An Introduction to Number Theory with CryptographyNumber theory has a rich history. For many years it was one of the purest areas of pure mathematics, studied because of the intellectual fascination with properties of integers. More recently, it has been an area that also has important applications to subjects such as cryptography. An Introduction to Number Theory with Cryptography presents number |
Contents
Chapter 0 Introduction | 1 |
Chapter 1 Divisibility | 9 |
Chapter 2 Unique Factorization | 59 |
Chapter 3 Applications of Unique Factorization | 71 |
Chapter 4 Congruences | 107 |
Chapter 5 Cryptographic Applications | 167 |
Chapter 6 Polynomial Congruences | 193 |
Chapter 7 Order and Primitive Roots | 207 |
Chapter 11 Geometry of Numbers | 337 |
Chapter 12 Arithmetic Functions | 367 |
Chapter 13 Continued Fractions | 383 |
Chapter 14 Gaussian Integers | 427 |
Chapter 15 Algebraic Integers | 453 |
Chapter 16 Analytic Methods | 479 |
Fermats Last Theorem | 503 |
Appendix A Supplementary Topics | 513 |
Chapter 8 More Cryptographic Applications | 241 |
Chapter 9 Quadratic Reciprocity | 263 |
Chapter 10 Primality and Factorization | 295 |
Appendix B Answers and Hints for OddNumbered Exercises | 535 |
Back Cover | 549 |
Other editions - View all
An Introduction to Number Theory with Cryptography James S. Kraft,Lawrence C. Washington No preview available - 2013 |
An Introduction to Number Theory with Cryptography James S. Kraft,Lawrence C. Washington No preview available - 2024 |
Common terms and phrases
ak+1 algebraic integers Alice and Bob assume b(mod binomial coefficient calculation Chapter CHECK YOUR UNDERSTANDING Chinese Remainder Theorem ciphertext common divisor composite compute congruence continued fraction Corollary cryptographic decryption discrete log divide Division Algorithm encryption equation Euler example exponent Extended Euclidean Algorithm Fermat's theorem formula Gaussian integers gcd(a gcd(b gcd(m gives Hint implies induction infinitely many primes irrational irreducible Lemma linear Mersenne Mersenne primes method mod 9 mod q modulus multiple nonzero number of primes number theory obtain odd prime plaintext polynomial positive integer prime and let prime factors prime numbers primitive root primitive root mod problem product of primes proof Proposition prove Pythagorean triples Quadratic Reciprocity rational numbers real number relatively prime says Section Show solution mod solve square mod Suppose true values write yields