Publications related to Logarithm

Elliptic and Hyperelliptic Curves: A Practical Security Analysis

Motivated by the advantages of using elliptic curves for discrete logarithm-based public-key cryptography, there is an active research area investigating the potential of using hyperelliptic curves of genus 2. For both types of curves, the best known algor ...

Springer Berlin Heidelberg2014

Breaking `128-bit Secure' Supersingular Binary Curves (or how to solve discrete logarithms in $\mathbb{F}_{2^{4 \cdot 1223}}$ and $\mathbb{F}_{2^{12 \cdot 367}}$)

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

In late 2012 and early 2013 the discrete logarithm problem (DLP) in finite fields of small characteristic underwent a dramatic series of breakthroughs, culminating in a heuristic quasi-polynomial time algorithm, due to Barbulescu, Gaudry, Joux and Thomé. U ...

Springer Berlin Heidelberg2014

Breaking `128-bit Secure' Supersingular Binary Curves

Robert Granger

The discrete logarithm problem (DLP) in finite fields of small characteristic recently enjoyed a dramatic series of breakthrough results and computational records, with its (heuristic) complexity dropping from subexponential to quasi-polynomial. While thes ...

2014

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Robert Granger, Jens Markus Zumbrägel

In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as

L_{q^n}(1/3,(4/9)1/3)

for computing arbitrary logarithms, but also in an heuristic polynomial time alg ...

Springer Berlin Heidelberg2013

Solving a $6120$-bit DLP on a Desktop Computer

Robert Granger, Jens Markus Zumbrägel

In this paper we show how some recent ideas regarding the discrete logarithm problem (DLP) in finite fields of small characteristic may be applied to compute logarithms in some very large fields extremely efficiently. By combining the polynomial time relat ...

Springer Berlin Heidelberg2013

Expert Judgements in Risk Analysis: a Strategy to Overcome Uncertainities

Thierry Meyer, Amela Groso, David Nicolas Plüss

There is a need for a risk analysis technique specific for academic research laboratories. Since accurate accident data, normally required for quantitative risk analysis, are not available for this environment, expert judgements are often used to describe ...

2013

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

Robust Log-Energy Estimation and its Dynamic Change Enhancement for In-car Speech Recognition

Hervé Bourlard, Weifeng Li

The log-energy parameter, typically derived from a full-band spectrum, is a critical feature commonly used in automatic speech recognition (ASR) systems. However, log-energy is difficult to estimate reliably in the presence of background noise. In this pap ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Tuning the length dispersion of multi-walled carbon nanotubes by ball milling

László Forró, Arnaud Magrez, Claudio Grimaldi, Richard Gaal, Marijana Mionic Ebersold, Rita Smajda, Primoz Rebernik Ribic

The statistical analysis of the length distribution of catalytic chemical vapour deposition synthesized multi-walled carbon nanotubes cut by planetary ball milling is reported. The nanotube lengths follow a log-normal distribution in a broad range of grind ...

Amer Inst Physics2013

A Simple Continuous Pitch Estimation Algorithm

Petr Motlicek, Philip Neil Garner, Milos Cernak

Recent work in text to speech synthesis has pointed to the benefit of using a continuous pitch estimate; that is, one that records pitch even when voicing is not present. Such an approach typically requires interpolation. The purpose of this paper is to sh ...

2013

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Elliptic and Hyperelliptic Curves: A Practical Security Analysis

Breaking `128-bit Secure' Supersingular Binary Curves (or how to solve discrete logarithms in $\mathbb{F}_{2^{4 \cdot 1223}}$ and $\mathbb{F}_{2^{12 \cdot 367}}$)

Breaking `128-bit Secure' Supersingular Binary Curves

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Solving a $6120$-bit DLP on a Desktop Computer

Expert Judgements in Risk Analysis: a Strategy to Overcome Uncertainities

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Robust Log-Energy Estimation and its Dynamic Change Enhancement for In-car Speech Recognition

Tuning the length dispersion of multi-walled carbon nanotubes by ball milling

A Simple Continuous Pitch Estimation Algorithm

A Simple Continuous Pitch Estimation Algorithm

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Breaking `128-bit Secure' Supersingular Binary Curves (or how to solve discrete logarithms in $\mathbb{F}_{2^{4 \cdot 1223}}$ and $\mathbb{F}_{2^{12 \cdot 367}}$)

Expert Judgements in Risk Analysis: a Strategy to Overcome Uncertainities

Solving a $6120$-bit DLP on a Desktop Computer

Robust Log-Energy Estimation and its Dynamic Change Enhancement for In-car Speech Recognition

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Breaking `128-bit Secure' Supersingular Binary Curves

Tuning the length dispersion of multi-walled carbon nanotubes by ball milling

Elliptic and Hyperelliptic Curves: A Practical Security Analysis