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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.

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Number theory. --- Cryptography. --- Number Theory --- Nombres, Théorie des --- Théorie des nombres --- Cryptography --- Number theory --- #TELE:SISTA --- 519.72 --- 519.72 Information theory: mathematical aspects --- Information theory: mathematical aspects --- Number study --- Numbers, Theory of --- Algebra --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- cryptografie --- Cryptographie --- Nombres, Théorie des. --- Cryptographie.

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Cryptography --- -#TELE:COSIC --- 519.72 --- 519.72 Information theory: mathematical aspects --- Information theory: mathematical aspects --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Data processing --- #TELE:COSIC --- Mathematical control systems --- cryptologie --- Cryptography. --- Data processing. --- Cryptographie --- Informatique --- Cryptography - Data processing

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On August 6, 2002,a paper with the title “PRIMES is in P”, by M. Agrawal, N. Kayal, and N. Saxena, appeared on the website of the Indian Institute of Technology at Kanpur, India. In this paper it was shown that the “primality problem”hasa“deterministic algorithm” that runs in “polynomial time”. Finding out whether a given number n is a prime or not is a problem that was formulated in ancient times, and has caught the interest of mathema- ciansagainandagainfor centuries. Onlyinthe 20thcentury,with theadvent of cryptographic systems that actually used large prime numbers, did it turn out to be of practical importance to be able to distinguish prime numbers and composite numbers of signi?cant size. Readily, algorithms were provided that solved the problem very e?ciently and satisfactorily for all practical purposes, and provably enjoyed a time bound polynomial in the number of digits needed to write down the input number n. The only drawback of these algorithms is that they use “randomization” — that means the computer that carries out the algorithm performs random experiments, and there is a slight chance that the outcome might be wrong, or that the running time might not be polynomial. To ?nd an algorithmthat gets by without rand- ness, solves the problem error-free, and has polynomial running time had been an eminent open problem in complexity theory for decades when the paper by Agrawal, Kayal, and Saxena hit the web.

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The third edition of this best-selling text provides unparalleled coverage of the use of cryptographic protocols that establish the steps that must be taken before any type of secret transmission can be completed. The author shows readers how the various parties to the transaction establish their cryptographic identities or keys, covers many of the cryptographic tools used in network security, and discusses topics that include copyright protection techniques and public key infrastructure. Cryptography: Theory and Practice, Third Edition is an outstanding text for senior undergraduate and graduate courses but also a useful reference for professionals interested in network security and cryptographic protocols.

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