Introduction to Modern Cryptography: Principles and ProtocolsCRC Press, 31. 8. 2007 - Počet stran: 552 Cryptography 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. |
Obsah
An individual Risk Model for a Short Period | 1 |
Random variables random vectors and their distributions | 10 |
Quantiles | 17 |
7 | 24 |
7 | 28 |
MOMENT GENERATING FUNCTIONS | 38 |
SOME BASIC DISTRIBUTIONS | 39 |
4 | 44 |
5 | 312 |
EXERCISES | 321 |
EXERCISES | 327 |
Random Processes II Brownian Motion and Martingales | 329 |
MARTINGALES | 338 |
EXERCISES | 359 |
Tradeoff between the premium and the initial surplus | 381 |
6 | 390 |
SOME FACTS AND FORMULAS FROM THE THEORY OF INTEREST | 50 |
COMPARISON OF R V S AND LIMIT THEOREMS | 79 |
EXPECTED UTILITY | 85 |
How we may determine the utility function in particular cases | 94 |
NONLINEAR CRITERIA | 108 |
3 | 121 |
1 | 122 |
THE AGGREGATE PAYMENT | 155 |
NORMAL AND OTHER APPROXIMATIONS | 162 |
3 | 180 |
Conditional Expectations | 191 |
FORMULA FOR TOTAL EXPECTATION | 204 |
A Collective Risk Model for a Short Period | 225 |
THE DISTRIBUTION OF THE AGGREGATE CLAIM | 241 |
NORMAL APPROXIMATION OF THE DISTRIBUTION | 251 |
2 | 257 |
Random Processes I Counting and Compound Processes | 269 |
POISSON AND OTHER COUNTING PROCESSES | 276 |
EXERCISES | 282 |
COMPOUND PROCESSES | 287 |
2 | 295 |
CRITERIA CONNECTED WITH PAYING DIVIDENDS | 402 |
EXERCISES | 410 |
The uniform distribution and simulation of r v | 414 |
204 | 425 |
A MULTIPLE DECREMENT MODEL | 429 |
MULTIPLE LIFE MODELS | 444 |
Life Insurance Models | 461 |
SOME PARTICULAR TYPES OF CONTRACTS | 467 |
Comparison of Random Variables Preferences of Individuals | 471 |
VARYING BENEFITS | 480 |
ON THE ACTUARIAL NOTATION | 491 |
Annuity Models | 499 |
SOME PARTICULAR TYPES OF LEVEL ANNUITIES EXAMPLES | 506 |
MORE ON VARYING PAYMENTS | 516 |
The case of many risks Normal approximation | 549 |
EXERCISES | 560 |
2 | 579 |
REINSURANCE MARKET | 598 |
EXERCISES | 604 |
260 | 608 |
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approximation Assume Brownian motion calculations called Certainly certainty equivalent clients coefficient compound Poisson process compute concave conditional expectation consider convergence corresponding criterion defined definition Denote density depend discrete distribution F distribution with parameter equal equation estimate Exercise expected value exponential distribution Find finite follows force of mortality formula geometric distribution given Gmax graph Hence independent integral interval loss event m₁ martingale matrix N₁ N₂ negative binomial negative binomial distribution notation Note number of claims Pareto distribution particular payment Poisson distribution Poisson process Poisson r.v. portfolio positive preference order premium proof Proposition prove random variables reader respectively risk aversion ruin probability Section situation of Example standard normal T-distribution take on values Theorem true uniformly distributed unit of money utility function Var{S Var{X variance vector w₁ write X₁ X1 and X2 zero