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  • 1
    Book
    Book
    Introduction to cryptography : with coding theory (2006)
    Upper Saddle River, NJ [u.a.] :Pearson Prentice Hall,
    Details
    UID:
    almahu_BV021324599
    Format: XIV, 577 S. : , graph. Darst.
    Edition: 2. ed., Pearson internat. ed.
    ISBN: 0-13-198199-4
    Content: This text is for a course in cryptography for advanced undergraduate and graduate students. Material is accessible to mathematically mature students having little background in number theory and computer programming. Core material is treated in the first eight chapters on areas such as classical cryptosystems, basic number theory, the RSA algorithm, and digital signatures. The remaining nine chapters cover optional topics including secret sharing schemes, games, and information theory. Appendices contain computer examples in Mathematica, Maple, and MATLAB. The text can be taught without computers.
    Language: English
    Subjects: Computer Science , Mathematics
    RVK:
    ST 276
    RVK:
    SK 170
    RVK:
    SK 180
    Keywords: Kryptologie ; Codierungstheorie ; Kryptologie ; Codierung
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  • 2
    Book
    Book
    Elliptic curves : number theory and cryptography (2003)
    Boca Raton [u.a.] :Chapman & Hall,
    Details
    UID:
    almahu_BV016992310
    Format: XI, 428 S. : graph. Darst.
    ISBN: 1-58488-365-0
    Series Statement: Discrete mathematics and its applications
    Language: English
    Subjects: Computer Science , Mathematics
    RVK:
    SK 180
    RVK:
    ST 276
    Keywords: Elliptische Kurve ; Zahlentheorie ; Kryptologie
    URL: Inhaltsverzeichnis
    URL: Inhaltstext
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  • 3
    Book
    Book
    Introduction to cyclotomic fields / (1997)
    New York :Springer,
    Details
    UID:
    almahu_BV011218363
    Format: XIV, 487 Seiten.
    Edition: Second edition
    ISBN: 0-387-94762-0 , 978-1-4612-7346-2
    Series Statement: Graduate texts in mathematics 83
    Note: Literaturverzeichnis Seite 424 - 482. - Hier auch später erschienene, unveränderte Nachdrucke
    Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-1-4612-1934-7
    Language: German
    Subjects: Mathematics
    RVK:
    SK 230
    RVK:
    SK 180
    Keywords: Kreiskörper ; Algebraische Zahlentheorie ; Algebraischer Zahlkörper ; Einführung
    URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007526267&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
    URL: Inhaltsverzeichnis
    URL: Verlagsangaben
    URL: Inhaltstext
    Author information: Washington, Lawrence C., 1951-
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  • 4
    Online Resource
    Online Resource
    Introduction to Cyclotomic Fields (1997)
    New York, NY :Springer New York :
    Details
    UID:
    almahu_9947362848702882
    Format: XIV, 490 p. , online resource.
    Edition: Second Edition.
    ISBN: 9781461219347
    Series Statement: Graduate Texts in Mathematics, 83
    Content: Introduction to Cyclotomic Fields is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory. Starting at an elementary level, the volume covers p-adic L-functions, class numbers, cyclotomic units, Fermat's Last Theorem, and Iwasawa's theory of Z_p-extensions, leading the reader to an understanding of modern research literature. Many exercises are included. The second edition includes a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture. There is also a chapter giving other recent developments, including primality testing via Jacobi sums and Sinnott's proof of the vanishing of Iwasawa's f-invariant.
