Publications related to Optimal algorithms for multiplication in certain finite fields using elliptic curves

COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine ...

Philadelphia2024

Fabrication and Characterization of High Aspect Ratio Amorphous Silicon Based Microchannel Plates

Christophe Ballif, Janina Christine Isabelle Löffler, Samira Alexandra Frey, Mohammad Beygi

This contribution focuses on the fabrication and characterization of microchannel plates made of hydrogenated amorphous silicon (AMCPs). Flexible fabrication processes and the semi-conducting nature of amorphous silicon could give these detectors the advan ...

2021

Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

Rachid Guerraoui, Sadegh Farhadkhani, El Mahdi El Mhamdi, Le Nguyen Hoang, Sébastien Louis Alexandre Rouault, Arsany Hany Abdelmessih Guirguis

We study Byzantine collaborative learning, where n nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and f < n nodes can behave arbitrarily. We prove that collaborati ...

2021

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

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

David Valentin Strütt

In this thesis, we study two distinct problems. The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...

EPFL2018

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

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

Faster ECC over $\mathbb{F}_{2^{521}-1}$

Robert Granger

In this paper we present a new multiplication algorithm for residues modulo the Mersenne prime

2^{521}−1

. Using this approach, on an Intel Haswell Core i7-4770, constant-time variable-base scalar multiplication on NIST’s (and SECG’s) curve P-521 requires ...

Springer Berlin Heidelberg2015

Generalised Mersenne Numbers Revisited

Robert Granger

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attrac ...

2013

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication

Jeanine Marie Van Order

We establish several results towards the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication over imaginary quadratic fields, namely (i) the existence of an appropriate p-adic L-function, building on works of H ...

2012

Optimal algorithms for multiplication in certain finite fields using elliptic curves

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COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

Fabrication and Characterization of High Aspect Ratio Amorphous Silicon Based Microchannel Plates

Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

Arithmetic and geometric structures in cryptography

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

Isogeny graphs of ordinary abelian varieties

Computational Aspects of Jacobians of Hyperelliptic Curves

Faster ECC over $\mathbb{F}_{2^{521}-1}$

Generalised Mersenne Numbers Revisited

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication

Generalised Mersenne Numbers Revisited

COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

Computational Aspects of Jacobians of Hyperelliptic Curves

Fabrication and Characterization of High Aspect Ratio Amorphous Silicon Based Microchannel Plates

Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

Isogeny graphs of ordinary abelian varieties

Arithmetic and geometric structures in cryptography

Faster ECC over $\mathbb{F}_{2^{521}-1}$