# On Modular Inverses of Cyclotomic Polynomials and the Magnitude of their Coefficients

## TL;DR

This paper investigates bounds on the coefficients of inverses of cyclotomic polynomials modulo each other, with implications for cryptography, advancing understanding of their algebraic properties.

## Contribution

It provides new lower and upper bounds for these coefficients and discusses an application in torus-based cryptography.

## Key findings

- Established bounds for coefficients of inverse cyclotomic polynomials
- Connected bounds to cryptographic applications
- Enhanced understanding of cyclotomic polynomial inverses

## Abstract

Let p and r be two primes and n, m be two distinct divisors of pr. Consider the n-th and m-th cyclotomic polynomials. In this paper, we present lower and upper bounds for the coefficients of the inverse of one of them modulo the other one. We mention an application to torus-based cryptography.