Hashing (Message Digest)

1. Hashing (Message Digest)

2. Hashing (Message Digest) . . . . . . . . . . . .

3. Hashing (Message Digest) . . 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 2k outputs possible Hash needs to map to (2k)*(2k) values to get probability that two outputs are the same below ½.

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

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 . . . . . . . . . . . . Challenge R . . . . . . . . . . . . S S Client Monitor

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

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

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

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

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

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

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

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

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