搜索结果: 1-12 共查到“知识库 军事学 VARIETIES”相关记录12条 . 查询时间(0.078 秒)
Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem
Isogeny expander graph hyperelliptic curve cryptography
2017/2/20
Fix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism ring, by complex multip...
Isogeny graphs of ordinary abelian varieties
Jacobians of hyperelliptic curves genus 2 cryptography isogeny graphs
2016/12/8
Fix a prime number ГГ. Graphs of isogenies of degree a power of ГГ are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ord...
A Kummer variety is obtained as the quotient of an abelian variety by the automorphism
(−1) acting on it. Kummer varieties can be seen as a higher dimensional generalisation of the xcoordinate
...
A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties
Pairings Abelian varieties
2013/4/18
In this paper, we use the theory of theta functions to generalize to all abelian varieties the usual Miller's algorithm to compute a function associated to a principal divisor. We also explain how to ...
On the security of pairing-friendly abelian varieties over non-prime fields
pairing-friendly abelian non-prime fields pairing-based cryptosystem
2009/6/9
Let A be an abelian variety defined over a non-prime finite
field Fq that has embedding degree k with respect to a subgroup of prime
order r. In this paper we give explicit conditions on q, k, and r...
Pairing with Supersingular Trace Zero Varieties Revisited
Pairing Supersingular Trace Zero Silverberg's point compression algorithm
2009/6/9
A Trace Zero Variety is a specific subgroup of the group of
the divisor classes on a hyperelliptic curve C=Fq, which are rational over
a small degree extension Fqr of the definition field. Trace Zer...
A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties
Abelian varieties hyperelliptic curves pairing-based cryptosystems
2009/6/3
We give an algorithm that produces families ofWeil numbers
for ordinary abelian varieties over finite fields with prescribed embedding
degree. The algorithm uses the ideas of Freeman, Stevenhagen, a...
Abelian varieties with prescribed embedding degree
Abelian varieties prescribed embedding degree
2009/6/2
We present an algorithm that, on input of a CM-field K, an
integer k 1, and a prime r 1 mod k, constructs a q-Weil number
2 OK corresponding to an ordinary, simple abelian variety A over
the f...
Efficient and Generalized Pairing Computation on Abelian Varieties
pairing elliptic curves hyperelliptic curves
2009/6/2
In this paper, we propose a new method for constructing a bilinear pairing over
(hyper)elliptic curves, which we call the R-ate pairing. This pairing is a generalization
of the Ate and Atei pairing,...
THE BEST AND WORST OF SUPERSINGULAR ABELIAN VARIETIES IN CRYPTOLOGY
abelian varieties supersingular elliptic curves
2009/4/13
For certain security applications, including identity based encryption
and short signature schemes, it is useful to have abelian varieties with security
parameters that are neither too small nor too...
Efficient Pairing Computation on Supersingular Abelian Varieties
Tate pairing supersingular curves pairing-based cryptosystems
2009/4/3
We present a general technique for the efficient computation of pairings
on supersingular Abelian varieties. This formulation, which we call the eta
pairing, generalises results of Duursma and Lee f...
Ordinary abelian varieties having small embedding degree
Ordinary abelian varieties small embedding degree MNT
2009/4/3
Miyaji, Nakabayashi and Takano (MNT) gave families of
group orders of ordinary elliptic curves with embedding degree suitable
for pairing applications. In this paper we generalise their results by g...