Introduction to Modern Cryptography: Principles and Protocols

Přední strana obálky
CRC 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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O autorovi (2007)

Vladimir I. Rotar is a professor in the Department of Mathematics and Statistics at San Diego State University. Dr. Rotar has authored four books and more than 100 scientific papers on probability theory and its applications in leading mathematical journals.

Bibliografické údaje