Polynomials, with their simplicity and versatility, stand as pillars in the landscape of mathematics. These mathematical expressions, built from coefficients and variables raised to non-negative ...

Abstract: In the sparse polynomial multiplication problem, one is asked to multiply two sparse polynomials f and g in time that is proportional to the size of the input plus the size of the output.

One of the most appealing features of polynomials is their closure under addition and multiplication. This means that if you add or multiply two polynomials, the result is always another polynomial.

Several algorithms based on homogeneous polynomials for multiplication of large integers are described in the paper. The homogeneity of polynomials provides several simplifications: reduction of ...

This is an implementation of the Karatsuba polynomial multiplication algorithm in the LEGv8 assembly language, a RISC ISA part of the ARM architecture family. This was done as my final project for ECE ...

My Solutions of (Algorithmic-Toolbox ) Assignments from Coursera ( University of California San Diego ) With "Go In Depth" Part Which Contains More Details With Each of The Course Topics ...

Abstract: NIST has selected CRYSTALS-Kyber as the primary Key Encapsulation Mechanism (KEM) algorithm for the standardization process of post-quantum cryptography. This paper proposes a high-speed ...

We study real-life problems via mathematical models, which usually tend to be nonlinear systems, or equations. A standard trick is to “linearize” this nonlinear system. The newly obtained system then ...