Publications related to A Tale of Two Quasi-Polynomial Algorithms

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

We prove a Szemeredi-Trotter type theorem and a sum product estimate in the setting of finite quasifields. These estimates generalize results of the fourth author, of Garaev, and of Vu. We generalize results of Gyarmati and Sarkozy on the solvability of th ...

Academic Press Inc Elsevier Science2017

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

Computational Aspects of Jacobians of Hyperelliptic Curves

Alina Dudeanu

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

EPFL2016

Quasi-Polynomial Local Search for Restricted Max-Min Fair Allocation

Ola Nils Anders Svensson, Lukas Polacek

The restricted max-min fair allocation problem (also known as the restricted Santa Claus problem) is one of few problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, Asadpour et al. [2012] ...

Assoc Computing Machinery2016

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

Robert Granger, Philipp Svetolik Jovanovic

A popular approach to tweakable blockcipher design is via masking, where a certain primitive (a blockcipher or a permutation) is preceded and followed by an easy-to-compute tweak-dependent mask. In this work, we revisit the principle of masking. We do so a ...

Springer Int Publishing Ag2016

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

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

Robert Granger, Philipp Svetolik Jovanovic

A popular approach to tweakable blockcipher design is via masking, where a certain primitive (a blockcipher or a permutation) is preceded and followed by an easy-to-compute tweak-dependent mask. In this work, we revisit the principle of masking. We do so a ...

2015

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

Multi-Objective Quality-Driven Service Selection-A Fully Polynomial Time Approximation Scheme

Boi Faltings, Immanuel Trummer

The goal of multi-objective quality-driven service selection (QDSS) is to find service selections for a workflow whose quality-of-service (QoS) values are Pareto-optimal. We consider multiple QoS attributes such as response time, cost, and reliability. A s ...

Institute of Electrical and Electronics Engineers2014

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

A Tale of Two Quasi-Polynomial Algorithms

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

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Computational Aspects of Jacobians of Hyperelliptic Curves

Quasi-Polynomial Local Search for Restricted Max-Min Fair Allocation

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

On the discrete logarithm problem in finite fields of fixed characteristic

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

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

Multi-Objective Quality-Driven Service Selection-A Fully Polynomial Time Approximation Scheme

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

Computational Aspects of Jacobians of Hyperelliptic Curves

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

Quasi-Polynomial Local Search for Restricted Max-Min Fair Allocation

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

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

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

Multi-Objective Quality-Driven Service Selection-A Fully Polynomial Time Approximation Scheme

On the discrete logarithm problem in finite fields of fixed characteristic

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

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