Basic Arithmetic Foundations

Abstract

In cryptography, the Integer Factorization Problem (IFP) has significant importance because many cryptosystems with public keys ground their security on the hardness assumption of it. For example, RSA Laboratories launched many competitions that targeted IFPs [1]. The IFP problem consists of writing an arbitrary integer as a product of powers of prime numbers. Note that every integer number can be written as a product of prime numbers and that product is unique. At the same time, IFP is interesting because it combines elements of number theory with elements of complexity theory.