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Unformatted text preview: that monks in a temple tower were given 64 rings at the beginning of time. They were told to play the above game, and that the world would end when they were ﬁnished. Assuming that the monks worked in shifts twenty-four hours per day, moving one ring per second without any errors, how many years does the world last? 2. EXTRA CREDIT from HW2 (10 points) Prove that the number of iterations of the Euclidean algorithm to ﬁnd gcd( a,b ) is O (log b ). (Note that this holds for both b ≤ a and b ≥ a .) 3. EXTRA CREDIT from HW3 (10 points) Describe the most eﬃcient algorithm you can for computing x b mod n , if b is an arbi-trary integer. Your solution should be eﬃcient enough to use for RSA encoding. HINT: We have already seen in class how to do this if b is of the form b = 2 l for some integer l ....
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This note was uploaded on 10/07/2010 for the course C S 52475 taught by Professor Gal during the Fall '10 term at University of Texas.
- Fall '10