On The Number Of Ordinary Conics

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We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...

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n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

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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 ...

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Suppose d > 2, n > d+1, and we have a set P of n points in d-dimensional Euclidean space. Then P contains a subset Q of d points such that for any p ∈ P, the convex hull of Q∪{p} does not contain the origin in its interior. We also show that for non-emp ...

In 1999, Smart has shown how to solve in linear time ECDLP for elliptic curves of trace 1 defined over a prime finite field Fp, the so-called anomalous elliptic curves. In this article, we show how to construct such cryptographically weak curves for primes ...

On The Number Of Ordinary Conics

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Some Mordell-Weil lattices and applications to sphere packings

Isogeny Problems with Level Structure

Exploring SIDH-Based Signature Parameters

The Lang-Trotter conjecture for products of non-CM elliptic curves

3D Smith chart constant quality factor semi-circles contours for positive and negative resistance circuits

Arithmetic and geometric structures in cryptography

Algebraic and topological methods in combinatorics

Some consequences of Masser's counting theorem on elliptic curves

Ambiguous Joint Chance Constraints under Mean and Dispersion Information

On some algebraic and extremal problems in discrete geometry

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

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

Points surrounding the origin

Generating anomalous elliptic curves