Elliptic Curve Public Key CryptosystemsSpringer Science & Business Media, 1993/07/31 - 128 ページ Elliptic curves have been intensively studied in algebraic geometry and number theory. In recent years they have been used in devising efficient algorithms for factoring integers and primality proving, and in the construction of public key cryptosystems. Elliptic Curve Public Key Cryptosystems provides an up-to-date and self-contained treatment of elliptic curve-based public key cryptology. Elliptic curve cryptosystems potentially provide equivalent security to the existing public key schemes, but with shorter key lengths. Having short key lengths means smaller bandwidth and memory requirements and can be a crucial factor in some applications, for example the design of smart card systems. The book examines various issues which arise in the secure and efficient implementation of elliptic curve systems. Elliptic Curve Public Key Cryptosystems is a valuable reference resource for researchers in academia, government and industry who are concerned with issues of data security. Because of the comprehensive treatment, the book is also suitable for use as a text for advanced courses on the subject. |
目次
III | 1 |
IV | 3 |
V | 4 |
VI | 5 |
VII | 6 |
VIII | 7 |
IX | 10 |
X | 13 |
XXXIX | 62 |
XL | 63 |
XLI | 66 |
XLII | 68 |
XLIII | 69 |
XLIV | 72 |
XLV | 77 |
XLVII | 79 |
XI | 14 |
XII | 15 |
XIII | 17 |
XIV | 19 |
XV | 20 |
XVI | 21 |
XVII | 23 |
XVIII | 28 |
XIX | 32 |
XX | 34 |
XXI | 35 |
XXII | 37 |
XXIV | 39 |
XXV | 40 |
XXVI | 41 |
XXVII | 46 |
XXVIII | 48 |
XXIX | 49 |
XXX | 50 |
XXXI | 51 |
XXXII | 52 |
XXXIII | 54 |
XXXV | 55 |
XXXVI | 57 |
XXXVII | 59 |
XXXVIII | 61 |
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多く使われている語句
a2x² abelian group admissible changes arithmetic baby-step giant-step change of variables Chapter classes of elliptic computing logarithms curve y² curves isomorphic curves over F2m cyclic group defined over F denote discrete logarithm problem divisor E(F₁ E(Fq E₁ efficient eigenvalue ElGamal cryptosystem elliptic curve cryptosystems elliptic curve defined elliptic curve logarithm encryption F₁ factor field elements fields of characteristic finite field group of order Hence implementation index calculus method inversion ISBN isomorphism classes Lemma mod fi(x mod q modulo n₁ non-supersingular curve normal basis odd prime ord(P P₁ pair point of order private key probabilistic polynomial problem in F public key cryptography public key cryptosystem random integer rational function reduced Schoof's algorithm Section signature scheme solutions subexponential supersingular curves supersingular elliptic curves t₁ Theorem Type Weierstrass equation Weil pairing x-coordinate y₁ y²+xy