Modern Cryptography and Elliptic Curves by Thomas R. Shemanske
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Modern Cryptography and Elliptic Curves

Modern Cryptography and Elliptic Curves


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About the Book

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 Bezouts theorem as well as the construction of projective space. The structure of the unit group of the integers modulo a prime explains RSA encryption, Pollards method of factorization, Diffie-Hellman key exchange, and ElGamal encryption, while the group of points of an elliptic curve over a finite field motivates Lenstras 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.

About the Author

Thomas R. Shemanske, Dartmouth College, Hanover, NH.


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Product Details
  • ISBN-13: 9781470435820
  • Publisher: American Mathematical Society
  • Binding: Paperback
  • Height: 143 mm
  • No of Pages: 261
  • Spine Width: 17 mm
  • Width: 220 mm
  • ISBN-10: 1470435829
  • Publisher Date: 30 Aug 2017
  • Edition: Student Mathematical Library
  • Language: English
  • Returnable: Y
  • Weight: 370 gr


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