1. Digital Signatures

2. Anononymity and the Internet

3. Potential For Mischief

4. Potential For Mischief

5. Dilemma • Need encryption for security • Encryption needs shared key

6. Dilemma • Need encryption for security • Encryption needs shared key • Diffie Hellman produces shared key

7. Dilemma • Need encryption for security • Encryption needs shared key • Diffie Hellman produces key • But with who???

8. Symmetric Cryptography • Traditional cryptography • Same secret encrypts and decrypts:Shift by three lettersXOR with bits

9. Asymmetric Cryptography • Symmetric cryptography:Key for encoding same as key for decoding • Shift three letters

10. Asymmetric Cryptography • Asymmetric cryptography:Key for encoding different than for decoding

11. Asymmetric Cryptography • Keys work in both directions

12. Asymmetric Cryptography • You can't unlock with key used to lock

13. Public/Private Keys • Make an A/B pair of asymmetric keys • Give one away : Public Key • Keep one secret : Private Key

14. Private Key • Only owner can lock with private key • Anyone can unlock Message is "Signed"

15. Public Key • Everyone can lock with public key • Only private key holder can unlock

16. Key Distribution Problem • How do you get the right public key from Wells Fargo?

17. Key Distribution Problem • How do you get the right public key from Wells Fargo? Sure, I'm Wells Fargo, here is my public key!!!

18. Signature Bank • Record of signatures

19. Authenticating a Key • Official key bank?? Wells Fargo

20. Can't Trust Internet Bank • Same problem: Key Bank Sure, I'm the key bank, here is Wells Fargo's key!!!

21. Authenticating a Key • Computers & Browsers come with public keys from Certification Authorities

22. Authenticating a Key • Browsers come with public keys of known banks called Certification Authorities

23. Authenticating a Key • Certification Authorities use private key to lock up public keys of other companies "Certificate"

24. Authenticating a Key • If your computer can open box with Verisign public key you can trust what is inside "Certificate"

25. Chain Of Trust • Reality may involve chain of locks

26. Chain Of Trust • Reality may involve chain of locks

27. Web Security • HTTPS : Secure web connection • Browser asks server for certificated public key • Browser picks shared secret • Encrypts with public key, sends to server

28. Web Security • HTTPS : Secure web connection • Browser asks server for public key • Browser picks shared secret,encrypts with public key, sendsto server

29. Asymmetric Math • Use same tricks as Diffie-Hellman: • Exponents • Mod

30. Asymmetric Math • Possible to pick numbers A, B, C so that:

31. Asymmetric Math • Example: A = 3, B = 7, C = 22 • Encrypt with A, decrypt with B

32. Asymmetric Math • Example: A = 3, B = 7, C = 22 • OR encrypt with B, decrypt with A

33. RSA • How do we pick A, B, C that work together??? • RSA algorithm invented in 1977(Rivest, Shamir, Adelman)

34. Picking Keys • Start with two prime numbers p, q – multiply to make clock size (C)

35. Picking Keys • Start with two prime numbers p, q – multiply to make clock size (C) • Pick (A) that will be part of your private key: {A, C}

36. Picking Keys • Start with two prime numbers p, q – multiply to make clock size (C) • Pick (A) that will be part of your private key: {A, C} • Calculate (B) from p, q and (A). This makes your public key:{B, C}

37. Picking Keys • Start with two prime numbers p, q – multiply to make clock size (C) • Pick (A) that will be part of your private key: {A, C} • Calculate (B) from p, q and (A). This makes your public key:{B, C} • If anyone figures out p and q they can use B to calculate A !!!

38. Picking Keys • Start with two prime numbers p, q – multiply to make clock size (C) … • If anyone figures out p and q they can use B to calculate A !!! • To get p and qyou have to factor C

39. Factoring • Factoring large numbers is hard • But we are getting faster

40. Factoring • Factoring large numbers is hard • But we are getting faster • Larger keys : 2048 bits (prime numbers with 100's of digits)

41. Signed Message • Messages can be anything • Data, Other keys • Any attempt to modify encrypted box will mess up the message

42. Four messages: • I sent four messages "signed" with private key • My public key: exponent 3, clock 34 message = encrypted ^ exponent mod clock • One message was modified, which one is it? • Three should check out, one should not