Cryptography

1. Cryptography

2. Activity What is cryptography ?

3. Introduction • Cryptography is the study of Encryption • Greek kryptos means “hidden” and graphia means “writtings” • Encryption is an ancient form of information protection. … dates back 4,000 years. • process by which plaintext is converted into ciphertext. • Decryption is the inverse of Encryption.

4. Introduction … • A sender S wanting to transmit message M to a receiver R • To protect the message M, the sender first encrypts it into meaningless message M’ • After receipt of M’, R decrypts the message to obtain M • M is called the plaintext • What we want to encrypt • M’ is called the ciphertext • The encrypted output

5. Introduction… • Notation Given P=Plaintext C=CipherText • C = EK (P) Encryption • P = DK ( C) Decryption

6. Terminologies • Cryptography: Schemes for encryption and decryption • Encryption algorithm: technique or rules selected for encryption. • Key: is secret value used to encrypt and/or decrypt the text. • Cryptanalysis: The study of “breaking the code”. • Cryptology: Cryptography and cryptanalysis together constitute the area of cryptology.

7. Encryption vs. C-I-A • Encryption provides : • Confidentiality/Secrecy • keeps our data secret. • Integrity • protect against forgery or tampering

8. Cryptographic systems are characterized along three dimensions • operations used for transforming • Substitution: Replace (bit, letter, group of bits letters • Transposition: Rearrange the order • Product :use multiple stages of both • number of keys used • Symmetric: same key , secret-key, private-key • Asymmetric: different key , public-key • way in which the plaintext is processed • block cipher • Stream cipher

9. Transposition and Substitution • SimpleSimple Substitution Transposition security security security Encryption Encryption Encryption cusetyri tfdvsjuz 19 5 3 20 18 9 19 25

10. Classical Substitution • Caesar Cipher: used by Julius Caesar's military • substitutes each letter of the alphabet with the letter standing three places further down the alphabet

11. Caesar cipher

12. Activity • Convert it ....to Caesar Ciphertext? • Plaintext: are you ready • Ciphertext: duh brxuhdgb Plaintext Ciphertext

13. Caesar Cipher • the algorithm can be expressed as, for each plaintext letter P, substitute ciphertext letter C. • C = E(3, p) = (p + 3) mod 26 • mathematically give each letter a number 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 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 • General Caesar algorithm as: c = E(k, p) = (p + k) mod (26) p = D(k, c) = (c – k) mod (26) • Where k is [1 to 25]. Secret-key

14. Classical Transposition • Spartans cipher , fifth century B.C. Start the war today Rewrite it by reading down Srhaoytterdatwta Encryption: rearrange the text in 3 columns S t a r t t h e w a r t o d a y

15. Cryptanalysis • objective to recover key not just message • general approaches: • cryptanalytic attack • exploits the characteristics of the algorithm • brute-force attack • try every possible key on a piece of ciphertext • if either succeed all key use compromised

16. Cryptanalytic Attacks • ciphertext only • only know algorithm & ciphertext, is statistical, know or can identify plaintext .Most difficult • known plaintext • know/suspect plaintext & ciphertext • chosen plaintext • select plaintext and obtain ciphertext • chosen ciphertext • select ciphertext and obtain plaintext • chosen text • select plaintext or ciphertext to en/decrypt

17. More Definitions • unconditional security • no matter how much computer power or time is available, the cipher cannot be broken since the ciphertext provides insufficient information to uniquely determine the corresponding plaintext • computational security • given limited computing resources (eg time needed for calculations is greater than age of universe), the cipher cannot be broken • it either takes too long, or is too expensive,

18. Cryptanalysis… • given a ciphertextCaesar cipher, then a brute-force is easy performed: • simply try all the 25 possible keys. • Assuming language of the plaintext is known. • Thus, Caesar cipher is far from secure.

19. Introducing • Alice • Bob • Trudy

20. 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

21. 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, statistical techniques

22. Brute Force Search • always possible to simply try every key • assume either know / recognise plaintext • impractical if we use an algorithm that employs a large number of keys. • most basic attack, proportional to key size

23. Language Redundancy and Cryptanalysis • human languages are redundant • 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

24. English Letter Frequencies

25. 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

26. Example Cryptanalysis • given ciphertext: UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ • count relative letter frequencies • 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

27. Given this cipher text UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ • Relative frequency of the letters in the text P 13.33 H 5.83 F 3.33 B 1.67 C 0.00 Z 11.67 D 5.00 W 3.33 G 1.67 K 0.00 S 8.33 E 5.00 Q 2.50 Y 1.67 L 0.00 U 8.33 V 4.17 T 2.50 I 0.83 N 0.00 O 7.50 X 4.17 A 1.67 J 0.83 R 0.00 M 6.67

28. UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ t a e ete a that e e a a t VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX e t ta t ha e ee a e th t a EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ e e e tat e the t • Continued analysis of frequencies plus trial and error should easily yield a solution from this point it was disclosed yesterday that several informal but direct contacts have been made with political representatives of the viet cong in moscow.

