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1.
In their seminal paper, Miyaji et al. [13] describe a simple method for the creation of elliptic curves of prime order with
embedding degree 3, 4, or 6. Such curves are important for the realisation of pairing-based cryptosystems on ordinary (non-supersingular)
elliptic curves. We provide an alternative derivation of their results, and extend them to allow for the generation of many
more suitable curves.
Research supported by Enterprise Ireland grant IF/2002/0312/N. 相似文献
2.
At Eurocrypt '96, Meyer and Müller presented a new Rabin-type cryptosystem based on elliptic curves. In this paper, we will show that this cryptosystem may be reduced to the cryptosystem of Rabin-Williams. 相似文献
3.
For pairing based cryptography we need elliptic curves defined over finite fields
whose group order is divisible by some prime
with
where k is relatively small. In Barreto et al. and Dupont et al. [Proceedings of the Third Workshop on Security in Communication Networks (SCN 2002), LNCS, 2576, 2003; Building curves with arbitrary small Mov degree over finite fields, Preprint, 2002], algorithms for the construction of ordinary elliptic curves over prime fields
with arbitrary embedding degree k are given. Unfortunately, p is of size
.We give a method to generate ordinary elliptic curves over prime fields with p significantly less than
which also works for arbitrary k. For a fixed embedding degree k, the new algorithm yields curves with
where
or
depending on k. For special values of k even better results are obtained.We present several examples. In particular, we found some curves where
is a prime of small Hamming weight resp. with a small addition chain.AMS classification: 14H52, 14G50 相似文献
4.
Ottavio G. Rizzo 《Compositio Mathematica》2003,136(1):1-23
We give some examples of families of elliptic curves with nonconstant j-invariant where the parity of the (analytic) rank is not equidistributed among the fibres. 相似文献
5.
David Grant 《Compositio Mathematica》2000,122(2):151-164
We prove a conjecture of Duke on the number of elliptic curves over the rationals of bounded height which have exceptional primes. 相似文献
6.
On the Linear Complexity and Multidimensional Distribution of Congruential Generators over Elliptic Curves 总被引:3,自引:0,他引:3
We show that the elliptic curve analogue of the linear congruential generator produces sequences with high linear complexity and good multidimensional distribution.communicated by: A. MenezesAMS Classification: 11T23, 14H52, 65C10 相似文献
7.
Root Numbers of Non-Abelian Twists of Elliptic Curves 总被引:2,自引:0,他引:2
We study the global root number of the complex L-function oftwists of elliptic curves over Q by real Artin representations.We obtain examples of elliptic curves over Q which, while nothaving any rational points of infinite order, conjecturallymust have points of infinite order over the fields for every cube-free m > 1. We describe analogousphenomena for elliptic curves over the fields , and in the towers and , where r 3 is prime.2000 Mathematics Subject Classification 11G40, 11G05. 相似文献
8.
Daniel Delbourgo 《Compositio Mathematica》1998,113(2):123-154
In this paper we examine the Iwasawa theory of modular elliptic curves E defined over Q without semi-stable reduction at p. By constructing p-adic L-functions at primes of additive reduction, we formulate a "Main Conjecture" linking this L-function with a certain Selmer group for E over the Zp-extension. Thus the leading term is expressible in terms of IIIE, E(Q)tors and a p-adic regulator term. 相似文献
9.
10.
Gang Yu 《Compositio Mathematica》2003,135(3):331-356
In this paper, we consider a family of elliptic curves over with 2-torsion part 2. We prove that, for every such elliptic curve, a positive proportion of quadratic twists have Mordell–Weil rank 0. 相似文献
11.
Let A be any one of the three elliptic curves over Q with conductor11. We show that A has MordellWeil rank zero over itsfield of 5-division points. In each case we also compute the5-primary part of the TateShafarevich group. Our calculationsmake use of the Galois equivariance of the CasselsTatepairing. 2000 Mathematics Subject Classification 11G05, 11Y40,11R23. 相似文献
12.
