The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography.

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About this book Introduction This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems.

Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required.

This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.

The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffieâ€”Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.

The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling.

Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included. Keywords coding theory digital signatures discrete logarithms elliptic curves information theory lattices and cryptography probability theory Authors and affiliations.

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## HOFFSTEIN PIPHER SILVERMAN PDF

The final prices may differ from the prices shown due to specifics of VAT rules About this Textbook This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. About the authors Dr.

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## An Introduction to Mathematical Cryptography

Research Research Overview I use a combination of analytic and algebraic techniques to study L-series associated to number fields and automorphic forms on GL n. One of my early accomplishments was one of the first applications of a higher rank group GL 3 , to break down a stone wall that had impeded the foundations of the spectral theory of ordinary automorphic forms. This is the the paper Coefficients of Maass forms and the Siegel Zero, in the Annals of Mathematics, which has been cited times, and its Appendix, which has been cited 71 times. For the past 25 years or so, one of my main themes has been the development of the theory of multiple Dirichlet series as a technique to tie together and study families of L-series. The analysis of these series led to a tie in with finite Dynkin diagrams, and ultimately an entirely unexpected connection with combinatorial representation theory, which was the subject of a one semester program at ICERM in the Spring of , bringing together researchers in both fields. The ultimate goal of this program is the Lindelof Hypothesis, which is related to the question of finding upper bounds for automorphic L-series on the center line of the critical strip. The barrier to this is the extension of the theory of automorphic forms over groups of finite rank groups, to Kac-Moody groups and algebras.

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The final prices may differ from the prices shown due to specifics of VAT rules About this Textbook This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffieâ€”Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.