Mathematics of Public Key Cryptography (Record no. 59165)

MARC details
000 -LEADER
fixed length control field 04766nam a22002777a 4500
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20220921161337.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 220505b |||||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781107013926
028 ## - DISTRIBUTOR NAME
Distributor Name :International Book Distributors
Distributor address :Flat No 17, Prakash Apartment 4405/2, 5 Ansari Road Darya Ganj New Delhi
Bill Number :117716
Bill Date :22/04/2022
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 003.54 GAL
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name Galbraith, Steven D.
245 ## - TITLE STATEMENT
Title Mathematics of Public Key Cryptography
Statement of responsibility, etc / Steven D Galbraith
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc Cambridge
Name of publisher, distributor, etc : Cambridge University Press
Date of publication, distribution, etc 2012.
300 ## - PHYSICAL DESCRIPTION
Extent xiv, 615p.
Dimensions 24cm.
365 ## - TRADE PRICE
Price amount 5339
505 ## - FORMATTED CONTENTS NOTE
Contents note Cover; MATHEMATICS OF PUBLIC KEY CRYPTOGRAPHY; Title; Copyright; Contents; Preface; Acknowledgements; 1: Introduction; 1.1 Public key cryptography; 1.2 The textbook RSA cryptosystem; 1.3 Formal definition of public key cryptography; 1.3.1 Security of encryption; 1.3.2 Security of signatures; PART I: BACKGROUND; 2: Basic algorithmic number theory; 2.1 Algorithms and complexity; 2.1.1 Randomised algorithms; 2.1.2 Success probability of a randomised algorithm; 2.1.3 Reductions; 2.1.4 Random self-reducibility; 2.2 Integer operations; 2.2.1 Faster integer multiplication; 2.3 Euclid's algorithm. 2.4 Computing Legendre and Jacobi symbols2.5 Modular arithmetic; 2.6 Chinese remainder theorem; 2.7 Linear algebra; 2.8 Modular exponentiation; 2.9 Square roots modulo p; 2.10 Polynomial arithmetic; 2.11 Arithmetic in finite fields; 2.12 Factoring polynomials over finite fields; 2.13 Hensel lifting; 2.14 Algorithms in finite fields; 2.14.1 Constructing finite fields; 2.14.2 Solving quadratic equations in finite fields; 2.14.3 Isomorphisms between finite fields; 2.15 Computing orders of elements and primitive roots; 2.15.1 Sets of exponentials of products. 2.15.2 Computing the order of a group element2.15.3 Computing primitive roots; 2.16 Fast evaluation of polynomials at multiple points; 2.17 Pseudorandom generation; 2.18 Summary; 3: Hash functions and MACs; 3.1 Security properties of hash functions; 3.2 Birthday attack; 3.3 Message authentication codes; 3.4 Constructions of hash functions; 3.5 Number-theoretic hash functions; 3.6 Full domain hash; 3.7 Random oracle model; PART II: ALGEBRAIC GROUPS; 4: Preliminary remarks on algebraic groups; 4.1 Informal definition of an algebraic group; 4.2 Examples of algebraic groups. 4.3 Algebraic group quotients4.4 Algebraic groups over rings; 5: Varieties; 5.1 Affine algebraic sets; 5.2 Projective algebraic sets; 5.3 Irreducibility; 5.4 Function fields; 5.5 Rational maps and morphisms; 5.6 Dimension; 5.7 Weil restriction of scalars; 6: Tori, LUC and XTR; 6.1 Cyclotomic subgroups of finite fields; 6.2 Algebraic tori; 6.3 The group Gq,2; 6.3.1 The torus T2; 6.3.2 Lucas sequences; 6.4 The group Gq,6; 6.4.1 The torus T6; 6.4.2 XTR; 6.5 Further remarks; 6.6 Algebraic tori over rings; 7: Curves and divisor class groups; 7.1 Non-singular varieties; 7.2 Weierstrass equations. 7.3 Uniformisers on curves7.4 Valuation at a point on a curve; 7.5 Valuations and points on curves; 7.6 Divisors; 7.7 Principal divisors; 7.8 Divisor class group; 7.9 Elliptic curves; 8: Rational maps on curves and divisors; 8.1 Rational maps of curves and the degree; 8.2 Extensions of valuations; 8.3 Maps on divisor classes; 8.4 Riemann-Roch spaces; 8.5 Derivations and differentials; 8.6 Genus zero curves; 8.7 Riemann-Roch theorem and Hurwitz genus formula; 9: Elliptic curves; 9.1 Group law; 9.2 Morphisms between elliptic curves; 9.3 Isomorphisms of elliptic curves; 9.4 Automorphisms.
520 ## - SUMMARY, ETC.
Summary, etc Public key cryptography is a major interdisciplinary subject with many real-world applications, such as digital signatures. A strong background in the mathematics underlying public key cryptography is essential for a deep understanding of the subject, and this book provides exactly that for students and researchers in mathematics, computer science and electrical engineering. Carefully written to communicate the major ideas and techniques of public key cryptography to a wide readership, this text is enlivened throughout with historical remarks and insightful perspectives on the development of the subject. Numerous examples, proofs and exercises make it suitable as a textbook for an advanced course, as well as for self-study. For more experienced researchers it serves as a convenient reference for many important topics: the Pollard algorithms, Maurer reduction, isogenies, algebraic tori, hyperelliptic curves and many more."--Provided by publisher
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Computer Science
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Systems
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Coding theory.
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Coding theory.
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics -- Discrete Mathematics.
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Public-Key-Kryptosystem
700 ## - ADDED ENTRY--PERSONAL NAME
Personal name Galbraith, Steven D.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type Books
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Home library Current library Date acquired Source of acquisition Cost, normal purchase price Full call number Barcode Date last seen Price effective from Koha item type Public note
    Dewey Decimal Classification   Not For Loan SNU LIBRARY SNU LIBRARY 05/05/2022 International Book Distributors 5339.00 003.54 GAL 28680 05/05/2022 05/05/2022 Books Books Shifted to Mathematics Dept.
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