A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

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Post-quantum cryptography is a branch of cryptography which deals with cryptographic algorithms whose hardness assumptions are not based on problems known to be solvable by a quantum computer, such as the RSA problem, factoring or discrete logarithms. This ...

This paper reports on the computation of a discrete logarithm in the finite field F-230750, breaking by a large margin the previous record, which was set in January 2014 by a computation in F-29234. The present computation made essential use of the elimina ...

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Let F-q be a finite field of q elements, where q is a large odd prime power and Q = a(1)x(1)(c1) + ..... + a(d)x(d)(cd) is an element of F-q[x(1) ,...,x(d)], where 2

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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 ...

We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. ...

The difficulty of obtaining annotations to build training databases still slows down the adoption of recent deep learning approaches for biomedical image analysis. In this paper, we show that we can train a Deep Net to perform 3D volumetric delineation giv ...

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

A method of encoding data for transmission from a source to a destination over a communications channel is provided. The method operates on an ordered set of input symbols and includes generating a plurality of redundant symbols from the input symbols base ...

We consider the problem of finding an optimal transport plan between an absolutely continuous measure and a finitely supported measure of the same total mass when the transport cost is the unsquared Euclidean distance. We may think of this problem as close ...

For~

q

a prime power, the discrete logarithm problem (DLP) in~

\F_{q}

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer~

x

such that

g^x = h

. We present an algorithm for computing discrete logarithm ...

We prove that Hausel’s formula for the number of rational points of a Nakajima quiver variety over a finite field also holds in a suitable localization of the Grothendieck ring of varieties. In order to generalize the arithmetic harmonic analysis in his pr ...

A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

Chattez avec Graph Search

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The multivariate Serre conjecture ring

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Computation Of A 30750-Bit Binary Field Discrete Logarithm

The domain of definition of the Levy white noise

Erdos Distinct Distances Problem and Extensions over Finite Spaces

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Convex optimization in sums of Banach spaces

Elliptic curves over a finite field and the trace formula

Patching And Weak Approximation In Isometry Groups

Isogeny graphs of ordinary abelian varieties

On arithmetic progressions in symmetric sets in finite field model

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Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Multiple-field based code generator and decoder for communications systems

Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case

On the discrete logarithm problem in finite fields of fixed characteristic

Motivic Classes of Nakajima Quiver Varieties