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    An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) (Hardback) By (author) Jeffrey Hoffstein, By (author) Jill Pipher, By (author) J. H. Silverman

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    DescriptionAn Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a specific area of mathematical cryptography and provides an extensive list of exercises. It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background.


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    Title
    An Introduction to Mathematical Cryptography
    Authors and contributors
    By (author) Jeffrey Hoffstein, By (author) Jill Pipher, By (author) J. H. Silverman
    Physical properties
    Format: Hardback
    Number of pages: 544
    Width: 163 mm
    Height: 236 mm
    Thickness: 28 mm
    Weight: 885 g
    Language
    English
    ISBN
    ISBN 13: 9780387779935
    ISBN 10: 0387779930
    Classifications

    BIC E4L: MAT
    B&T Book Type: NF
    Nielsen BookScan Product Class 3: S7.9T
    LC subject heading:
    B&T Modifier: Region of Publication: 01
    B&T Modifier: Academic Level: 01
    Libri: KRYP5500, VERS1800
    BISAC V2.8: COM031000
    BIC subject category V2: PBH, GPJ
    DC22: 003.54
    LC classification: QA
    Ingram Subject Code: MA
    LC subject heading:
    B&T General Subject: 227
    LC classification: QA76.9.D35
    B&T Merchandise Category: COM
    B&T Approval Code: A51150000
    BISAC V2.8: COM014000, MAT029000
    LC classification: QA76.9.A25
    Warengruppen-Systematik des deutschen Buchhandels: 16240
    BISAC V2.8: MAT002000
    LC subject heading:
    BISAC V2.8: COM053000, MAT008000, MAT003000, COM051240
    LC subject heading:
    B&T Approval Code: A93174000, A93470000
    BISAC V2.8: MAT022000
    LC classification: QA268
    DC22: 652.80151
    LC subject heading:
    LC classification: QA1-939, QA241-247.5
    LC subject heading: ,
    LC classification: QA171.5, QA172-172.4, QA10.4, Q350-390
    Thema V1.0: UYZM, GPF, PBW, PBH, PBF, GPJ
    Illustrations note
    1, black & white illustrations
    Publisher
    Springer-Verlag New York Inc.
    Imprint name
    Springer-Verlag New York Inc.
    Publication date
    01 September 2008
    Publication City/Country
    New York, NY
    Author Information
    Dr. Jeffrey Hoffstein has been a professor at Brown University since 1989 and has been a visiting professor and tenured professor at several other universities since 1978. His research areas are number theory, automorphic forms, and cryptography. He has authored more than 50 publications. Dr. Jill Pipher has been a professor at Brown Univesity since 1989. 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. Dr. Joseph Silverman has been a professor at Brown University 1988. He served as the Chair of the Brown Mathematics department from 2001-2004. 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 than120 publications and has had more than 20 doctoral students.
    Review quote
    From the reviews: "The book is devoted to public key cryptography, whose principal goal is to allow two or more people to exchange confidential information ... . The material is very well organized, and it is self-contained: no prerequisites in higher mathematics are needed. In fact, everything is explained and carefully covered ... . there is abundance of examples and proposed exercises at the end of each chapter. ... This book is ideal as a textbook for a course aimed at undergraduate mathematics or computer science students." (Fabio Mainardi, The Mathematical Association of America, October, 2008) "This book focuses on public key cryptography ... . Hoffstein, Pipher, and Silverman ... provide a thorough treatment of the topics while keeping the material accessible. ... The book uses examples throughout the text to illustrate the theorems, and provides a large number of exercises ... . The volume includes a nice bibliography. ... Summing Up: Highly recommended. Upper-division undergraduate through professional collections." (C. Bauer, Choice, Vol. 46 (7), March, 2009) "For most undergraduate students in mathematics or computer science (CS), mathematical cryptography is a challenging subject. ... it is written in a way that makes you want to keep reading. ... The authors officially targeted the book for advanced undergraduate or beginning graduate students. I believe that this audience is appropriate. ... it could even be used with students who are just learning how to execute rigorous mathematical proofs. ... I strongly believe that it finds the right tone for today's students ... ." (Burkhard Englert, ACM Computing Reviews, March, 2009) "The exercises and text would make an excellent course for undergraduate independent study. ... This is an excellent book. Hoffstein, Pipher and Silverman have written as good a book as is possible to explain public key cryptography. ... This book would probably be best suited for a graduate course that focused on public key cryptography, for undergraduate independent study, or for the mathematician who wants to see how mathematics is used in public key cryptography." (Jintai Ding and Chris Christensen, Mathematical Reviews, Issue 2009 m)
    Back cover copy
    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. 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.
    Table of contents
    An Introduction to Cryptography.- Discrete Logarithms and Diffie-Hellman.- Integer Factorization and RSA.- Probability Theory and Information Theory.- Elliptic Curves and Cryptography.- Lattices and Cryptography.- Digital Signatures.- Additional Topics in Cryptology.