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

Playfair’s Cryptosystem N 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

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

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

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

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 http://www.picturehistory.com/ April 18, 2005 copyright Kevin O'Bryant

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: 6 5 2 8 9 7 1 4 3 April 18, 2005 copyright Kevin O'Bryant

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

Rectangular Transposition 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 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

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

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 84327615 April 18, 2005 copyright Kevin O'Bryant

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 84327615 April 18, 2005 copyright Kevin O'Bryant

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 84327615 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 84327615 April 18, 2005 copyright Kevin O'Bryant

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