    Note: 1 Fermat’s Last Theorem -- 2 Basic Results -- 3 Dirichlet Characters -- 4 Dirichlet L-series and Class Number Formulas -- 5 p-adic L-functions and Bernoulli Numbers -- 5.1. p-adic functions -- 5.2. p-adic L-functions -- 5.3. Congruences -- 5.4. The value at s = 1 -- 5.5. The p-adic regulator -- 5.6. Applications of the class number formula -- 6 Stickelberger’s Theorem -- 6.1. Gauss sums -- 6.2. Stickelberger’s theorem -- 6.3. Herbrand’s theorem -- 6.4. The index of the Stickelberger ideal -- 6.5. Fermat’s Last Theorem -- 7 Iwasawa’s Construction of p-adic L-functions -- 7.1. Group rings and power series -- 7.2. p-adic L-functions -- 7.3. Applications -- 7.4. Function fields -- 7.5. µ = 0 -- 8 Cyclotomic Units -- 8.1. Cyclotomic units -- 8.2. Proof of the p-adic class number formula -- 8.3. Units of $$ \mathbb{Q}\left( {{\zeta _p}} \right)$$ and Vandiver’s conjecture -- 8.4. p-adic expansions -- 9 The Second Case of Fermat’s Last Theorem -- 9.1. The basic argument -- 9.2. The theorems -- 10 Galois Groups Acting on Ideal Class Groups -- 10.1. Some theorems on class groups -- 10.2. Reflection theorems -- 10.3. Consequences of Vandiver’s conjecture -- 11 Cyclotomic Fields of Class Number One -- 11.1. The estimate for even characters -- 11.2. The estimate for all characters -- 11.3. The estimate for hm- -- 11.4. Odlyzko’s bounds on discriminants -- 11.5. Calculation of hm+ -- 12 Measures and Distributions -- 12.1. Distributions -- 12.2. Measures -- 12.3. Universal distributions -- 13 Iwasawa’s Theory of $$ {\mathbb{Z}_p} -$$ extensions -- 13.1. Basic facts -- 13.2. The structure of A-modules -- 13.3. Iwasawa’s theorem -- 13.4. Consequences -- 13.5. The maximal abelian p-extension unramified outside p -- 13.6. The main conjecture -- 13.7. Logarithmic derivatives -- 13.8. Local units modulo cyclotomic units -- 14 The Kronecker—Weber Theorem -- 15 The Main Conjecture and Annihilation of Class Groups -- 15.1. Stickelberger’s theorem -- 15.2. Thaine’s theorem -- 15.3. The converse of Herbrand’s theorem -- 15.4. The Main Conjecture -- 15.5. Adjoints -- 15.6. Technical results from Iwasawa theory -- 15.7. Proof of the Main Conjecture -- 16 Miscellany -- 16.1. Primality testing using Jacobi sums -- 16.2. Sinnott’s proof that µ = 0 -- 16.3. The non-p-part of the class number in a $$ {\mathbb{Z}_p} -$$ extension -- 1. Inverse limits -- 2. Infinite Galois theory and ramification theory -- 3. Class field theory -- Tables -- 1. Bernoulli numbers -- 2. Irregular primes -- 3. Relative class numbers -- 4. Real class numbers -- List of Symbols.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9781461273462
    Language: English
    DOI: 10.1007/978-1-4612-1934-7
    URL: http://dx.doi.org/10.1007/978-1-4612-1934-7
    URL: Volltext
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  • 5
    Book
    Book
    Introduction to cyclotomic fields / (1982)
    New York [u.a.] :Springer,
    Details
    UID:
    almafu_BV000030239
    Format: XI, 389 S. : , graph. Darst.
    ISBN: 0-387-90622-3 , 3-540-90622-3
    Series Statement: Graduate texts in mathematics 83
    Language: English
    Subjects: Mathematics
    RVK:
    SK 180
    RVK:
    SK 230
    Keywords: Kreiskörper ; Algebraische Zahlentheorie ; Algebraischer Zahlkörper
    URL: Inhaltsverzeichnis
    URL: Cover
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  • 6
    Book
    Book
    Introduction to cyclotomic fields (1982)
    New York [u.a.] : Springer
    Details
    UID:
    b3kat_BV000030239
    Format: XI, 389 S. , graph. Darst.