29. Cryptograph cont’… • Playfair cipher • Polyalphabetic ciphers • Vigenère cipher • Vernam cipher • One-timepad • More on Transposition • Rail fence cipher • Message in rectangle ( row transposition ) • Rotor machine

30. Playfair Cipher • A.k.aPlayfair square • A manual symmetric encryption technique • It was the first literal digraph substitution cipher. • The scheme was invented in 1854 by Charles Wheatstone, but bears the name of Lord Playfairwho promoted the use of the cipher. • Used in WWI and WWII

31. Playfair Key Matrix • a 5X5 matrix of letters based on a keyword • fill in letters of keyword (no duplicates, i & j) • fill rest of matrix with other letters • eg. using the keyword (key) simple

32. Playfair Cipher • Use filler letter to separate repeated letters • eg. "balloon" encrypts as "ba lx lo on" Encrypt two letters together • Same row– >followed letters • ac--bd • Same column–> letters under • qw--wi • Otherwise—>square’s corner at same row • ar--bq

33. Activity • Q: construct the playfair matrix using the keyword MONARCHY ? • Plaintext: Ethiopia • Ciphertext: klbfhvsb

34. Security of Playfair Cipher • security much improved over monoalphabetic • But, still has much of plaintext structure. • it can be broken, given a few hundred letters • With ciphertext only, possible to analyse frequency of occurrence of digrams(pairs of letters) • Obtaining the key is relatively straightforward if both plaintext and ciphertext are known.

35. Polyalphabetic ciphers

36. Polyalphabetic ciphers • using multiple substitution alphabets. • make cryptanalysis harder with more alphabets to guess and flatter frequency distribution • use a key to select which alphabet is used for each letter of the message • use each alphabet in turn • repeat from start after end of key is reached

37. Vigenere Cipher • simplest polyalphabetic substitution cipher • meaning that instead of there being a one-to-one relationship between each letter and its substitute, there is a one-to-many relationship between each letter and its substitutes. • The encipherer chooses a keyword and repeats it until it matches the length of the plaintext

38. Vigenère Cipher • Basically multiple Caesar ciphers • key is multiple letters long • K = k1 k2 ... kd • ith letter specifies ith alphabet to use • use each alphabet in turn, repeating from start after d letters in message • Plaintext: THISPROCESSCANALSOBEEXPRESSEDKeyword: CIPHERCIPHERCIPHERCIPHERCIPHE Ciphertext: VPXZTIQKTZWTCVPSWFDMTETIGAHLH

39. Vigenère Cipher • write the plaintext out • write the keyword repeated above it • use each key letter as a caesar cipher key • encrypt the corresponding plaintext letter

40. Activity • Q: encrypt the given plaintext letter using Vigenère Cipher use keyword deceptive • plaintext: wearediscoveredsaveyourself • Key: • Ciphertext: deceptivedeceptivedeceptive • zicvtwqngrzgvtwavzhcqyglmgj

41. Security of Vigenère Ciphers • have multiple ciphertext letters for each plaintext letter • hence letter frequencies are masked • but not totally lost • start with letter frequencies • see if look monoalphabetic or not • if not, then need to determine number of alphabets, since then can attach each

42. Kasiski Method • method developed by Babbage / Kasiski • repetitions in ciphertext give clues to period • so find same plaintext an exact period apart • which results in the same ciphertext. • eg repeated “VTW” in previous activity • suggests size of 3 or 9 • then attack each monoalphabetic cipher individually using same techniques as before

43. Autokey Cipher • ideally want a key as long as the message • Vigenère proposed the autokey cipher • with keyword is prefixed to message as key • knowing keyword can recover the first few letters • use these in turn on the rest of the message • but still have frequency characteristics to attack • eg. given key deceptive key: deceptivewearediscoveredsav plaintext: wearediscoveredsaveyourself ciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLA

44. Vernam Cipher • ultimate defense is to use a key as long as the plaintext • with no statistical relationship to it • invented by AT&T engineer Gilbert Vernam in 1918 • Originally proposed using a very long but eventually repeating key • His system works on binary data (bits rather than letters)

45. One-Time Pad • if a truly random key as long as the message is used, the cipher will be secure. • 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 • problems in generation & safe distribution of key

46. One-time Pad: Encryption e=000 h=001 i=010 k=011 l=100 r=101 s=110 t=111 Encryption: Plaintext  Key = Ciphertext Plaintext: Key: Ciphertext:

47. One-time Pad: Decryption e=000 h=001 i=010 k=011 l=100 r=101 s=110 t=111 Decryption: Ciphertext  Key = Plaintext Ciphertext: Key: Plaintext:

48. One-time Pad Double agent claims sender used following “key” Ciphertext: “key”: “Plaintext”: e=000 h=001 i=010 k=011 l=100 r=101 s=110 t=111

49. One-time Pad Or sender is captured and claims the key is… Ciphertext: “Key”: “Plaintext”: e=000 h=001 i=010 k=011 l=100 r=101 s=110 t=111

50. One-time pad… • the only cryptosystem that exhibits what is referred to as perfect secrecy • Drawbacks • it requires secure exchange of the one-time pad material, which must be as long as the message • pad disposed of correctly and never reused • In practice • Generate a large number of random keys, • Exchange the key material securely between the users before sending an one-time enciphered message, • Keep both copies of the key material for each message securely until they are used, and • Securely dispose of the key material after use, thereby ensuring the key material is never reused.