Elliptic Curves: Number Theory and Cryptography, Second EditionCRC Press, 03.04.2008 - 536 Seiten Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application |
Inhalt
| 1 | |
| 9 | |
Torsion Points | 77 |
Elliptic Curves over Finite Fields | 95 |
The Discrete Logarithm Problem | 143 |
Elliptic Curve Cryptography | 169 |
Other Applications | 189 |
Elliptic Curves over Q | 199 |
Isogenies | 381 |
Hyperelliptic Curves | 407 |
Zeta Functions | 429 |
Fermats Last Theorem | 445 |
Number Theory | 471 |
Groups | 477 |
Fields | 481 |
Computer Packages | 489 |
Andere Ausgaben - Alle anzeigen
Elliptic Curves: Number Theory and Cryptography, Second Edition Lawrence C. Washington Keine Leseprobe verfügbar - 2008 |
Häufige Begriffe und Wortgruppen
abelian group algebraic integer algebraically closed algorithm Alice assume automorphism calculation characteristic choose coefficients compute coordinates Corollary corresponds cryptography curve over Q defined over Q degree denominator denote discrete log problem div(f dividing E(Fp E(Fq elements elliptic curve defined elliptic curve y2 endomorphism ring example exists factor finite field formulas Frobenius Frobenius endomorphism Galois given by y2 homomorphism implies intersection isogeny isomorphic j-invariant kernel lattice Lemma method mod q modular form nonzero number theory obtain p-adic p-adic integers P₁ point of order poles polynomial prime principal divisors PROOF Let Proposition proved quadratic rational functions rational numbers reduction root of unity satisfies Section Show Similarly square mod subgroup supersingular Suppose tangent line Tate-Lichtenbaum pairing torsion points torsion subgroup values Weierstrass equation Weierstrass form Weil pairing x-coordinate yields zero
Verweise auf dieses Buch
Advances in Elliptic Curve Cryptography Ian F. Blake,Gadiel Seroussi,Nigel P. Smart Eingeschränkte Leseprobe - 2005 |
An Invitation to Modern Number Theory Steven J. Miller,Steven J.. Miller,Ramin Takloo-Bighash Eingeschränkte Leseprobe - 2006 |