cse101_9_26_11

cse101_9_26_11 - Numeric algorithms 1 Cryptography A...

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Numeric algorithms 1. Cryptography A. Public-key cryptography has enabled e-commerce. It relies upon the algorithmic status of two classical problems. a. Factoring: given a number return its prime factorization (cannot be solved in polynomial time) There is no efficient (polynomial0 algorithm for this. b. Primality: given a number, say whether it is prime or composite. Can be solved efficiently. 2. The decimal system B. The unary system eg. 11111111 = 8. 10 100 – In unary the space required would exceed the # of particles in the universe. In decimal, need only 101 digits. C. Quantifying size – writing the number N in many require N characters. In decimal, you need log n n digits. N -> log N, exponentially smaller representation. Roman system: only a constant beter than unary, still O(N) space). D. In decimal, using d digits, you can write numbers in the range 0 to 10 d – 1. Therefore in order to write N in decimal, # of digit needed is the smallest integer d such that N <= 10 d – 1. D >= log 10 (N+1). Size = ceiling (log 10 (N+1)) ~ log 10 N E.
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