A Practical Analysis of the Fermat Factorization and Pollard Rho Method for Factoring Integers

The development of public-key cryptography generation using the factoring method is very important in practical cryptography applications. In cryptographic applications, the urgency of factoring is very risky because factoring can crack public and private keys, even though the strength in cryptographic algorithms is determined mainly by the key strength generated by the algorithm. However, solving the composite number to find the prime factors is still very rarely done. Therefore, this study will compare the Fermat factorization algorithm and Pollard rho by finding the key generator public key algorithm's prime factor value. Based on the series of test and analysis factoring integer algorithm using Fermat's Factorization and Pollards' Rho methods, it could be concluded that both methods could be used to factorize the public key which specifically aimed to identify the prime factors. During the public key factorizing process within 16 bytes – 64 bytes, Pollards' Rho's average duration was significantly faster than Fermat's Factorization.

Building Recommendation Systems Using the Algorithms KNN and SVD

<p>Recommendation systems are used successfully to provide items (example:<br />movies, music, books, news, images) tailored to user preferences.<br />Among the approaches proposed, we use the collaborative filtering approach<br />of finding the information that satisfies the user by using the<br />reviews of other users. These ratings are stored in matrices that their<br />sizes increase exponentially to predict whether an item is interesting<br />or not. The problem is that these systems overlook that an assessment<br />may have been influenced by other factors which we call the cold start<br />factor. Our objective is to apply a hybrid approach of recommendation<br />systems to improve the quality of the recommendation. The advantage<br />of this approach is the fact that it does not require a new algorithm<br />for calculating the predictions. We we are going to apply the two Kclosest<br />neighbor algorithms and the matrix factorization algorithm of<br />collaborative filtering which are based on the method of (singular value<br />decomposition).</p>

On the Redundancy in the Rank of Neural Network Parameters and Its Controllability

In this paper, we show that parameters of a neural network can have redundancy in their ranks, both theoretically and empirically. When viewed as a function from one space to another, neural networks can exhibit feature correlation and slower training due to this redundancy. Motivated by this, we propose a novel regularization method to reduce the redundancy in the rank of parameters. It is a combination of an objective function that makes the parameter rank-deficient and a dynamic low-rank factorization algorithm that gradually reduces the size of this parameter by fusing linearly dependent vectors together. This regularization-by-pruning approach leads to a neural network with better training dynamics and fewer trainable parameters. We also present experimental results that verify our claims. When applied to a neural network trained to classify images, this method provides statistically significant improvement in accuracy and 7.1 times speedup in terms of number of steps required for training. Furthermore, this approach has the side benefit of reducing the network size, which led to a model with 30.65% fewer trainable parameters.