A Non-linear Generalization of Singular Value Decomposition and its Application to Cryptanalysis

TL;DR

This paper introduces a nonlinear extension of Singular Value Decomposition (SVD) to detect and measure nonlinearity in time series data, demonstrated through applications to nonlinear maps and differential equations.

Contribution

It presents a novel nonlinear SVD method that enhances the analysis of nonlinearity in time series beyond traditional linear techniques.

Findings

Effective detection of nonlinearity in time series

Quantitative assessment of nonlinearity levels

Application to nonlinear maps and differential equations

Abstract

Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD with the help of data generated from nonlinear maps and flows (differential equations).