Publications related to Factoring multivariate polynomials over algebraic number fields

Considerations for Rank-based Cryptosystems

Cryptosystems based on rank metric codes have been considered as an alternative to McEliece cryptosystems due to the relative difficulty of solving the rank syndrome decoding problem. Generic attacks have recently seen several improvements, notably in the ...

Ieee2016

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

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 ...

2016

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Frank de Zeeuw

Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...

Duke Univ Press2016

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

Giovanni Migliorati

We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is ...

Elsevier2015

On the discrete logarithm problem in finite fields of fixed characteristic

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For

q

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

\mathbb{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 log ...

2015

Isometries of quadratic spaces

Eva Bayer Fluckiger

Let k be a global field of characteristic not 2, and let f is an element of k[X] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the compl ...

European Mathematical Soc2015

Polynomial-Time Computation Of Homotopy Groups And Postnikov Systems In Fixed Dimension

For several computational problems in homotopy theory, we obtain algorithms with running time polynomial in the input size. In particular, for every fixed k >= 2, there is a polynomial-time algorithm that, for a 1-connected topological space X given as a f ...

Siam Publications2014

On Sub-determinants and the Diameter of Polyhedra

Friedrich Eisenbrand, Martin Niemeier, Marco Di Summa, Nicolas Bonifas

We derive a new upper bound on the diameter of a polyhedron , where . The bound is polynomial in and the largest absolute value of a sub-determinant of , denoted by . More precisely, we show that the diameter of is bounded by . If is bounded, then we show ...

Springer2014

Bounds for the Euclidean minima of function fields

Piotr Aleksander Maciak

In this paper, we define Euclidean minima for function fields and give some bound for this invariant. We furthermore show that the results are analogous to those obtained in the number field case. (C) 2013 The Authors. Published by Elsevier Inc. All rights ...

Academic Press Inc Elsevier Science2014

Algebraic algorithms for network information flow

Javad Ebrahimi Boroojeni

Ahlswede et al. in the seminal paper [1] have shown that in data transfer over networks, processing the data at the nodes can significantly improve the throughput. As proved by Li et al. in [2], even with a simple type of operation, namely linear operation ...

EPFL2013

Factoring multivariate polynomials over algebraic number fields

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Considerations for Rank-based Cryptosystems

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

On the discrete logarithm problem in finite fields of fixed characteristic

Isometries of quadratic spaces

Polynomial-Time Computation Of Homotopy Groups And Postnikov Systems In Fixed Dimension

On Sub-determinants and the Diameter of Polyhedra

Bounds for the Euclidean minima of function fields

Algebraic algorithms for network information flow

Considerations for Rank-based Cryptosystems

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Polynomials Vanishing On Cartesian Products: The Elekes-Szabo Theorem Revisited

Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets

On the discrete logarithm problem in finite fields of fixed characteristic

Bounds for the Euclidean minima of function fields

Polynomial-Time Computation Of Homotopy Groups And Postnikov Systems In Fixed Dimension

Isometries of quadratic spaces

Algebraic algorithms for network information flow

On Sub-determinants and the Diameter of Polyhedra