Discrete Algebraic Methods : (Record no. 110961)
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| fixed length control field | 06157nam a22005653i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC4533883 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729130520.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2016 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783110413335 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9783110413328 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC4533883 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL4533883 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr11214970 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaONFJC)MIL927184 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)951223219 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA162.D5413 2016 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 511.3/3 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Diekert, Volker. |
| 245 10 - TITLE STATEMENT | |
| Title | Discrete Algebraic Methods : |
| Remainder of title | Arithmetic, Cryptography, Automata and Groups. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Berlin/Boston : |
| Name of producer, publisher, distributor, manufacturer | Walter de Gruyter GmbH, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2016. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2016. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (354 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | De Gruyter Textbook Series |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Intro -- Contents -- Preface -- 1. Algebraic structures -- 1.1 Groups -- 1.2 Regular polygons -- 1.3 Symmetric groups -- 1.4 Rings -- 1.5 Modular arithmetic -- 1.5.1 Euclidean algorithm -- 1.5.2 Ideals in the integers -- 1.5.3 Chinese remainder theorem -- 1.5.4 Euler's totient function -- 1.6 Polynomials and formal power series -- 1.7 Hilbert's basis theorem -- 1.8 Fields -- 1.9 Finite fields -- 1.10 Units modulo n -- 1.11 Quadratic reciprocity -- Exercises -- Summary -- 2. Cryptography -- 2.1 Symmetric encryption methods -- 2.2 Monoalphabetic cipher -- 2.3 Polyalphabetic cipher -- 2.4 Frequency analysis and coincidence index -- 2.5 Perfect security and the Vernam one-time pad -- 2.6 Asymmetric encryption methods -- 2.7 RSA cryptosystem -- 2.8 Rabin cryptosystem -- 2.9 Diffie-Hellman key exchange -- 2.10 ElGamal cryptosystem -- 2.11 Cryptographic hash functions -- 2.12 Digital signatures -- 2.13 Secret sharing -- 2.14 Digital commitment -- 2.15 Shamir's attack on the Merkle-Hellman cryptosystem -- Exercises -- Summary -- 3. Number theoretic algorithms -- 3.1 Runtime analysis of algorithms -- 3.2 Fast exponentiation -- 3.3 Binary GCD -- 3.4 Probabilistic recognition of primes -- 3.4.1 Fermat primality test and Carmichael numbers -- 3.4.2 Solovay-Strassen primality test -- 3.4.3 Miller-Rabin primality test -- 3.4.4 Applications of the Miller-Rabin scheme -- 3.4.5 Miller-Rabin versus Solovay-Strassen -- 3.5 Extracting roots in finite fields -- 3.5.1 Tonelli's algorithm -- 3.5.2 Cipolla's algorithm -- 3.6 Integer factorization -- 3.6.1 Pollard's p - 1 algorithm -- 3.6.2 Pollard's rho algorithm for factorization -- 3.6.3 Quadratic sieve -- 3.7 Discrete logarithm -- 3.7.1 Shanks' baby-step giant-step algorithm -- 3.7.2 Pollard's rho algorithm for the discrete logarithm -- 3.7.3 Pohlig-Hellman algorithm for group order reduction -- 3.7.4 Index calculus. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 3.8 Multiplication and division -- 3.9 Discrete fourier transform -- 3.10 Primitive roots of unity -- 3.11 Schönhage-Strassen integer multiplication -- Exercises -- Summary -- 4. Polynomial time primality test -- 4.1 Basic idea -- 4.2 Combinatorial tools -- 4.3 Growth of the least common multiple -- 4.4 Of small numbers and large orders -- 4.5 Agrawal-Kayal-Saxena primality test -- Summary -- 5. Elliptic curves -- 5.1 Group law -- 5.1.1 Lines -- 5.1.2 Polynomials over elliptic curves -- 5.1.3 Divisors -- 5.1.4 Picard group -- 5.2 Applications of elliptic curves -- 5.2.1 Diffie-Hellman key exchange with elliptic curves -- 5.2.2 Pseudocurves -- 5.2.3 Factorization using elliptic curves -- 5.2.4 Goldwasser-Kilian primality certificates -- 5.3 Endomorphisms of elliptic curves -- Exercises -- Summary -- 6. Combinatorics on words -- 6.1 Commutation, transposition and conjugacy -- 6.2 Fine and Wilf's periodicity lemma -- 6.3 Kruskal's tree theorem -- Exercises -- Summary -- 7. Automata -- 7.1 Recognizable sets -- 7.2 Rational sets -- 7.3 Regular languages -- 7.4 Star-free languages -- 7.5 Krohn-Rhodes theorem -- 7.6 Green's relations -- 7.7 Automata over infinite words -- 7.7.1 Deterministic Büchi automata -- 7.7.2 Union and intersection -- 7.7.3 Omega-rational languages -- 7.7.4 Recognizability of omega-regular languages -- 7.7.5 Monadic second-order logic over infinite words -- 7.8 Presburger arithmetic -- 7.9 Solutions of linear Diophantine systems -- Exercises -- Summary -- 8. Discrete infinite groups -- 8.1 Classical algorithmic problems -- 8.2 Residually finite monoids -- 8.3 Presentations -- 8.4 Rewriting systems -- 8.4.1 Termination and confluence -- 8.4.2 Semi-Thue systems -- 8.5 Solving the word problem in finitely presented monoids -- 8.6 Free partially commutative monoids and groups -- 8.7 Semidirect products. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 8.8 Amalgamated products and HNN extensions -- 8.9 Rational sets and Benois' theorem -- 8.10 Free groups -- 8.11 The automorphism group of free groups -- 8.12 The special linear group SL(2, Z) -- Exercises -- Summary -- Solutions to exercises -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Bibliography -- Index. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Ordered algebraic structures--Textbooks. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Algorithms--Textbooks. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Computer science--Mathematics--Textbooks. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Cryptography--Textbooks. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Algebra--Textbooks. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Kufleitner, Manfred. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Rosenberger, Gerhard. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Hertrampf, Ulrich. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Diekert, Volker |
| Title | Discrete Algebraic Methods |
| Place, publisher, and date of publication | Berlin/Boston : Walter de Gruyter GmbH,c2016 |
| International Standard Book Number | 9783110413328 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #3 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | De Gruyter Textbook Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4533883">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4533883</a> |
| Public note | Click to View |
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