## Introduction to Modern Cryptography: Principles and ProtocolsCryptography plays a key role in ensuring the privacy and integrity of data and the security of computer networks. Introduction to Modern Cryptography provides a rigorous yet accessible treatment of modern cryptography, with a focus on formal definitions, precise assumptions, and rigorous proofs. The authors introduce the core principles of modern cryptography, including the modern, computational approach to security that overcomes the limitations of perfect secrecy. An extensive treatment of private-key encryption and message authentication follows. The authors also illustrate design principles for block ciphers, such as the Data Encryption Standard (DES) and the Advanced Encryption Standard (AES), and present provably secure constructions of block ciphers from lower-level primitives. The second half of the book focuses on public-key cryptography, beginning with a self-contained introduction to the number theory needed to understand the RSA, Diffie-Hellman, El Gamal, and other cryptosystems. After exploring public-key encryption and digital signatures, the book concludes with a discussion of the random oracle model and its applications. Serving as a textbook, a reference, or for self-study, Introduction to Modern Cryptography presents the necessary tools to fully understand this fascinating subject. |

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### Contents

Some Preliminary Notions and Facts from Probability Theory | 7 |

Comparison of Random Variables Preferences of Individuals | 63 |

COMPARISON OF R V S AND LIMIT THEOREMS | 79 |

NONLINEAR CRITERIA | 111 |

OPTIMAL PAYMENT FROM THE STANDPOINT OF THE INSURED 125 | 125 |

An individual Risk Model for a Short Period | 137 |

CHAPTERS Conditional Expectations | 191 |

A GENERAL APPROACH TO CONDITIONAL EXPECTATIONS | 215 |

Global Characteristics of the Surplus Process Ruin Models | 363 |

CHAPTERS Survival Distributions | 413 |

Life Insurance Models | 461 |

Annuity Models | 499 |

Premiums and Reserves | 531 |

Reinsurance and Coinsurance | 565 |

Tables | 607 |

Answers to Exercises | 619 |

A Collective Risk Model for a Short Period | 225 |

CHAPTERS Random Processes I Counting and Compound Processes | 269 |

Random Processes II Brownian Motion and Martingales | 329 |

### Common terms and phrases

Actuarial annuity approximation Assume benefit Brownian motion calculations called Casualty Actuarial Society certainty equivalent Chapter clients coefficient compound Poisson process compute conditional expectation consider continuous convergence corresponding criterion death defined definition Denote density depend discrete distribution F distribution with parameter equal equation estimate event Exercise expected value exponential distribution F-distribution Find finite follows force of mortality formula geometric distribution given graph Hence heuristic initial surplus integral interval lifetime loss martingale negative binomial distribution notation Note number of claims optimal Pareto Pareto optimal particular payment period Poisson distribution Poisson process portfolio positive premium present value proof Proposition prove reader reinsurance respectively ruin probability Section Show situation of Example solution standard normal survival function term Theorem true uniformly distributed unit of money utility function Var{X variance vector whole life insurance write zero