DTTF/NB479: Dszquphsbqiz Day 25

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Presentation transcript:

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

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

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

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.

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…