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 letters XOR 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 Message is "Signed" 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, sends to 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 (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 q you 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:
Message 5 4 15 8
Encrypted Version 11 30 12 2
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
private key 11