عنوان

Modern cryptography and elliptic curves :

شابک

1470435829

شابک

9781470435820

عنوان اصلي

Modern cryptography and elliptic curves :

نام عام مواد

[Book]

ساير اطلاعات عنواني

a beginner's guide /

نام نخستين پديدآور

Thomas R. Shemanske.

محل نشرو پخش و غیره

Providence, Rhode Island :

نام ناشر، پخش کننده و غيره

American Mathematical Society,

تاریخ نشرو بخش و غیره

[2017]

تاریخ نشرو بخش و غیره

©2017

نام خاص و کميت اثر

xii, 250 pages :

ساير جزييات

illustrations ;

ابعاد

22 cm.

عنوان فروست

Student mathematical library ;

مشخصه جلد

volume 83

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

Three Motivating Problems -- Back to the Beginning -- Some Elementary Number Theory -- A Second View of Modular Arithmetic -- Public-Key Cryptography and RSA -- A Little More Algebra -- Curves in Affine and Projective Space -- Applications of Elliptic Curves -- Appendix A: Deeper Results and Concluding Thoughts -- Appendix B: Answers to Selected Exercises

بدون عنوان

0

متن يادداشت

This book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC). Elements of abstract algebra, number theory, and affine and projective geometry are introduced and developed, and their interplay is exploited. Algebra and geometry combine to characterize congruent numbers via rational points on the unit circle, and group law for the set of points on an elliptic curve arises from geometric intuition provided by Bézout's theorem as well as the construction of projective space. The structure of the unit group of the integers modulo a prime explains RSA encryption, Pollard's method of factorization, Diffie-Hellman key exchange, and ElGamal encryption, while the group of points of an elliptic curve over a finite field motivates Lenstra's elliptic curve factorization method and ECC. The only real prerequisite for this book is a course on one-variable calculus; other necessary mathematical topics are introduced on-the-fly. Numerous exercises further guide the exploration. -- Provided by publisher.

موضوع مستند نشده

Cryptography, Textbooks.

موضوع مستند نشده

Curves, Elliptic, Textbooks.

موضوع مستند نشده

Geometry, Algebraic, Textbooks.

موضوع مستند نشده

Algebraic geometry-- Arithmetic problems. Diophantine geometry-- Applications to coding theory and cryptography.

موضوع مستند نشده

Computer science-- Instructional exposition (textbooks, tutorial papers, etc.)

موضوع مستند نشده

Computer science-- Theory of data-- Data encryption.

موضوع مستند نشده

Computersicherheit

موضوع مستند نشده

Cryptography.

موضوع مستند نشده

Curves, Elliptic.

موضوع مستند نشده

Elliptische Kurve

موضوع مستند نشده

Geometry, Algebraic.

موضوع مستند نشده

Information and communication, circuits-- Communication, information-- Cryptography.

موضوع مستند نشده

Kryptologie

موضوع مستند نشده

Number theory-- Arithmetic algebraic geometry (Diophantine geometry)-- Elliptic curves over global fields.

موضوع مستند نشده

Number theory-- Computational number theory-- Factorization.

موضوع مستند نشده

Number theory-- Elementary number theory-- Elementary number theory.

موضوع مستند نشده

Number theory-- Finite fields and commutative rings (number-theoretic aspects)-- Algebraic coding theory; cryptography.

موضوع مستند نشده

Number theory-- Instructional exposition (textbooks, tutorial papers, etc.)

موضوع مستند نشده

Public-Key-Kryptosystem

موضوع مستند نشده

Quantencomputer

موضوع مستند نشده

Quantum theory-- Axiomatics, foundations, philosophy-- Quantum computation.

شماره

ويراست

شماره رده

نشانه اثر

شماره رده

شماره رده

کد سيستم

کد سيستم

مستند نام اشخاص تاييد نشده

Shemanske, Thomas R.,1952-

مستند نام تنالگان تاييد نشده

American Mathematical Society,issuing body.

تاريخ عمليات

20200823025755.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y