 2, …, n
replace each letter of plaintext with its coordinates.
rearrange text into to n columns, and then read down the column labeled 1, then 2, then 3, etc.
Break into 5-grams A D F G V X i w o u l d e f r y a 9 b c 1 g h j k 2 m n 7 p 3 q s 6 t 4 v x 5 z 8
April 18, 2005
copyright Kevin O'Bryant

12. copyright Kevin O'Bryant
ADFGVX Cryptosystem
Exercise: encrypt
“From one day to another, another nation is made out to be utterly depraved and fiendish, while one's own nation stands for everything that is good and noble.”
using the key from
the previous slide. A D F G V X i w o u l d e f r y a 9 b c 1 g h j k 2 m n 7 p 3 q s 6 t 4 v x 5 z 8
April 18, 2005
copyright Kevin O'Bryant

13. copyright Kevin O'Bryant
ADFGVX Example
“from one
day to”
f  DD
r  DF
o  AF
m  GG
n  GV
e  DA
d  AX
a  DX
y  DG
t  VX
DDDFAFGG
AFGVDAAX
DXDGVXAF
becomes
GAA FVG
DGD DFX
GXF FAX
ADV DAD
GAAFV GDGDD FXGXF FAXAD VDAD A D F G V X i w o u l d e f r y a 9 b c 1 g h j k 2 m n 7 p 3 q s 6 t 4 v x 5 z 8
April 18, 2005
copyright Kevin O'Bryant

14. copyright Kevin O'Bryant
Summary
Playfair is like a monoalphabetic substitution, but substituting pairs of letters with other pairs.
Rectangular Transposition consists of rearranging letters
ADFGVX is a substitution followed by a rectangular transposition.
In ADFGVX, the symbol for “a” in the plaintext is typically split, and one half may be near the beginning of the ciphertext and the other near the end.
Transposition (including ADFGVX) requires the entire message before encryption.
Write down strengths and weaknesses of these three cryptosystems. Which ones form a group? How many keys for each?
April 18, 2005
copyright Kevin O'Bryant