Large-Integer Multiplication Based on Homogeneous Polynomials

Large Integer Multiplication on Hypercubes

Large Integer Multiplication on Massively Parallel Processors

We present results of a technique for multiplying large integers using the Fermat Number Transform. When the Fermat Number Transform was first proposed, word length constraints limited its effectiveness. Despite the development of multidimensional techniques to extend the length of the FNT, the relatively small word length of existing machines made the transform of little more than academic int...

Fast Modular Reduction for Large-Integer Multiplication

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Projective P - Orderings and Homogeneous Integer - Valued Polynomials

Bhargava defined p-orderings of subsets of Dedekind domains and with them studied polynomials which take integer values on those subsets. In analogy with this construction for subsets of Z(p) and p-local integer-valued polynomials in one variable, we define projective p-orderings of subsets of Z(p). With such a projective p-ordering for Z(p) we construct a basis for the module of homogeneous, p...

On integer Chebyshev polynomials

We are concerned with the problem of minimizing the supremum norm on [0, 1] of a nonzero polynomial of degree at most n with integer coefficients. We use the structure of such polynomials to derive an efficient algorithm for computing them. We give a table of these polynomials for degree up to 75 and use a value from this table to answer an open problem due to P. Borwein and T. Erdélyi and impr...