Publications related to Lattices and factorization of polynomials

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

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

Torsion homology of arithmetic lattices and K-2 of imaginary fields

Vincent Emery

Let be a symmetric space of noncompact type. A result of Gelander provides exponential upper bounds in terms of the volume for the torsion homology of the noncompact arithmetic locally symmetric spaces . We show that under suitable assumptions on this resu ...

Springer Heidelberg2014

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

On the size of Satake parameters for unitary cuspidal automorphic representations for GL(4)

Nahid Walji

Let Pi be a cuspidal automorphic representation for GL(4) over a number field F. We obtain unconditional lower bounds on the number of places at which the Satake parameters are not "too large". In the case of self-dual Pi with non-trivial central character ...

Academic Press Inc Elsevier Science2013

Properties of Network Polynomials

Christina Fragouli, Javad Ebrahimi Boroojeni

It is well known that transfer polynomials play an important role in the network code design problem. In this paper we provide a graph theoretical description of the terms of such polynomials. We consider acyclic networks with arbitrary number of receivers ...

2012

Properties of Network Polynomials

Javad Ebrahimi Boroojeni

It is well known that transfer polynomials play an important role in the network code design problem. In this paper we provide a graph theoretical description of the terms of such polynomials. We consider acyclic networks with arbitrary number of receivers ...

Ieee2012

A Probabilistic Approach of Sum Rules for Heat Polynomials

Olivier Lévêque

In this paper, we show that the sum rules for generalized Hermite polynomials derived by Daboul and Mizrahi (2005 J. Phys. A: Math. Gen. 38 427-48) and by Graczyk and Nowak (2004 C. R. Acad. Sci., Ser. 1 338 849) can be interpreted and easily recovered usi ...

2012

Lattices and factorization of polynomials

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Considerations for Rank-based Cryptosystems

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

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

Torsion homology of arithmetic lattices and K-2 of imaginary fields

Algebraic algorithms for network information flow

On the size of Satake parameters for unitary cuspidal automorphic representations for GL(4)

Properties of Network Polynomials

Properties of Network Polynomials

A Probabilistic Approach of Sum Rules for Heat Polynomials

A Probabilistic Approach of Sum Rules for Heat Polynomials

Properties of Network Polynomials

On the size of Satake parameters for unitary cuspidal automorphic representations for GL(4)

Algebraic algorithms for network information flow

Torsion homology of arithmetic lattices and K-2 of imaginary fields

On the discrete logarithm problem in finite fields of fixed characteristic

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

Considerations for Rank-based Cryptosystems

Properties of Network Polynomials