Four algorithms to solve symmetric multi-type non-negative matrix tri-factorization problem

Reduction of the integer factorization complexity upper bound to the complexity of the Diffie–Hellman problem

Discrete Mathematics and Applications ◽

10.1515/dma-2021-0001 ◽

2021 ◽

Vol 31 (1) ◽

pp. 1-4

Author(s):

Mikhail A. Cherepnev

Keyword(s):

Upper Bound ◽

Polynomial Algorithm ◽

Integer Factorization ◽

Factorization Problem ◽

Diffie Hellman ◽

Integer Factorization Problem

Abstract We construct a probabilistic polynomial algorithm that solves the integer factorization problem using an oracle solving the Diffie–Hellman problem.

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Model order selection for approximate Boolean matrix factorization problem

Knowledge-Based Systems ◽

10.1016/j.knosys.2021.107184 ◽

2021 ◽

pp. 107184

Author(s):

Martin Trnecka ◽

Marketa Trneckova

Keyword(s):

Matrix Factorization ◽

Boolean Matrix ◽

Order Selection ◽

Model Order Selection ◽

Model Order ◽

Factorization Problem ◽

Selection For

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A Block Coordinate Descent-Based Projected Gradient Algorithm for Orthogonal Non-Negative Matrix Factorization

Mathematics ◽

10.3390/math9050540 ◽

2021 ◽

Vol 9 (5) ◽

pp. 540

Author(s):

Soodabeh Asadi ◽

Janez Povh

Keyword(s):

Matrix Factorization ◽

Synthetic Data ◽

Coordinate Descent ◽

The Other ◽

Gradient Algorithm ◽

Block Coordinate Descent ◽

Projected Gradient Method ◽

Projected Gradient ◽

Factorization Problem ◽

Non Negative Matrix Factorization

This article uses the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalize the orthonormality constraints and apply the PG method via a block coordinate descent approach. This means that at a certain time one matrix factor is fixed and the other is updated by moving along the steepest descent direction computed from the penalized objective function and projecting onto the space of non-negative matrices. Our method is tested on two sets of synthetic data for various values of penalty parameters. The performance is compared to the well-known multiplicative update (MU) method from Ding (2006), and with a modified global convergent variant of the MU algorithm recently proposed by Mirzal (2014). We provide extensive numerical results coupled with appropriate visualizations, which demonstrate that our method is very competitive and usually outperforms the other two methods.

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Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography

Journal of Applied Mathematics ◽

10.1155/2014/630607 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 4

Author(s):

Lize Gu ◽

Shihui Zheng

Keyword(s):

Performance Analysis ◽

Quantum Algorithm ◽

Integer Factorization ◽

Algebraic Structures ◽

Cryptographic Primitives ◽

Factorization Problem ◽

Integer Factorization Problem ◽

Modern Cryptography ◽

Nonabelian Groups

To resist known quantum algorithm attacks, several nonabelian algebraic structures mounted upon the stage of modern cryptography. Recently, Baba et al. proposed an important analogy from the integer factorization problem to the factorization problem over nonabelian groups. In this paper, we propose several conjugated problems related to the factorization problem over nonabelian groups and then present three constructions of cryptographic primitives based on these newly introduced conjugacy systems: encryption, signature, and signcryption. Sample implementations of our proposal as well as the related performance analysis are also presented.

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