Classical Encryption

1. Classical Encryption Part 2 By Dr. Shadi Masadeh

2. 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

3. 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

4. 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

5. English Letter Frequencies

6. Use in Cryptanalysis • key concept - monoalphabetic substitution ciphers do not change relative letter frequencies • discovered by Arabian scientists in 9th 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

7. 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

8. 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

9. Playfair Key Matrix • a 5X5 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

10. Encrypting and Decrypting • plaintext is encrypted two letters at a time • 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

11. 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 WW1 • it can be broken, given a few hundred letters • since still has much of plaintext structure

12. Playfair Cipher Example • http://www.simonsingh.net/The_Black_Chamber/playfaircipher.htm

13. Hill Cipher • Multiletter cipher, developed in 1929 • Take , successive letters and substitutes for them m ciphertexts letters. • For m=3: • C1=(k11p1,+k12p2+k13p3) mod 26 • C2=(k21p1,+k22p2+k23p3) mod 26 • C3=(k31p1,+k32p2+k33p3) mod 26 • C=kp mod 26 • Where K; key, C; ciphertexts, P; plaintext; and operations performed mod 26

14. Hill Cipher • C=Ek(P)= KP mod 26 • P=Dk(C)= K-1C mod 26 = K-1KP = P • C3=(k31p1,+k32p2+k33p3) 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

15. 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-1C mod 26 = K-1KP = 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. Rotor Machines • before modern ciphers, rotor machines were most common product cipher • were widely used in WW2 • 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

23. Hagelin Rotor Machine

24. 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

25. 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