Classical Encryption Part 2 By Dr Shadi Masadeh

Classical Encryption Part 2 By Dr. Shadi Masadeh Company LOGO 1

Monoalphabetic Cipher § rather than just shifting the alphabet § could shuffle (jumble) the letters arbitrarily § each plaintext letter maps to a different random ciphertext letter § hence key is 26 letters long Plain: abcdefghijklmnopqrstuvwxyz Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN Plaintext: ifwewishtoreplaceletters Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA 2

Monoalphabetic Cipher Security § § now have a total of 26! = 4 x 1026 keys with so many keys, might think is secure but would be !!!WRONG!!! problem is language characteristics 3

Language Redundancy and Cryptanalysis § § human languages are redundant eg "th lrd s m shphrd shll nt wnt" letters are not equally commonly used in English E is by far the most common letter followed by T, R, N, I, O, A, S § other letters like Z, J, K, Q, X are fairly rare § have tables of single, double & triple letter frequencies for various languages 4

English Letter Frequencies 5

Use in Cryptanalysis § 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/plots against known values § if caesar cipher look for common peaks/troughs peaks at: A-E-I triple, NO pair, RST triple troughs at: JK, X-Z § for monoalphabetic must identify each letter tables of common double/triple letters help 6

Example Cryptanalysis § given cipher text: UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ § § count relative letter frequencies (see text) guess P & Z are e and t guess ZW is 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 7

Playfair Cipher § 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 8

Playfair Key Matrix § § a 5 X 5 matrix of letters based on a keyword fill in letters of keyword (sans duplicates) fill rest of matrix with other letters eg. using the keyword MONARCHY M O N A R C H Y B D E F G I/J K L P Q S T U V W X Z 9

Encrypting and Decrypting § plaintext is encrypted two letters at a time 1. 2. 3. 4. if a pair is a repeated letter, insert filler like 'X’ if both letters fall in the same row, replace each with letter to right (wrapping back to start from end) if both letters fall in the same column, replace each with the letter below it (again wrapping to top from bottom) otherwise each letter is replaced by the letter in the same row and in the column of the other letter of the pair 10

Security of Playfair Cipher § 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. by US & British military in WW 1 § it can be broken, given a few hundred letters § since still has much of plaintext structure 11

Playfair Cipher Example § http: //www. simonsingh. net/The_Black_Ch amber/playfaircipher. htm 12

Hill Cipher § Multiletter cipher, developed in 1929 § Take , successive letters and substitutes for them m ciphertexts letters. § For m=3: § C 1=(k 11 p 1, +k 12 p 2+k 13 p 3) mod 26 § C 2=(k 21 p 1, +k 22 p 2+k 23 p 3) mod 26 § C 3=(k 31 p 1, +k 32 p 2+k 33 p 3) mod 26 § C=kp mod 26 § Where K; key, C; ciphertexts, P; plaintext; and operations performed mod 26 13

Hill Cipher § § § C=Ek(P)= KP mod 26 P=Dk(C)= K-1 C mod 26 = K-1 KP = P C 3=(k 31 p 1, +k 32 p 2+k 33 p 3) mod 26 Example: plaintext is july The encryption is carried out as: K= 11 8 K-1= 7 18 § § § 3 7 23 11 Ju = (9, 20) and ly = (11, 24) C=KP mod 26 (9, 20) 11 8 3 7 = 99+60, 72+140= (3, 4) =DE (11, 24) 11 8 3 7 = 121+72, 88+168= (11, 22)= LW 14

Hill Cipher The decryption is carried out as: § K= 11 8 K-1= 7 18 § § § 3 7 23 11 DELW = (3, 4, 11, 22) P=Dk(C)= K-1 C mod 26 = K-1 KP = P (3, 4) 7 18 23 11 = 21+92, 54+44= (9, 20) =ju (11, 22) 7 18 23 11 = 77+506, 198+242= (11, 24)= ly 15

One-Time Pad § if a truly random key as long as the message is used, the cipher will be secure § called a One-Time pad § is unbreakable since ciphertext bears no statistical relationship to the plaintext § since for any plaintext & any ciphertext there exists a key mapping one to other § can only use the key once though § have problem of safe distribution of key 16

Transposition Ciphers § now consider classical transposition or permutation ciphers § these hide the message by rearranging the letter order § without altering the actual letters used § can recognise these since have the same frequency distribution as the original text 17

Rail Fence cipher § write message letters out diagonally over a number of rows § then read off cipher row by row § eg. write message out as: m e m a t r h t g p r y e t e f e t e o a a t § giving ciphertext MEMATRHTGPRYETEFETEOAAT 18

Row Transposition Ciphers § a more complex scheme § write letters of message out in rows over a specified number of columns § then reorder the columns according to some key before reading off the rows Key: 4 3 1 2 5 6 7 Plaintext: a t t a c k p o s t p o n e d u n t i l t w o a m x y z Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ Representation of the ciphertext: 03 10 17 24 04 11 18 25 02 09 16 23 01 08 15 22 05 12 19 26 06 13 20 27 07 14 21 28 The original message was; attackpostponeduntiltwoam 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 19

Row Transposition Ciphers § Pure transposition is easy to recognize § Make it more secure; by performing more than one stage of transposition Key: 4 3 1 2 5 6 7 Plaintext: t t n a a p t m t s u o a o d w c o i x k n l y p e t z Ciphertext: NSCYAUOPTTWLTMDNAOIEPAXTTOKZ Number representation of the ciphertext: 17 09 05 27 24 16 12 07 10 02 22 20 03 25 15 13 04 23 19 14 11 01 26 21 18 08 06 28 20

Product Ciphers § ciphers using substitutions or transpositions are not secure because of language characteristics § hence consider using several ciphers in succession to make harder, but: two substitutions make a more complex substitution two transpositions make more complex transposition but a substitution followed by a transposition makes a new much harder cipher § this is bridge from classical to modern ciphers 21

Rotor Machines § before modern ciphers, rotor machines were most common product cipher § were widely used in WW 2 German Enigma, Allied Hagelin, Japanese Purple § implemented a very complex, varying substitution cipher § used a series of cylinders, each giving one substitution, which rotated and changed after each letter was encrypted § with 3 cylinders have 263=17576 alphabets 22

Hagelin Rotor Machine 23

Steganography § an alternative to encryption § hides existence of message using only a subset of letters/words in a longer message marked in some way using invisible ink hiding in LSB in graphic image or sound file § has drawbacks high overhead to hide relatively few info bits 24

Summary § have considered: classical cipher techniques and terminology monoalphabetic substitution ciphers cryptanalysis using letter frequencies Playfair cipher polyalphabetic ciphers transposition ciphers product ciphers and rotor machines stenography 25