ICS 268 Syllabus

# Cryptography: Theory and Practice

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ICS 268, Fall'04 Lecture Summaries, Homeworks, Solutions, Handouts [+ a tentative schedule for what's to come] [back to course main page] Lectures 1-2 (lect1.pdf) Lectures 3-4 (h1-primes.pdf) , (h2-composites.pdf) , (Dana Angluin's notes on computation and number theory.pdf ) . We covered some basic modular arithmetic in the "primes" handout, and the extended Euclidean algorithm for computing gcd and modular inverses from chapter 4 of Dana's notes. Lecture 5 We showed that modular exponentation can be done efficiently (polynomial time), but we posed the inverse of the exponentiation, namely the discrete logarithm problem, as a problem for which no known efficient algorithm is known. We looked at two trivial attacks against discrete logarithm: exhaustive search and guessing, and concluded that the first runs in exponential time while the second one has a negligible probability of success. We saw Shank's discrete logarithm running in time O(\sqrt(q)) and the index calculus methods which run in time about O(2^{|p| ^{1/3}), and we translated these two algorithms into bounds on the size of p and q needed to achieve security for the discrete logarithm in practice. Finally, we stated the discrete logarihtm assumption. Reading: Most of this material is in Stinson, chapter 6, sections 6.1, 6.2 (esp 6.2.1, the other attacks are an optional reading), and 6.6. In the next lecture we'll abstract the assumption that discrete logarithm is hard into an assumption that "exponentiation is a one-way function". The best lecture notes which introduce one-way functions is Yevgeni Dodis's lecture notes #2.pdf . For now read up sections 1-7.

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