1. Hashing (Message Digest)

2. ............

3. ............ Hello There

4. Hashing (Message Digest)............ What not

5. Hash Function – One way Needed properties for cryptographically secure hash: 1. Computationally infeasible to find the message that has given the hash 2. Should be impossible for two messages to hash to the same number (and to find two messages with the same hash). Message substitution possible otherwise

6. Hash Function – One way Appearrance to a cracker: 1. Looking at output, any bit should be 1 about ½ the time 0010111...1...001110 2. Each output should have about ½ of its bits set to 1 3. Any two outputs should be uncorrelated no matter how similar the inputs are

7. Hash Function – One way Birthday Problem: Assume a completely random hash function If the number of output bits is k, then 2 k outputs possible Hash needs to map to (2 k )*(2 k ) values to get probability that two outputs are the same below ½.

8. Hashing (Message Digest)............ Secret The little brown fox jumped over the lazy dog's back

9. Hashing (Message Digest)............ The little brown fox jumped over the lazy dog's back

10. Hashing (Message Digest)............ The little brown fox jumped over the lazy dog's back

11. Hashing (Message Digest)............ The little brown fox jumped over the lazy dog's back

12. Hashing (Message Digest)............ The little brown fox jumped over the lazy dog's back

13. Hashing (Message Digest)............ The little brown fox jumped over the lazy dog's back

14. Hashing (Message Digest)............ The little brown fox jumped over the lazy dog's back Output

15. Hashing - authentication........................ S S Client Monitor

16. Hashing - authentication........................ S S Client Monitor Challenge R

17. Hashing - authentication........................ S S Client Monitor Hash(S | R)

18. Hashing - authentication........................ S S Client Monitor Check Hash(S | R)?

19. Hashing - authentication........................ S S Client Monitor Challenge P

20. Hashing - authentication........................ S S Client Monitor Hash(S | P)

21. Hashing - authentication........................ S S Client Monitor Check Hash(S | P)?

22. Hashing - Message Authenication Same as authentication except concatenate the message with the secret and pad.

23. Hashing - Message Authenication Same as authentication except concatenate the message with the secret and pad. Unfortunately, attacker can append a message since s/he knows Hash(S | M) and the Hash algorithm.

24. Hashing - Message Authenication Same as authentication except concatenate the message with the secret and pad. Unfortunately, attacker can append a message since s/he knows Hash(S | M) and the Hash algorithm. Here is what to do: 1. Concatenate secret to front of message 2. Take the hash 3. Concatenate the secret to the front of the hash 4. Take the hash

25. Hashing - encryption............ Secret The little brown fox jumped over the lazy dog's back Initialization Vector + To receiver

26. Hashing - encryption............ Secret The little brown fox jumped over the lazy dog's back +

27. Hashing - encryption............ Secret The little brown fox jumped over the lazy dog's back + To receiver

28. Hashing - encryption............ Secret The little brown fox jumped over the lazy dog's back +

29. Hashing - encryption............ Secret The little brown fox jumped over the lazy dog's back + To receiver