The Vigenère cipher is a stronger version of the Caesar cipher The encryption key is a word/sentence/random text ( and )

Transcription

1 A Better Cipher The Vigenère cipher is a stronger version of the Caesar cipher The encryption key is a word/sentence/random text ( and ) To the first letter, add 1 To the second letter, add 14 To the third letter, add 4

2 A Better Cipher The Vigenère cipher is a stronger version of the Caesar cipher The encryption key is a word/sentence/random text ( and ) To the first letter, add 1 To the second letter, add 14 To the third letter, add 4 To the fourth letter, add 1 To the fifth letter, add 14 To the sixth letter, add 4

3 A Better Cipher The Vigenère cipher is a stronger version of the Caesar cipher The encryption key is a word/sentence/random text ( and ) To the first letter, add 1 To the second letter, add 14 To the third letter, add 4 To the fourth letter, add 1 To the fifth letter, add 14 To the sixth letter, add 4 Repeat as necessary

4 Vigenère Cipher Encrypt university using the key kentucky

5 Vigenère Cipher Encrypt university using the key kentucky A: GTXQAVEIFE B: GTXQAVDHED C: FSWPZUDHED D: FSWPZUEIFE E: None of the above

6 Vigenère Cipher Encrypt university using the key kentucky u n i v e r s i t y

7 Vigenère Cipher Encrypt university using the key kentucky u n i v e r s i t y encode

8 Vigenère Cipher Encrypt university using the key kentucky u n i v e r s i t y encode key

9 Vigenère Cipher Encrypt university using the key kentucky u n i v e r s i t y encode key add

10 Vigenère Cipher Encrypt university using the key kentucky u n i v e r s i t y encode key add decode F S W P Z U D H E D The correct answer is FSWPZUDHED (C)

11 Vigenère Cipher EPHHFLH was encrypted using the Vigenère cipher with the encryption key coffee. What is the plaintext?

12 Vigenère Cipher EPHHFLH was encrypted using the Vigenère cipher with the encryption key coffee. What is the plaintext? A: babbled B: badgers C: bagpipe D: baggage E: None of the above

13 Vigenère Cipher E P H H F L H

14 Vigenère Cipher E P H H F L H encode

15 Vigenère Cipher E P H H F L H encode encryption key

16 Vigenère Cipher E P H H F L H encode decryption key

17 Vigenère Cipher E P H H F L H encode decryption key add

18 Vigenère Cipher E P H H F L H encode decryption key add decode b a b b a g e

19 Vigenère Cipher E P H H F L H encode decryption key add decode b a b b a g e The correct answer is E

20 Modular Arithmetic In Z m, we can multiply elements

21 Modular Arithmetic In Z m, we can multiply elements [a][b] = [ab]

22 Modular Arithmetic In Z m, we can multiply elements [a][b] = [ab] Any number in [a] times any number in [b] will be in [ab]

23 Modular Arithmetic In Z m, we can multiply elements

24 Modular Arithmetic In Z m, we can multiply elements In Z 7 :

25 Modular Arithmetic In Z m, we can multiply elements In Z 7 : [3][2] =

26 Modular Arithmetic In Z m, we can multiply elements In Z 7 : [3][2] =[6]

27 Modular Arithmetic In Z m, we can multiply elements In Z 7 : [3][2] =[6] [4][2] =

28 Modular Arithmetic In Z m, we can multiply elements In Z 7 : [3][2] =[6] [4][2] =[8]

29 Modular Arithmetic In Z m, we can multiply elements In Z 7 : [3][2] =[6] [4][2] =[8]= [1]

30 Modular Arithmetic In Z m, we can multiply elements In Z 7 : [3][2] =[6] [4][2] =[8]= [1] [5][4] =

31 Modular Arithmetic In Z m, we can multiply elements In Z 7 : [3][2] =[6] [4][2] =[8]= [1] [5][4] =[20]

32 Modular Arithmetic In Z m, we can multiply elements In Z 7 : [3][2] =[6] [4][2] =[8]= [1] [5][4] =[20]= [6]

33 New Attempt for a Cipher Idea for Multiplicative Shift Encode the message using Z 26 as before

34 New Attempt for a Cipher Idea for Multiplicative Shift Encode the message using Z 26 as before Choose an number in Z 26 as a key

