## Complexity and Cryptography: An IntroductionCryptography plays a crucial role in many aspects of today's world, from internet banking and ecommerce to email and web-based business processes. Understanding the principles on which it is based is an important topic that requires a knowledge of both computational complexity and a range of topics in pure mathematics. This book provides that knowledge, combining an informal style with rigorous proofs of the key results to give an accessible introduction. It comes with plenty of examples and exercises (many with hints and solutions), and is based on a highly successful course developed and taught over many years to undergraduate and graduate students in mathematics and computer science. |

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### Contents

249 | |

250 | |

Appendix 2 | 252 |

Algebra and number theory | 253 |

Probability theory | 257 |

Hints to selected exercises and problems | 261 |

Appendix 6 | 268 |

### Other editions - View all

Complexity and Cryptography: An Introduction, Volume 13 John Talbot,D. J. A. Welsh Limited preview - 2006 |

### Common terms and phrases

Alice Alice and Bob binary operation Blum prime certificate Chapter 7 Exercises Chinese Remainder Theorem clique compute Consider coprime cryptograms denote the set DESK(M Discrete Logarithm edges encounters a state/symbol encryptions end of ﬁrst end of string event exists fact factor ﬁnished ﬁrst string found end graph G group G halt HAMILTON CYCLE Hence Inequality input k-colouring mod n mod q modn monomial multiplication NP-complete Number theory one-time pad ord(g outputs P/poly pairs of vertices pairwise parameters partition polynomial time algorithm possible value Pr[A Pr[B Pr[n Prime Number Theorem primitive roots mod probability at least Problems 2.2 proof of Proposition proof of Theorem public key quadratic residue mod random variable satisﬁes satisfying second string Show state/symbol combination string found subgroup of G success probability takes time O(log3 tape alphabet Theorem A3.8 TRAVELLING SALESMAN var[X vertex write f(n zero