Matthew A. Papanikolas 《Compositio Mathematica》2000,122(3):299-313
Let
be the rational function field with finite constant field and characteristic
, and let K/k be a finite separable extension. For a fixed place v of k and an elliptic curve E/K which has ordinary reduction at all places of K extending v, we consider a canonical height pairing
which is symmetric, bilinear and Galois equivariant. The pairing
for the infinite place of k is a natural extension of the classical Néron–Tate height. For v finite, the pairing
plays the role of global analytic p-adic heights. We further determine some hypotheses for the nondegeneracy of these pairings. 相似文献
13.
Shu-Leung Tang 《Transactions of the American Mathematical Society》1997,349(2):837-856
Let be a congruence subgroup of type and of level . We study congruences between weight 2 normalized newforms and Eisenstein series on modulo a prime above a rational prime . Assume that , is a common eigenfunction for all Hecke operators and is ordinary at . We show that the abelian variety associated to and the cuspidal subgroup associated to intersect non-trivially in their -torsion points. Let be a modular elliptic curve over with good ordinary reduction at . We apply the above result to show that an isogeny of degree divisible by from the optimal curve in the -isogeny class of elliptic curves containing to extends to an étale morphism of Néron models over if . We use this to show that -adic distributions associated to the -adic -functions of are -valued.
14.
Michael Spiess 《K-Theory》1999,17(4):363-383
Let E1, E2 be elliptic curves with good reduction over a local field k of residue characteristic p. Let X be the smooth projective model of E1 × E2 over the ring of integers of k. We show that KerCH2(X) CH2 (E1 × E2)) is a finite p-group, by giving a new construction of indecomposable elements of H1
Zar(E1 × E2, K2). As an application we show that the prime to p part of the torsion subgroup of CH2(E1 × E2) is finite. 相似文献
15.
Mathieu Ciet Marc Joye Kristin Lauter Peter L. Montgomery 《Designs, Codes and Cryptography》2006,39(2):189-206
Recently, Eisenträger et al. proposed a very elegant method for speeding up scalar multiplication on elliptic curves. Their method relies on improved formulas for evaluating S=(2P + Q) from given points P and Q on an elliptic curve. Compared to the naive approach, the improved formulas save a field multiplication each time the operation is performed. This paper proposes a variant which is faster whenever a field inversion is more expensive than six field multiplications. We also give an improvement when tripling a point, and present a ternary/binary method to perform efficient scalar multiplication. 相似文献
16.
§ 1. IntroductionThepurposeofthispaperistostudytheoscillatorybehaviorofsolutionsofcertainquasi linearellipticequationsdiv( |Du|m -2 A(x)Du) + p(x) |u|m -2 u=0 ,x∈Ω Rn,(E)whereΩisanexteriordomain ,m >1 ,andfunctionsA(x) ,p(x)aretobespecifiedinthefollowingtext.Recently ,USAMI [6]consideredEq .(E)whenA(x)≡I (identitymatrix) ,andob tainedoscillationcriteriaforEq .(E)with“infiniteintegral”coefficient [cf.[6],Theorem 4].However,asfarasthepresentreferencesisconcerned ,therearefewo… 相似文献
17.
本文得出一类形如:-Div(g(|Du|)|Du|^p-2Du+f(x,u))=B(x,u,Du)在一定的条件下在W^1.p空间中的弱解的Holder连续性。 相似文献
18.
19.
In this paper we consider the Dirichlet problem to a degenerate elliptic equation in a domain whose interior contains a degenerate surface. By means of the method of expansion of Poisson kernel and applying the properties of special functions, we obtain the twice continuously differentiable solution of the problem on the entire space including infinity. 相似文献
20.
研究定义在向量u=(u~1,…,u~N):Ω■R~n→R~N上的各项异性积分泛函F(u)=∫_Ωf(x,Du(x))dx和非线性椭圆型方程组-Σi=1nDi(aiα(x,Du(x)))=-Σi=1nDiFiα(x),α=1,2,…,N.在密度函数f:Ω×R~(N×n)→R和矩阵a=(a_i~α):Ω×R~(N×n)→R~(N×n)满足某单调不等式条件下,得到u整体有界. 相似文献