1. Announcements: 1. Term project groups and topics formed 2. HW6 due tomorrow. Questions? This week: Discrete Logs, Diffie-Hellman, ElGamal Discrete Logs, Diffie-Hellman, ElGamal Hash Functions Hash Functions DTTF/NB479: DszquphsbqizDay 25

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

3. Pollig-Hellman Useful when (p-1) has only small prime factors Did long derivation Introduced problem 2 x =12 (mod 19) Finish for Homework 6. 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 p 1/2 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. 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 We skip to make time for some applications of discrete logs Although the football game prediction analogy is interesting… Although the football game prediction analogy is interesting…