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Shared Secrets

Shared Secrets. Keeping secrets on the web. Encryption. Goal : hidden in plain sight. Encryption. Goal : hidden in plain sight Internet is plain sight. Encryption. Goal : hidden in plain sight Internet is plain sight Encryption is only form of privacy. Caesar Cipher.

latifah-jensen
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Shared Secrets

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  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

  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 ýw

  12. Binary Keys • 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

  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 10possible valuesthen cycle…

  33. Powers of 2 Mod 4 • Powers of 2 mod 4: Prime clock sizes work better…

  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 • Public Private Number: • Given base = 2, clocksize = 11, private number = 8:

  38. Diffie Hellman • Derive a secret number • Calculate public-private numbers

  39. Diffie Hellman • Derive a secret number • Use other ppn as base to calculate shared secret

  40. Shared Secret Number • Shared Secret Number:ss • Given private number = 8, clocksize = 11, other ppn = 6:

  41. Diffie Hellman • Derive a secret number • Use other ppn as base to calculate shared secret

  42. Sue's dilemma • Sue knows:2x mod 11 = 62y mod 11 = 36y mod 11 = ssn3xmod 11 = ssn Where y = your private number And x = Arnolds

  43. Sue's dilemma • Sue knows:2x mod 11 = 62y mod 11 = 36y mod 11 = ssn3xmod 11 = ssn • Mod is one way – must guess and check

  44. Sue's dilemma • Sue knows:2x mod 11 = 62y mod 11 = 36y mod 11 = ssn3xmod 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 My PPN:4?? mod 13 = 10 Your PPN:48 mod 13 = 3 Your Private Number: 8 My Private Number: ?? SSN = (myPPN)(your privatenumber) mod (clock size)

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