Publications related to On The Number Of Ordinary Conics

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

Separation with restricted families of sets

János Pach, Gábor Tardos, Márton Naszódi, Zsolt Langi

Given a finite n-element set X, a family of subsets F subset of 2(X) is said to separate X if any two elements of X are separated by at least one member of F. It is shown that if vertical bar F vertical bar > 2(n-1), then one can select vertical bar log n ...

Academic Press Inc Elsevier Science2016

Height of rational points on quadratic twists of a given elliptic curve

Pierre Francis André Le Boudec

We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion rational point on a quadratic twist of a given elliptic curve, as the twist varies. This conjecture seems to be very deep and we can prove only partial resul ...

Oxford Univ Press2016

On the Analysis of Public-Key Cryptologic Algorithms

Andrea Miele

The RSA cryptosystem introduced in 1977 by Ron Rivest, Adi Shamir and Len Adleman is the most commonly deployed public-key cryptosystem. Elliptic curve cryptography (ECC) introduced in the mid 80's by Neal Koblitz and Victor Miller is becoming an increasin ...

EPFL2015

Large simplices determined by finite point sets

János Pach, Filip Moric

Given a set P of n points in ℝd, let d1 > d2 >...denote all distinct inter-point distances generated by point pairs in P. It was shown by Schur, Martini, Perles, and Kupitz that there is at most oned-dimensional regular simplex of edge length d1 whos ...

Springer-Verlag2013

On Polygons Excluding Point Sets

Radoslav Fulek, Balázs Keszegh, Filip Moric

By a polygonization of a finite point set S in the plane we understand a simple polygon having S as the set of its vertices. Let B and R be sets of blue and red points, respectively, in the plane such that is in general position, and the convex hull of B c ...

Springer Japan2013

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication

Jeanine Marie Van Order

We establish several results towards the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication over imaginary quadratic fields, namely (i) the existence of an appropriate p-adic L-function, building on works of H ...

2012

Efficient and side-channel-aware implementations of elliptic curve cryptosystems over prime fields

Yusuf Leblebici

Elliptic curve cryptosystems (ECCs) are utilised as an alternative to traditional public-key cryptosystems, and are more suitable for resource-limited environments because of smaller parameter size. In this study, the authors carry out a thorough investiga ...

2010

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

Robert Granger

We show that for any elliptic curve

E(\mathbb{F}_{q^n})

, if an adversary has access to a Static Diffie-Hellman Problem (Static DHP) oracle, then by making

O(q^{1-\frac{1}{n+1}})

Static DHP oracle queries during an initial learning phase, for fixed $n>1 ...

Springer Berlin Heidelberg2010

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

Robert Granger

Recent work by Koblitz and Menezes has highlighted the existence, in some cases, of apparent separations between the hardness of breaking discrete logarithms in a particular group, and the hardness of solving in that group problems to which the security of ...

2010

On The Number Of Ordinary Conics

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Isogeny graphs of ordinary abelian varieties

Separation with restricted families of sets

Height of rational points on quadratic twists of a given elliptic curve

On the Analysis of Public-Key Cryptologic Algorithms

Large simplices determined by finite point sets

On Polygons Excluding Point Sets

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication

Efficient and side-channel-aware implementations of elliptic curve cryptosystems over prime fields

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

On the Analysis of Public-Key Cryptologic Algorithms

Height of rational points on quadratic twists of a given elliptic curve

Large simplices determined by finite point sets

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication

Efficient and side-channel-aware implementations of elliptic curve cryptosystems over prime fields

Isogeny graphs of ordinary abelian varieties

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

On Polygons Excluding Point Sets

Separation with restricted families of sets