Related papers: Approximating Euler Totient Function using Linear …
The basic properties of RSA cryptosystems and some classical attacks on them are described. Derived from geometric properties of the Euler functions, the Euler function rays, a new ansatz to attack RSA cryptosystems is presented. A…
We present an algorithm to invert the Euler function $\phi(m)$. The algorithm, for a given $n \geq 1$, in polynomial time ``on average'', finds the set $\Psi(n)$ of all solutions $m$ to $\phi(m) = n$. In fact, in the worst case, $\Psi(n)$…
Euler totient function $\phi(n)$ plays a central role in number theory and is applied in areas such as cryptography. In this paper, we study iterations of the totient function. We first prove that for any integer $n>2$, iteratively applying…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…
Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
Motivated by an application of semigroup variants to the discrete log problem in groups and related cryptographic applications, we introduce a new kind of totient function, related to both Euler's function and a generalisation of Euler's…
We study the approximation of $\mathbb{E}f(X_T)$ by a Monte Carlo algorithm, where $X$ is the solution of a stochastic differential equation and $f$ is a given function. We introduce a new variance reduction method, which can be viewed as a…
In the context of statistical supervised learning, the noiseless linear model assumes that there exists a deterministic linear relation $Y = \langle \theta_*, X \rangle$ between the random output $Y$ and the random feature vector $\Phi(U)$,…
This project involves an implementation of the Rivest Shamir Adleman (RSA) encryption algorithm in C. It consists of generation of two random prime numbers and a number co- prime to phi(n) also called euler toitent function. These three are…
Representational Similarity Analysis (RSA) is a popular method for analyzing neuroimaging and behavioral data. Here we evaluate the accuracy and reliability of RSA in the context of model selection, and compare it to that of regression.…
Machine unlearning focuses on efficiently removing specific data from trained models, addressing privacy and compliance concerns with reasonable costs. Although exact unlearning ensures complete data removal equivalent to retraining, it is…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…
We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…
In this paper we study the variance of the Euler totient function (normalized to $\varphi(n)/n$) in the integers $\mathbb{Z}$ and in the polynomial ring $\mathbb{F}_q[T]$ over a finite field $\mathbb{F}_q$. It turns out that in…
Machine unlearning updates machine learning models to remove information from specific training samples, complying with data protection regulations that allow individuals to request the removal of their personal data. Despite the recent…
The availability of precise and accurate simulation is a limiting factor for interpreting and forecasting data in many fields of science and engineering. Often, one or more distinct simulation software applications are developed, each with…
We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…