35 New Attempt for a Cipher Idea for Multiplicative Shift Encode the message using Z 26 as before Choose an number in Z 26 as a key Multiply the message by the key

36 New Attempt for a Cipher Encode there are three books using the key d = [4]

37 New Attempt for a Cipher Encode there are three books using the key d = [4] A: YCQQQAQQYCQQQEEEOU B: ZCQQQAQQZCQQQEEEOU C: YCQQQQQQYCQQQEEEOU D: YCQQQAQQYCQQQEEEUO E: None of the above

38 New Attempt for a Cipher Encrypt there are three books using the key [4] t h e r e a r e t h r e e b o o k s

39 New Attempt for a Cipher Encrypt there are three books using the key [4] t h e r e a r e t h r e e b o o k s

40 New Attempt for a Cipher Encrypt there are three books using the key [4] t h e r e a r e t h r e e b o o k s

41 New Attempt for a Cipher Encrypt there are three books using the key [4] t h e r e a r e t h r e e b o o k s

42 New Attempt for a Cipher Encrypt there are three books using the key [4] t h e r e a r e t h r e e b o o k s Y C Q Q Q A Q Q Y C Q Q Q E E E O U

43 New Attempt for a Cipher Encrypt there are three books using the key [4] t h e r e a r e t h r e e b o o k s Y C Q Q Q A Q Q Y C Q Q Q E E E O U The ciphertext is YCQQQAQQYCQQQEEEOU (A)

44 New Attempt for a Cipher Problems?

45 New Attempt for a Cipher Problems? We will never be able to decrypt this!

46 New Attempt for a Cipher Problems? We will never be able to decrypt this! After encrypting, we can t tell e and r apart (nor b and o)

47 New Attempt for a Cipher Problems? We will never be able to decrypt this! After encrypting, we can t tell e and r apart (nor b and o) How do we undo multiplication by [4]?

48 New Attempt for a Cipher Problems? We will never be able to decrypt this! After encrypting, we can t tell e and r apart (nor b and o) How do we undo multiplication by [4]? Division is not well-defined

49 New Attempt for a Cipher Problems? We will never be able to decrypt this! After encrypting, we can t tell e and r apart (nor b and o) How do we undo multiplication by [4]? Division is not well-defined 1 = [4] [4] = [30] =?? [4]

50 New Attempt for a Cipher Problems? To undo multiplying by [4], we want to multiply by [k] so that [4k] = [1]

51 New Attempt for a Cipher Problems? To undo multiplying by [4], we want to multiply by [k] so that [4k] = [1] But [4][13] = [52] = [0]

52 New Attempt for a Cipher Problems? To undo multiplying by [4], we want to multiply by [k] so that [4k] = [1] But [4][13] = [52] = [0] If [k] existed, [13] = [k][4][13] = [k][0] = [0], a contradiction

53 New Attempt for a Cipher Problems? To undo multiplying by [4], we want to multiply by [k] so that [4k] = [1] But [4][13] = [52] = [0] If [k] existed, [13] = [k][4][13] = [k][0] = [0], a contradiction We will only choose encryption keys with a multiplicative inverse

54 Multiplication Tables The multiplication table for Z 5 :

55 Multiplication Tables The multiplication table for Z 5 : [0] [1] [2] [3] [4] [0] [0] [0] [0] [0] [0] [1] [0] [1] [2] [3] [4] [2] [0] [2] [4] [1] [3] [3] [0] [3] [1] [4] [2] [4] [0] [4] [3] [2] [1]

56 Multiplication Tables The multiplication table for Z 5 : [0] [1] [2] [3] [4] [0] [0] [0] [0] [0] [0] [1] [0] [1] [2] [3] [4] [2] [0] [2] [4] [1] [3] [3] [0] [3] [1] [4] [2] [4] [0] [4] [3] [2] [1] So [1], [2], [3], [4] all have inverses (they are units)