Publications related to Computation Of A 30750-Bit Binary Field Discrete Logarithm

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An FFT-based Numerical Method for Elasto-Plastic Contact

Jean-François Molinari, Guillaume Anciaux, Lucas Henri Galilée Frérot

Contact of rough surfaces is of prime importance in the study of friction and wear. Numerical simulations are well suited for this non-linear problem, but natural surfaces being fractal [1], they have high discretization requirements. There is therefore a ...

2018

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

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham

Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

AMER MATHEMATICAL SOC2018

Coordinate-descent adaptation over networks

Ali H. Sayed, Bicheng Ying, Chengcheng Wang

This work examines the mean-square error performance of diffusion stochastic algorithms under a generalized coordinate-descent scheme. In this setting, the adaptation step by each agent is limited to a random subset of the coordinates of its stochastic gra ...

2017

Recompression Of Hadamard Products Of Tensors In Tucker Format

Daniel Kressner, Lana Perisa

The Hadamard product features prominently in tensor-based algorithms in scientific computing and data analysis. Due to its tendency to significantly increase ranks, the Hadamard product can represent a major computational obstacle in algorithms based on lo ...

Siam Publications2017

Computation of a 768-Bit Prime Field Discrete Logarithm

Arjen Lenstra, Thorsten Kleinjung

This paper reports on the number field sieve computation of a 768-bit prime field discrete logarithm, describes the different parameter optimizations and resulting algorithmic changes compared to the factorization of a 768-bit RSA modulus, and briefly disc ...

Springer International Publishing Ag2017

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 solving LPN using BKW and variants Implementation and Analysis

Serge Vaudenay, Sonia Mihaela Bogos, Florian Tramèr

The Learning Parity with Noise problem (LPN) is appealing in cryptography as it is considered to remain hard in the post-quantum world. It is also a good candidate for lightweight devices due to its simplicity. In this paper we provide a comprehensive anal ...

Springer2016

Computation Of A 30750-Bit Binary Field Discrete Logarithm

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An FFT-based Numerical Method for Elasto-Plastic Contact

Arithmetic and geometric structures in cryptography

Four-Variable Expanders Over The Prime Fields

LPN in Cryptography

Coordinate-descent adaptation over networks

Recompression Of Hadamard Products Of Tensors In Tucker Format

Computation of a 768-Bit Prime Field Discrete Logarithm

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

Computational Aspects of Jacobians of Hyperelliptic Curves

On solving LPN using BKW and variants Implementation and Analysis

Arithmetic and geometric structures in cryptography

Four-Variable Expanders Over The Prime Fields

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

Coordinate-descent adaptation over networks

Computational Aspects of Jacobians of Hyperelliptic Curves

An FFT-based Numerical Method for Elasto-Plastic Contact

LPN in Cryptography

On solving LPN using BKW and variants Implementation and Analysis

Recompression Of Hadamard Products Of Tensors In Tucker Format

Computation of a 768-Bit Prime Field Discrete Logarithm