Class-4-5-10

Class-4-5-10 - More Number Theory (Elementary) next Modular...

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More Number Theory (Elementary) next

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Modular Arithmetic A = B q + r y = x (mod p ) y = p q + x y = “a -1 1 . For small p inverses are obtained from the multiplication modulo p table 2. For large p we use the euclidean algorithm y a =1 (mod p ) Quotient Remainder 3 . Recall that GCD of two numbers A an B is the largest number that divides them both and is denoted (A,B) 4 . A fundamental fact: It is always possible to ±nd to integers H and K giving (A,B) = H A + K B 5 . (A,B) as well as H and K will be obtained from the Euclidean Algorithm next 0 x<p 0 r < B
A RANDOM NUMBER GENERATOR next A random number in the interval [0,1]

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Homophonic Substitution Key: “GOLF” Add 25 to second row, 50 to third row, 75 to frst row, etc . . . Message: The box will arrive by train Plaintext: T H E B O X W I L L A R R I V E B Y T R A I N 7 Ciphertext: next
THE EUCLIDEAN ALGORITHM Berlekamp’s version The Euclidean algorithm is the process which yields the greatest common divisor d of two given integers

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This note was uploaded on 09/22/2010 for the course MATH MATH187 taught by Professor Math187 during the Spring '10 term at UCSD.

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Class-4-5-10 - More Number Theory (Elementary) next Modular...

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