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 ...

Multiplication is an essential step in a lot of calculations. In this paper we look at multiplication of 2 binary polynomials of degree at most n − 1, modulo an irreducible polynomial of degree n with ...

Abstract: In this paper, we consider coded computation for matrix multiplication tasks in distributed computing to mitigate straggler effects. We assume that the stragglers’ computation results can be ...

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 ...

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 ...

ABSTRACT: The purpose of this paper is to introduce and investigate new unification of unified family of Apostol-type polynomials and numbers based on results given in [1] [2]. Also, we derive some ...

A paper posted online in March 2019 presents what may be essentially the fastest possible algorithm for one of the oldest problems in mathematics: whole number ...

In the coefficient representation, it takes $O(n^2)$ operations to multiply two polynomials $A(X)\cdot B(X) = C(X)$: $$ \begin{aligned} A(X) &= a_0 + a_1X + a_2X^2 ...