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 theory along with many interesting applications. Designed for an undergraduate-level course, it covers standard number theory topics and gives instructors the option of integrating several other topics into their coverage. The "Check Your Understanding" problems aid in learning the basics, and there are numerous exercises, projects, and computer explorations of varying levels of difficulty. |
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Contents
| 1 | |
| 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 |
Common terms and phrases
algebraic integers Alice and Bob Alice’s assume binomial coefficient calculation Chapter CHECK YOUR UNDERSTANDING Chinese Remainder Theorem ciphertext common divisor composite compute congruence continued fraction Corollary cryptographic decryption denominator discrete log divide Division Algorithm encryption equation example exponent Extended Euclidean Algorithm Fermat’s Last Theorem Fermat’s theorem formula Gaussian integers gcd(a gcd(a,b gcd(b gcd(m gives Here’s Hint implies induction infinitely many primes irrational irreducible last digit Lemma linear Mersenne primes method mod 9 mod q modulus multiple nonzero number of primes number theory obtain odd number odd prime plaintext polynomial positive integer prime and let prime factors prime numbers primitive root primitive root mod problem product of primes Proposition prove Pythagorean triples Quadratic Reciprocity rational numbers real number relatively prime says Section sends Show solution mod solve square mod Suppose true unique values write yields
Bibliographic information
| Title | An Introduction to Number Theory with Cryptography |
| Authors | James S. Kraft, Lawrence C. Washington |
| Edition | illustrated |
| Publisher | CRC Press, 2016 |
| ISBN | 1482214423, 9781482214420 |
| Length | 572 pages |
| Subjects | › Mathematics / Applied Mathematics / Combinatorics Mathematics / Number Theory |
| Export Citation | BiBTeX EndNote RefMan |