1. Shared Secrets Keeping secrets on the web

2. Encryption Goal : hidden in plain sight

3. Encryption Goal : hidden in plain sight – Internet is plain sight

4. Encryption Goal : hidden in plain sight – Internet is plain sight – Encryption is only form of privacy

5. Caesar Cipher Shift each letter in a message a certain amount:

6. Caesar Cipher Right shift of three: – Key: is +3 Encrypted message:

7. Breaking a Cipher Guess and check

8. XOR XOR with 0 = don't change XOR with 1 = change In0In1Out 101 110 In0In1Out 000 011

9. Binary Keys 1 or 0 with XOR = 1 bit encryption – 1 or 0 is key… 2 possibilities

10. Binary Keys 1 or 0 with XOR = 1 bit encryption – 1 or 0 is key… 2 possibilities For stronger key, need more bits: – 32 bit key = 4 billion possibilities – Real encryption uses 128/256/512/1025/2048 bits!

11. Binary Keys XOR key with message to produce encrypted message W i k i ??? Ä ý w

12. XOR key with encrypted message to reproduce message ??? Ä ý w W i k i More info: https://fr.khanacademy.org/math/applied-math/cryptography/ciphers/e/bitwise-operators https://fr.khanacademy.org/math/applied-math/cryptography/ciphers/e/bitwise-operators Binary Keys

13. Shared Keys Need to share a key – How do we do it if someone is always listening?

14. Secret Colors Deriving a secret color:

15. Secret Colors Deriving a secret color: – Pick a public color

16. Secret Colors Deriving a secret color: – Pick private colors

17. Secret Colors Deriving a secret color: – Make public mixtures with private colors

18. Secret Colors Deriving a secret color: – Mix other person's public with your private

19. Secret Colors Eve can't reproduce color – too much red

20. Attempting with Math Not so secret…

21. Attempting with Math Not so secret…

22. One Way Function One way function: – Can not be reversed Multiplication two way x ∙ 7 = 42

23. Clock Math http://www.shodor.org/interactivate/activities/ClockArithmetic/

24. Modulo Modulo ( mod or % ) – Divide and keep remainder 14 mod 12 = 2 8 mod 12 = 8 19 mod 12 = 7 24 mod 12 = 0 26 mod 12 = 2

25. Calculating Mods Wolfram Alpha

26. One Way Math Clock Math/Modulo is One Way X mod 12 = 2 …what is X???

27. One Way Math Clock Math/Modulo is One Way X mod 12 = 2 …what is X??? 14 mod 12 = 2 26 mod 12 = 2 38 mod 12 = 2 …

28. Hard Math Some problems are relatively slow to solve: – Factoring numbers – Taking logarithms

29. Hard Math Some problems are relatively slow to solve: – Factoring numbers – Taking logarithms Slow is good for encryption – Avoid brute force attacks

30. Diffie Hellman Derive a secret number

31. Diffie Hellman Derive a secret number – Pick two public numbers – clock size and base Clock size: 11 Base : 2

32. Powers of 2 Mod 11 Powers of 2 mod 11: Mod 11 means 10 possible values then cycle… Power of 2ValueMod 11 122 244 388 4165 53210 6649 71287 82563 95126 1010241 1120482 1240964

33. Powers of 2 Mod 4 Powers of 2 mod 4: Prime clock sizes work better… Power of 2ValueMod 4 122 240 380 4160 5320 6640 71280 82560 95120 1010240 1120480 1240960

34. Diffie Hellman Derive a secret number – Pick two public numbers – clock size and base Clock size: 11 Base : 2

35. Diffie Hellman Derive a secret number – Pick private numbers

36. Diffie Hellman Derive a secret number – Calculate public-private numbers…

37. Public Private Number

38. Diffie Hellman

39. Derive a secret number – Use other ppn as base to calculate shared secret

40. Shared Secret Number

41. Diffie Hellman

42. Sue's dilemma Sue knows: 2 x mod 11 = 6 2 y mod 11 = 3 6 y mod 11 = ssn 3 x mod 11 = ssn Where y = your private number And x = Arnolds

43. Sue's dilemma Sue knows: 2 x mod 11 = 6 2 y mod 11 = 3 6 y mod 11 = ssn 3 x mod 11 = ssn Mod is one way – must guess and check

44. Sue's dilemma Sue knows: 2 x mod 11 = 6 2 y mod 11 = 3 6 y mod 11 = ssn 3 x mod 11 = ssn Solving for x or y involves logarithms – very slow for computers

45. What is our secret? Calculate our shared secret: clock size = 13, base = 4 Then go to: faculty.chemeketa.edu/ascholer/SSN.html Your Private Number: 8 My Private Number: ?? Your PPN: 4 8 mod 13 = 3 My PPN: 4 ?? mod 13 = 10 SSN = (myPPN) (your private number) mod (clock size)