It seems that you're in Germany. We have a dedicated site for Germany. 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.

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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:. Jeffrey Hoffstein has been a professor at Brown University since and has been a visiting professor and tenured professor at several other universities since His research areas are number theory, automorphic forms and cryptography.

He has authored more than 50 publications. Jill Pipher has been a professor at Brown University since She has been an invited lecturer and has received numerous awards and honors. Her research areas are harmonic analysis, elliptic PDE, and cryptography. She has authored over 40 publications. Joseph Silverman has been a professor at Brown University since He served as the Chair of the Brown Mathematics department from — He has received numerous fellowships, grants and awards and is a frequently invited lecturer.

His research areas are number theory, arithmetic geometry, elliptic curves, dynamical systems and cryptography. He has authored more than publications and has had more than 20 doctoral students.

An Introduction 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 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. List of Notation.

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## An Introduction to Mathematical Cryptography

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.

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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. The book includes an extensive bibliography and index; supplementary materials are available online.

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