## Introduction to Cryptography with Open-Source SoftwareOnce the privilege of a secret few, cryptography is now taught at universities around the world. Introduction to Cryptography with Open-Source Software illustrates algorithms and cryptosystems using examples and the open-source computer algebra system of Sage. The author, a noted educator in the field, provides a highly practical learning experienc |

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### Contents

1 | |

Chapter 2 Basic number theory | 23 |

Chapter 3 Classical cryptosystems | 55 |

Chapter 4 Introduction to information theory | 79 |

Chapter 5 Publickey cryptosystems based on factoring | 93 |

Chapter 6 Publickey cryptosystems based on logarithms and knapsacks | 119 |

Chapter 7 Digital signatures | 145 |

Chapter 8 Block ciphers and the data encryption standard | 167 |

Chapter 11 Hash functions | 267 |

Chapter 12 Elliptic curves and cryptosystems | 295 |

Chapter 13 Random numbers and stream ciphers | 333 |

Chapter 14 Advanced applications and protocols | 361 |

Appendix A Introduction to Sage | 395 |

Appendix B Advanced computational number theory | 411 |

425 | |

Back Cover
| 435 |

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### Common terms and phrases

algorithm Alice and Bob Alice chooses Alice’s attack binary bits block cipher Bob’s bytes Chapter Chinese remainder theorem chooses a random ciphertext coin column congruences corresponding cryptanalysis cryptographic decryption defined determine digital signature discrete logarithm problem elements elliptic curve encryption entropy equation example extended Euclidean algorithm factor Fermat’s theorem finite field Gamal given hash function Here’s implemented input integer inverse key stream keyword large number large primes letters matrix method mod q modular multiplication Note obtained operation output pairs Peggy permutation plaintext polynomial possible prime numbers private key produce protocol public key public-key cryptosystem quadratic residue Rabin random number relatively prime result Rijndael S-box sage sends sequence Show signature scheme solve square roots step stream cipher string subkey super-increasing Suppose User verify Victor Vigen`ere cipher vote zero knowledge proof