Cryptography

1. Cryptography

2. Cryptography • Secret (crypto) Writing(graphy) • [Greek word] • Practice and study of hiding information • Concerned with developing algorithms for: • Conceal the context of some message from all except the sender & recipient and/or • Verify the correctness of a msg. to the recipient(authentication) • Form basis of many technological solutions to computer & communications security problems

3. Symmetric Encryption • (Or) conventional / private-key / single-key • sender and recipient share a common key • all classical encryption algorithms are private-key • was only type prior to invention of public-key in 1970’s

4. Basic Terminology • plaintext- the original message • ciphertext - the coded message • cipher - algorithm for transforming plaintext to ciphertext • key- info used in cipher known only to sender/receiver • encipher (encrypt) - converting plaintext to ciphertext • decipher (decrypt) - recovering ciphertext from plaintext • cryptography - study of encryption principles/methods • cryptanalysis (codebreaking)- the study of principles/ methods of deciphering ciphertext without knowing key • cryptology - the field of both cryptography and cryptanalysis

5. Basic Encryption/Decryption

6. Symmetric Cipher Model

7. 5 Basic Ingredients for Symmetric Encryption • plaintext • encryption algorithm – performs substitutions/transformations on plaintext • secret key – output depend on specific key used; control exact substitutions/transformations used in encryption algorithm • ciphertext • decryption algorithm – inverse of encryption algorithm

8. Requirements • two requirements for secure use of symmetric encryption: • a strong encryption algorithm • a secret key known only to sender / receiver C = EK(P) P = DK(C) • assume encryption algorithm is known; keep key secret. • implies a secure channel to distribute key

9. Symmetric algorithm • encryption, decryption keys are the same

10. Notation • denote plaintext P = <p1,p2, … , pm> • denote ciphertext C = <c1,c2, … , cn> • Key k of form k = <k1,k2, … , kj> • Example: • plaintext “Hello how are you” • P = <H,E,L,L,O,H,O,W,A,R,E,Y,O,U> • ciphertext “KHOOR KRHZ DUH BRX” • C = < K,H,O,O,R,K,R,H,Z,D,U,H,B,R,X > • More formally: • C=Ek(P) P=Dk (C) • P=Dk (Ek (P))

11. Cryptography • Can be characterized on 3 independent dimensions: • type of encryption operations used • substitution / transposition / product • number of keys used • single-key or private / two-key or public • way in which plaintext is processed • block / stream

12. Cryptanalysis • 2 approaches for attacking a conventional encryption scheme: • Cryptanalysis • Nature of algorithm • Some knowledge of general characteristics of plaintext • Or some sample plaintext - ciphertext pairs • Deduce a specific plaintext or key • Brute-force attack • Try every possible key on a ciphertext • On the average,half the keys must be tried for success

13. Types of Cryptanalytic Attacks • ciphertext only • only know algorithm / ciphertext, statistical, can identify plaintext • known plaintext • know/suspect plaintext & ciphertext to attack cipher • chosen plaintext • select plaintext and obtain ciphertext to attack cipher • chosen ciphertext • select ciphertext and obtain plaintext to attack cipher • chosen text • select either plaintext or ciphertext to en/decrypt to attack cipher

14. Brute Force Search • always possible to simply try every key • most basic attack, proportional to key size • assume either know / recognise plaintext

15. Classical Substitution Ciphers • where letters of plaintext are replaced by other letters or symbols by numbers • or if plaintext is viewed as a sequence of bits, then substitution involves replacingplaintext bit patterns with ciphertext bit patterns • Simple systems

16. Caesar Cipher • earliest known substitution cipher • by Julius Caesar • first attested use in military affairs • replaces each letter by 3rd letter on • example: meet me after the toga party PHHW PH DIWHU WKH WRJD SDUWB

17. Caesar Cipher • Shift plaintext chars. three characters P: a b c d e f g h i j k l m C: D E F G H I J K L M N O P P: n o p q r s t u v w x y z C: Q R S T U V W X Y Z A B C meet me after the toga party PHHW PH DIWHU WKH WRJD SDUWB

18. Caesar Cipher • mathematically give each letter a number a b c d e f g h i j k l m 0 1 2 3 4 5 6 7 8 9 10 11 12 n o p q r s t u v w x y Z 13 14 15 16 17 18 19 20 21 22 23 24 25 • then have Caesar cipher as: C = E(p) = (p + 3) mod (26) p = D(C) = (C – 3) mod (26) • Shift cipher C = E(p) = (p + k) mod (26) p = D(C) = (C – k) mod (26)

