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  9.1 Copyright © The McGraw-Hill Companies, Inc. Permission required or reproduction or display. Chapter 9Mathematics of Cryptography Part III: Primes and Related Congruence Equations  9.2 Objectives  ❏ To introduce prime numbers and their applications in cryptography.  ❏ To discuss some primality test algorithms and their efficiencies.  ❏ To discuss factorization algorithms and their applications in cryptography.  ❏ To describe the Chinese remainder theorem and its application.  ❏ To introduce quadratic congruence.  ❏ To introduce modular exponentiation and logarithm. Chapter 9  9.3 9-1 PRIMES9-1 PRIMES  Asymmetric-key cryptography uses primes extensively.  Asymmetric-key cryptography uses primes extensively. The topic of primes is a large part of any book on The topic of primes is a large part of any book on number theory. This section discusses only a few number theory. This section discusses only a few concepts and facts to pave the way for Chapter 10.concepts and facts to pave the way for Chapter 10. 9.1.1efinition9.1.!Cardinality of rimes9.1.#Chec$ing for rimeness9.1.%&uler's hi()unction9.1.*)ermat's +ittle Theorem9.1.,&uler's Theorem9.1.-enerating rimes Topics discussed in this sectionT    opics discussed in this section  9.4 !.1.1 efinition )igure 9.1 Three groups of positive integers / prime is divisible only by itself and 1.  #ote
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