A quantum architecture for multiplying signed integers

A quantum architecture for multiplying signed integers

Multiplying huge integers using Fourier transforms

Multiplying huge integers of n digits can be done in time O(n log(n)) using Fast Fourier Transforms (FFT), instead of the O(n) time complexity normally required. In this paper we present this technique from the viewpoint of polynomial multiplication, explaining a recursive divide-and-conquer approach to FFT multiplication. We have compared both methods of multiplication quantitatively and prese...

More On Squaring and Multiplying Large Integers

t = vzge(b,w,a)

Optimal Signed-Binary Representation for Integers

The signed-binary (SB) number system uses digits 0, 1, and –1 to recode integers. The SB representation for integers is very useful in computations for elliptic curve cryptography, digital signatures, and batch verifications, all of which are popular security solutions in today’s communication industry. What is an optimal SB representation? How to find it? This article gives easy-to-understand ...

On binary signed digit representations of integers

Applications of signed digit representations of an integer include computer arithmetic, cryptography, and digital signal processing. An integer of length n bits can have several binary signed digit (BSD) representations and their number depends on its value and varies with its length. In this paper, we present an algorithm that calculates the exact number of BSD representations of an integer of...