19. k => 1 to 25 • example: k=5 • A: 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 • C: F G H I J K L M N O P Q R S T U V W X Y Z A B C D E • “summer vacation was too short” encrypts to • XZRR JWAF HFYN TSBF XYTT XMTW Y

20. Problem

21. Breaking Shift Ciphers • How difficult? • How many possibilities?

22. Cryptanalysis of Caesar Cipher • only have 26 possible ciphers • A maps to A,B,..Z • could simply try each in turn • a brute force search • 3 characteristics: • Encryption & decryption algorithms are known • Only 25 keys to try • Language of plaintext is known & easily recognizable

24. 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

25. Monoalphabetic Cipher • how many possible substitution alphabets? • can we try all permutations? • how would you try to break them?

26. Monoalphabetic – Brute force • how many possible substitution alphabets? • 26! ≈ 4 * 1026 possible keys • can we try all permutations? • sure. have some time? • at 1 encryption/μsec 2* 1026 μsec = 6.4* 1012 years • how would you try to break them? • use what you know to reduce the possibilities

27. Monoalphabetic Cipher Security • now have a total of 26! = 4 x 1026 keys • with so many keys, might think is secure • !!!WRONG!!! • problem is language characteristics

28. Language Redundancy and Cryptanalysis • human languages are redundant • letters are not equally commonly used • Eg. in English e is by far the most common letter • look at common letters (E, T, O, A, N, ...) • single-letter words (I, and A) • two-letter words (of, to, in, ...) • three-letter words (the, and, ...) • double letters (ll, ee, oo, tt, ff, rr, nn, ...) • other tricks?

29. Language Redundancy and Cryptanalysis • Basic idea is to count the relative frequencies of letters • have tables of single, double & triple letter frequencies • calculate letter frequencies for ciphertext • compare counts/plots against known values

30. English Letter Frequencies

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

33. Example Cryptanalysis • given ciphertext: UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ

34. Example Cryptanalysis • guess P & Z are e and t • Relatively high frequency letters S,U,O,M,H => { a,h,i,n,o,r,s } • Letters with lowest frequency A,B,G,Y,I,J => { b,j,k,q,v,x,z } • guess ZW is th • hence ZWP is the • ZWSZ if a complete word =>th_t • So S equates with a

35. Example Cryptanalysis • So far t a e e te a that e e a a t e t ta t ha e ee a e th t a e e e tat e the et • proceeding with trial and error,we finally get: it was disclosed yesterday that several informal but direct contacts have been made with political representatives of the viet cong in moscow

36. Problem

37. Polyalphabetic Ciphers • another approach to improving security is to use multiple cipher alphabets • called polyalphabetic substitution ciphers • makes 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

38. Vigenère Cipher • simplest polyalphabetic substitution cipher is the Vigenère Cipher • multiple caesar ciphers • Vigenère tableau • Each of 26 ciphers arranged horizontally • Key letter for each on its left • Plaintext letters arranged on top row • Ciphertext occurs in intersection of key letter in row x and plaintext in coloumn y • decryption simply works in reverse

39. Modern VigenèreTableau

40. Example • write the plaintext out • write the keyword repeated above it • use each key letter as a caesar cipher key • encrypt the corresponding plaintext letter • eg using keyword deceptive key: deceptivedeceptivedeceptive plaintext: wearediscoveredsaveyourself ciphertext: ZICVTWQNGRZGVTWAVZHCQYGLMGJ

41. Security of Vigenère Ciphers • have multiple ciphertext letters for each plaintext letter • hence letter frequencies are obscured • but not totally lost • start with letter frequencies • see if monoalphabetic or not • if not, then need to determine length of keyword

42. Autokey Cipher • Ideally - a key as long as the message • Vigenère proposed the autokey cipher • keyword is prefixed to message as key • eg. given key deceptive Key: deceptivewearediscoveredsav plaintext:wearediscoveredsaveyourself ciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLA

43. 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

44. 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

45. Problem • Create Rail Fence DLTAOAHCNYEKTOTSPNR

46. Columnar Transposition Ciphers • a more complex scheme • write letters of message out in rows over a specified number of columns • then reorder the columns(permute) according to some key before reading off column by column. 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

47. Double 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

48. 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

49. 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

50. 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