Publications related to Function Field Sieve in Characteristic Three

Some Mordell-Weil lattices and applications to sphere packings

We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields.In some cases, these families of elliptic curves ...

EPFL2024

Attacks on some post-quantum cryptographic protocols: The case of the Legendre PRF and SIKE

Novak Kaluderovic

Post-quantum cryptography is a branch of cryptography which deals with cryptographic algorithms whose hardness assumptions are not based on problems known to be solvable by a quantum computer, such as the RSA problem, factoring or discrete logarithms.This ...

EPFL2022

On the Mordell-Weil lattice of y(2) = x(3) + bx plus t(3n+1) in characteristic 3

Gauthier Leterrier

We study the elliptic curves given by y(2) = x(3) + bx + t(3n+1) over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve u(3) ...

SPRINGER INT PUBL AG2022

Computation Of A 30750-Bit Binary Field Discrete Logarithm

Arjen Lenstra, Robert Granger, Thorsten Kleinjung, Benjamin Pierre Charles Wesolowski

This paper reports on the computation of a discrete logarithm in the finite field F-230750, breaking by a large margin the previous record, which was set in January 2014 by a computation in F-29234. The present computation made essential use of the elimina ...

AMER MATHEMATICAL SOC2021

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

EPFL2018

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

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

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

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

Function Field Sieve in Characteristic Three

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Some Mordell-Weil lattices and applications to sphere packings

Attacks on some post-quantum cryptographic protocols: The case of the Legendre PRF and SIKE

On the Mordell-Weil lattice of y(2) = x(3) + bx plus t(3n+1) in characteristic 3

Computation Of A 30750-Bit Binary Field Discrete Logarithm

Arithmetic and geometric structures in cryptography

Indiscreet logarithms in finite fields of small characteristic

Indiscreet discrete logarithms

Isogeny graphs of ordinary abelian varieties

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Computational Aspects of Jacobians of Hyperelliptic Curves

Attacks on some post-quantum cryptographic protocols: The case of the Legendre PRF and SIKE

Isogeny graphs of ordinary abelian varieties

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Computational Aspects of Jacobians of Hyperelliptic Curves

Computation Of A 30750-Bit Binary Field Discrete Logarithm

On the Mordell-Weil lattice of y(2) = x(3) + bx plus t(3n+1) in characteristic 3

Some Mordell-Weil lattices and applications to sphere packings

Indiscreet logarithms in finite fields of small characteristic

Indiscreet discrete logarithms

Arithmetic and geometric structures in cryptography