    ISBN: 0387906223 , 3540906223
    Series Statement: Graduate texts in mathematics 83
    Language: English
    Subjects: Mathematics
    RVK:
    SK 180
    RVK:
    SK 230
    Keywords: Kreiskörper ; Algebraische Zahlentheorie ; Algebraischer Zahlkörper
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  • 7
    Online Resource
    Online Resource
    Introduction to Cyclotomic Fields (1982)
    New York, NY : Springer US
    Details
    UID:
    b3kat_BV042421007
    Format: 1 Online-Ressource
    ISBN: 9781468401332 , 9781468401356
    Series Statement: Graduate Texts in Mathematics 83
    Note: This book grew. out of lectures given at the University of Maryland in 1979/1980. The purpose was to give a treatment of p-adic L-functions and cyclotomic fields, including Iwasawa's theory of Zp-extensions, which was accessible to mathematicians of varying backgrounds. The reader is assumed to have had at least one semester of algebraic number theory (though one of my students took such a course concurrently). In particular, the following terms should be familiar: Dedekind domain, class number, discriminant, units, ramification, local field. Occasionally one needs the fact that ramification can be computed locally. However, one who has a good background in algebra should be able to survive by talking to the local algebraic number theorist. I have not assumed class field theory; the basic facts are summarized in an appendix. For most of the book, one only needs the fact that the Galois group of the maximal unramified abelian extension is isomorphic to the ideal class group, and variants of this statement. The chapters are intended to be read consecutively, but it should be possible to vary the order considerably. The first four chapters are basic. After that, the reader willing to believe occasional facts could probably read the remaining chapters randomly. For example, the reader might skip directly to Chapter 13 to learn about Zp-extensions. The last chapter, on the Kronecker-Weber theorem, can be read after Chapter 2
    Language: English
    Keywords: Kreiskörper ; Algebraische Zahlentheorie ; Algebraischer Zahlkörper
    DOI: 10.1007/978-1-4684-0133-2
    URL: Volltext
    Author information: Washington, Lawrence C. 1951-
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  • 8
    Book
    Book
    Introduction to cyclotomic fields (1997)
    New York [u.a.] : Springer-Verlag
    Details
    UID:
    kobvindex_ZLB12419600
    Format: XIV, 487 Seiten
    Edition: 2. ed.
    ISBN: 0387947620
    Series Statement: Graduate texts in mathematics 83
    Note: Text engl.
    Language: English
    Keywords: Algebraische Fläche ; Kreiskörper ; Kreiskörper ; Algebraische Zahlentheorie
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  • 9
    Online Resource
    Online Resource
    An introduction to number theory with cryptography (2018)
    Boca Raton, FL : CRC Press, Taylor & Francis Group
    Details
    UID:
    gbv_1657340821
    Format: 1 Online-Ressource (xxii, 578 Seiten) , Diagramme
    Edition: Second edition
    ISBN: 9781351664110
    Series Statement: Textbooks in mathematics
    Content: Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum.
    Additional Edition: ISBN 9781138063471
    Additional Edition: Erscheint auch als Druck-Ausgabe Kraft, James S. An introduction to number theory with cryptography Boca Raton, FL : CRC Press, Taylor & Francis Group, 2018 ISBN 9781138063471
    Additional Edition: ISBN 1138063479
    Language: English
    Subjects: Mathematics
    RVK:
    SK 180
    Keywords: Zahlentheorie ; Kryptologie
    DOI: 10.1201/9781351664110
    URL: https://doi.org/10.1201/9781351664110
    URL: https://www.taylorfrancis.com/books/9781351664110
    URL: lizenzpflichtig
    URL: Volltext
    URL: Inhaltstext
    Author information: Washington, Lawrence C. 1951-
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  • 10
    Book
    Book
    Elliptic curves : number theory and cryptography (2008)
    Boca Raton [u.a.] :Chapman & Hall/CRC,
    Details
    UID:
    almahu_BV025531848
    Edition: 2. ed.
    ISBN: 1-4200-7146-7 , 978-1-4200-7146-7
    Series Statement: Discrete mathematics and its applications
    Language: English
    Subjects: Computer Science , Mathematics
    RVK:
    SK 180
    RVK:
    ST 276
    Keywords: Elliptische Kurve ; Zahlentheorie ; Kryptologie
    URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020134914&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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