1. DTTF/NB479: Dszquphsbqiz Day 25
Announcements:
Term project groups and topics formed
HW6 due tomorrow.
Questions?
This week:
Discrete Logs, Diffie-Hellman, ElGamal
Hash Functions

2. Discrete Logs
Given
Find x
We denote this as
Why is this hard?

3. Pollig-Hellman Useful when (p-1) has only small prime factors
Did long derivation
Introduced problem 2x=12 (mod 19)
Finish for Homework 6.

4. Baby Step, Giant Step Like the meet-in-the-middle attack on Double-DES
Eve chooses , say
She makes 2 tables:
and looks for a match.
Why should there be one? Write x in base N.
Requires ~p comparisons,
but only p1/2 exponentiations
and space. Works for medium-size primes.

5. Some things we won’t cover in class about Discrete Logs
7.2.3 Index Calculus: like sieve method of factoring primes
The equation on p. 207 might help with some of homework 7.
Discrete logs mod 4 and bit commitment
We skip to make time for some applications of discrete logs
Although the football game prediction analogy is interesting…