Joseph H. Silverman – författare
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Arithmetic of Elliptic Curves
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712 kr
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Advanced Topics in the Arithmetic of Elliptic Curves
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Advanced Topics in the Arithmetic of Elliptic Curves
711 kr
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1 091 kr
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534 kr
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Diophantine Geometry
An Introduction
1 091 kr
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931 kr
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486 kr
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662 kr
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484 kr
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799 kr
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918 kr
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1 348 kr
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Arithmetic of Elliptic Curves
548 kr
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549 kr
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870 kr
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1 344 kr
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1 367 kr
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582 kr
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1 140 kr
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554 kr
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766 kr
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962 kr
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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:
classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, anddigital 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.766 kr
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1 030 kr
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1 668 kr
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The Judeo-Spanish folk literature of the Sephardic Jews of Bosnia, and with it their uncommonly rich balladry, has remained largely unknown to Western scholars. Since their move to Sarajevo in the sixteenth century, Serob-Croatian has displaced their original Spanish, and the entire culture is rapidly approaching extinction.This book preserved for posterity three fundamentally important groups of these rare ballads: Kalmi Baruch''s Spanski romanse; ballads collected from the readers of the Sarajevo newspaper Jevrejski Glas; and five previously unedited eighteenth-century Bosnian ballads from a manuscript in the Jewish National and University Library in Jerusalem.Notes, abstracts in English, reproductions of the music itself, and other scholarly aids serve to make this colorful and strangely modern literature fully accessible to Hispanists, folklorists, and all students of comparative literature and Judaic culture.
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The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry.
Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra''s elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat''s Last Theorem by Wiles et al. via the use of elliptic curves.
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