Primality testing and integer factorization, as identified by Gauss in his "Disquisitiones Arithmeticae", Article 329, in 1801, are the two most fundamental problems (as well as the two most important research fields) in computational number theory. Withthe advent of modern computers, unexpected applications have also been found in primality testing and integer factorization. Primality Testing and Integer Factorization in Public-Key Cryptography introduces various algorithms for primality testing and integer factorization, with their applications in public-key cryptography and information security. More specifically, this book explores basic concepts and results in number theory in Chapter 1. Chapter 2 discusses various algorithms for primality testingand prime number generation, with an emphasis on the Miller-Rabin probabilistic test, the Goldwasser-Kilian and Atkin-Morain elliptic curve tests, and the Agrawal-Kayal-Saxena deterministic test for primality. Chapter 3 introduces...

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