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Number Theory and Cryptography

Number Theory and Cryptography

Number Theory and Cryptography. Chapter 4. With Question/Answer Animations. Chapter Motivation. Number theory is the part of mathematics devoted to the study of the integers and their properties. Key ideas in number theory include divisibility and the primality of integers.

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1.94k views • 103 slides
Number Theory and Cryptography

Number Theory and Cryptography

Number Theory and Cryptography. Chapter 4. With Question/Answer Animations. Divisibility and Modular Arithmetic. Section 4.1. Division. Definition : If a and b are integers with a ? 0 , then a divides b if there exists an integer c such that b = ac .

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2.63k views • 56 slides
RSA

RSA

RSA. Preliminaries. Division Algorithm. Given integers a and b ?0 , there exist unique Integers q and r such that a = bq +r where 0 ? r < |b| a is the dividend , b is the divisor , and r is the remainder . b divides a or b is a factor of a if r=0.

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340 views • 21 slides
Integer Factorization

Integer Factorization

Integer Factorization. By: Josh Tuggle & Kyle Johnson. What Is It?. Integer Factorization - T he decomposition of a composite number into its primes. Not much of an actual problem until the number becomes very large. No efficient algorithm exists yet. Goal: Factor in polynomial time.

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387 views • 18 slides
CONGRUENCES AND MODULAR ARITHMETIC

CONGRUENCES AND MODULAR ARITHMETIC

CONGRUENCES AND MODULAR ARITHMETIC. Congruence and Modular Arithmetic Definition: a is congruent to b mod n means that n?a -b, (a-b) is divisible by n. Notation: a ? b (mod n) , a, b, n ? I, n ? b Ex . 42 ? 30 (mod 3)

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596 views • 15 slides
Chapter 3

Chapter 3

Chapter 3. 3.4 The Integers and Division Division The D ivision Algorithm Modular Arithmetic Applications of Congruences Cryptology. Division.

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270 views • 13 slides

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