Publications related to Solving a $6120$-bit DLP on a Desktop Computer

Indiscreet logarithms in finite fields of small characteristic

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

Recently, several striking advances have taken place regarding the discrete logarithm problem (DLP) in finite fields of small characteristic, despite progress having remained essentially static for nearly thirty years, with the best known algorithms being ...

2018

The role of inkjet printing in tissue engineering

Christopher Chi Wai Tse

A summary of using Inkjet printing in the field of Tissue Engineering ...

2017

Indiscreet discrete logarithms

Robert Granger

In 2013 and 2014 a revolution took place in the understanding of the discrete logarithm problem (DLP) in finite fields of small characteristic. Consequently, many cryptosystems based on cryptographic pairings were rendered completely insecure, which serves ...

2017

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

Van Thang Pham

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

Embeddings of maximal tori in classical groups over local and global fields

Eva Bayer Fluckiger, Ting-Yu Lee

Embeddings of maximal tori in classical groups over fields of characteristic not 2 are the subject matter of several recent papers. The aim of the present paper is to give necessary and sufficient conditions for such an embedding to exist, when the base fi ...

Turpion Ltd2016

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

A Tale of Two Quasi-Polynomial Algorithms

Robert Granger

In 2013 the Discrete Logarithm Problem in finite fields of small characteristic enjoyed a rapid series of developments, starting with the heuristic polynomial-time relation generation method due to Gologlu, Granger, McGuire and Zumbragel, and culminating w ...

2015

Asymptotics of action variables near semi-toric singularities

The presence of focus-focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action-Angle coordinates on such systems. At focus-focus critical points, the Liouville-Arnold-Mineur theorem does n ...

Elsevier2015

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

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Indiscreet logarithms in finite fields of small characteristic

The role of inkjet printing in tissue engineering

Indiscreet discrete logarithms

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

Embeddings of maximal tori in classical groups over local and global fields

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

On the discrete logarithm problem in finite fields of fixed characteristic

A Tale of Two Quasi-Polynomial Algorithms

Asymptotics of action variables near semi-toric singularities

Indiscreet discrete logarithms

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Indiscreet logarithms in finite fields of small characteristic

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

The role of inkjet printing in tissue engineering

On the discrete logarithm problem in finite fields of fixed characteristic

Embeddings of maximal tori in classical groups over local and global fields

A Tale of Two Quasi-Polynomial Algorithms

Asymptotics of action variables near semi-toric singularities

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