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Announcements: Term project groups and topics formed HW6 due tomorrow. Questions? This week:

This week's announcements include forming term project groups, homework 6 due date reminder, and topics covered (Discrete Logs, Diffie-Hellman, ElGamal). Quick humor with a funny XKCD comic and useful resources mentioned.

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Announcements: Term project groups and topics formed HW6 due tomorrow. Questions? This week:

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  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. Quick humor • http://xkcd.com/c247.html • Thanks to Ted Lyman, 2007

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

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

  5. 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.

  6. 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…

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