thomas shemanske (18 resultados)

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Paperback. Condición: New. 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 Bezout'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.

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Soft cover. Condición: New. Contents: Preface. Introduction. 1. Three Motivating Problems. 2. Back to the Beginning. 3. Some Elementary Number Theory. 4. A Second View of Modular Arithmetic: Z_{n} and U_{n}. 5. Public-Key Cryptography and RSA. 6. A Little More Algebra. 7. Curves in Affine and Projective Space. 8. Applications of Elliptic Curves. Appendices. Bibliography. Index. 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.

Condición: New. 2017. Paperback. . . . . .

Paperback. Condición: Brand New. 261 pages. 8.50x5.75x0.75 inches. In Stock.

Condición: New. pp. 252.

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Condición: New. pp. 252.

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Paperback. Condición: New. 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 Bezout'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.

Condición: Used: Like New. LIVRE A L?ETAT DE NEUF. EXPEDIE SOUS 3 JOURS OUVRES. NUMERO DE SUIVI COMMUNIQUE AVANT ENVOI, EMBALLAGE RENFORCE. EAN:9781470435820.

paperback. Condición: New. Language:Chinese.Paperback. Pub Date: 2025-03 Publisher: Higher Education Press This book provides a panoramic view of modern mathematics for lower-level undergraduates. helping them understand the arithmetic of elliptic curves over finite fields and their applications in modern cryptography by developing and presenting the necessary tools. This asymptotic introduction also makes a significant effort to teach students how to generate or discover proofs by treating mathematics as an exploratio.