# 2_NumberTheory - 2 pseudorandom numbers(RN The pseudorandom...

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Modular Arithmetic 8/30/11 Arithmetic of remainders resulting from divisions of integers by a positive integer. Theorem 4.

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Theorem 3.
Theorem 5. Fact: a (a mod m) (mod m). Why? By the division algorithm, there exist two unique integers q and r such that a = q m + r, 0 r < m. Since m | a-r, a r (mod m), where r = a mod m (by definition)

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Arithmetic modulo m Properties of + m and * m operations Closure: Associativity: Commutativity: Distributivity:
Identity elements 0 and 1 such that Additive inverse:

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Applications of congruences 1. Hash functions
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Unformatted text preview: 2. pseudorandom numbers (RN) The pseudorandom sequence is 2, 6, 7, 10, 8, 2, . .. replace each letter by the third letter to the left to get clear text. For A, B, C use X, Y, Z, respecitively. cipher text clear Text Encrypt: Decrypt: position of the letter that replaces the letter in the cyphier text position of a letter in the alphabet position of a letter in the alphabet position of the letter that replaces the letter in the clear text 3. Encryption/decryption Problem 7, Section 4.5...
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2_NumberTheory - 2 pseudorandom numbers(RN The pseudorandom...

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