# Faster truncated integer multiplication

## TL;DR

This paper introduces faster algorithms for computing specific parts of integer products, reducing computation time to about 75% of full multiplication, under certain algorithmic assumptions.

## Contribution

It presents novel algorithms that efficiently compute either the low or high bits of integer products, improving over traditional methods for large integers.

## Key findings

- Algorithms achieve approximately 75% of the time of full multiplication.
- Applicable when integer multiplication relies on cyclic convolution computations.
- Significantly speeds up partial product computations for large integers.

## Abstract

We present new algorithms for computing the low $n$ bits or the high $n$ bits of the product of two $n$-bit integers. We show that these problems may be solved in asymptotically 75% of the time required to compute the full $2n$-bit product, assuming that the underlying integer multiplication algorithm relies on computing cyclic convolutions of real sequences.