Publications related to Discrete 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

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

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

Quantitative Version Of The Kipnis-Varadhan Theorem And Monte Carlo Approximation Of Homogenized Coefficients

Jean-Christophe Mourrat

This article is devoted to the analysis of a Monte Carlo method to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. We consider the case of independent and identically distributed coefficients, and adopt the p ...

Inst Mathematical Statistics2013

Solving 112-bit prime ECDLP on game consoles using sloppy reduction

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung, Marcelo Kaihara

We describe a cell processor implementation of Pollard’s rho method to solve discrete logarithms in groups of elliptic curves over prime fields. The implementation was used on a cluster of PlayStation 3 game consoles to set a new record. We present in deta ...

2012

Hardness of Computing Individual Bits for One-way Functions on Elliptic Curves

Dimitar Petkov Jetchev, Alexandre Raphaël Duc

We prove that if one can predict any of the bits of the input to an elliptic curve based one-way function over a finite field, then we can invert the function. In particular, our result implies that if one can predict any of the bits of the input to a clas ...

Springer2012

Faster and Smoother - VSH Revisited

Juraj Sarinay

We reconsider the provably collision resistant Very Smooth Hash and propose a small change in the design aiming to improve both performance and security. While the original proofs of security based on hardness of factoring or discrete logarithms are preser ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2011

Efficient Fail-Stop Signatures from the Factoring Assumption

Khaled Ouafi, Atefeh Mashatan

In this paper, we revisit the construction of fail-stop signatures from the factoring assumption. These signatures were originally proposed to provide information-theoretic-based security against forgeries. In contrast to classical signature schemes, in wh ...

Springer2011

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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

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

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

Quantitative Version Of The Kipnis-Varadhan Theorem And Monte Carlo Approximation Of Homogenized Coefficients

Solving 112-bit prime ECDLP on game consoles using sloppy reduction

Hardness of Computing Individual Bits for One-way Functions on Elliptic Curves

Faster and Smoother - VSH Revisited

Efficient Fail-Stop Signatures from the Factoring Assumption

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

Elliptic and Hyperelliptic Curves: A Practical Security Analysis

Breaking `128-bit Secure' Supersingular Binary Curves

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

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

Quantitative Version Of The Kipnis-Varadhan Theorem And Monte Carlo Approximation Of Homogenized Coefficients

Hardness of Computing Individual Bits for One-way Functions on Elliptic Curves

Solving 112-bit prime ECDLP on game consoles using sloppy reduction

Faster and Smoother - VSH Revisited

Efficient Fail-Stop Signatures from the Factoring Assumption