## 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

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 Alice answer approximately assume base calculation called cards Chapter CHECK YOUR UNDERSTANDING chooses ciphertext coefficients common completes composite compute congruence continued fraction Corollary decryption digits divide divisible divisor elements encryption equal equation exactly example Exercise exist exponent fact Fermat formula function gcd(a gives implies induction infinitely irrational irreducible least Lemma less linear look means method mod n multiple Note obtain occurs pairs polynomial positive integer possible prime factors prime numbers primitive root problem proof Proposition prove quadratic quadratic irrational rational relatively prime remainder result says secret sends Show sides solution solve square square mod steps Suppose tells Test Theorem theory triple true unique unit values write yields