10 АНГЛІЙСЬКА КНИЖКИ ПОВ'ЯЗАНІ ІЗ «ISOGENY»
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isogeny з наступної бібліографічної підбірки. Книжки пов'язані зі словом
isogeny та короткі уривки з них для забезпечення контексту його використання в англійська літературі.
1
Number Theory: Volume I: Tools and Diophantine Equations
Thus, as algebraic curves, or equivalently, over an algebraically closed field
extension of the base field, a nonconstant isogeny induces an isomorphism from
E/Ker(φ) to E , where E/Ker(φ) must be suitably defined as an elliptic curve. If
there ...
2
Elliptic Curves and Their Applications to Cryptography: An ...
It is defined over k if it actually lies on E'k^Ey An isogeny is a rational map which
is furthermore a group homomorphism. E and E' are called isogenous if there is
an isogeny from E to E' ; they are called fc-isogenous if the isogeny is defined ...
3
Diophantine Geometry: An Introduction
A map a e Hom(Gi,G2) is called an isogeny if it is surjective, has finite kernel, and
dimGi — dimG2- The cardinality of ker(o:) is called the degree of a. (N.B. This
definition of the degree is appropriate only for separable maps.) It is clear that if
G2 ...
Marc Hindry, Joseph H. Silverman, 2000
4
Elliptic Curves in Cryptography
The map which sends every point on EI to O on E-i is also called an isogeny. It is
the zero isogeny, and is the only constant isogeny. Isogenies play a crucial role
in the theory of elliptic curves. In this section we summarize the main results that ...
Ian F. Blake, G. Seroussi, N. Smart, 1999
5
Number Fields and Function Fields – Two Parallel Worlds: Two ...
Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas.
Gerard B. M. van der Geer, BJJ Moonen, René Schoof, 2006
6
Advances in Elliptic Curve Cryptography
V111.3. Extending the GHS Attack Using Isogenies V111.3.1. The Basic Idea.
The GHS attack can be extended to a much larger class of curves by using
isogenies. Consider two elliptic curves 5 and 5' defined over K. An isogeny (b : 5
—> 5' ...
Ian F. Blake, Gadiel Seroussi, Nigel P. Smart, 2005
7
Mathematics of Public Key Cryptography
Let 1,0 : E —> E be another isogeny over 1k such that ker(1//) : G. Show that lb : A
o 42 where A is an automorphism of E (or, if 1k is finite, the composition of an
isogeny and a Frobenius map). Similarly, if 1/1 : E —> E2 is an isogeny over 1k ...
Steven D. Galbraith, 2012
8
Public Key Cryptography -- PKC 2004: 7th International ...
For the standard addition formulae, we also search the minimal isogeny degree
to a curve which we prefer for particularly efficient implementation, namely a = —
3 as described in section 2. We call the former as the minimal isogeny degree ...
Feng Bao, Robert Deng, Jianying Zhou, 2004
9
Arithmetic Geometry: Clay Mathematics Institute Summer ...
We say an abelian variety A of dimension g over a field K is supersingular if there
exists an isogeny A ®K k N E9 , where E is a supersingular elliptic curve. An
equivalent definition for an abelian variety in characteristic p to be supersingular
is ...
Clay Mathematics Institute. Summer School, Henri Darmon, 2009
10
Information Security Applications: 9th International ...
Using these probabilities and the cost to compute an l–isogeny, if we try to find a
resistant curve with the two initial methods, the l values and the computational
cost increase sharply. Nevertheless, if we try to do the same with the isogeny–
route ...
Kyo-Il Chung, Kiwook Sohn, Moti Yung, 2009
