THE IMPORTANCE OF THE FUNDAMENTAL THEOREM OF ARITHMETIC ON PUBLIC-KEY CRYPTOGRAPHY

Abstract

This paper aims to present the empirical importance of the fundamental theorem of arithmetic on public-key cryptography, where its role is indispensable in information security due to the difficulty of factoring a compound number on its prime factors. To achieve its goal, the research relies on bibliographic reviews with mathematical proofs of the theorem, as well as the prime numbers being infinite. In order to have experiments around that, the authors drew up an algorithm to decompose two numbers with different amounts of bits, highlighting by doing so, that this is an extensive and non-deterministic operation. In this regard, the research presents on a practical and mathematical matter how laborious would be the attempt to obtain inaproprial access to classified and encrypted information when it is being kept secured by an asymmetrical algorithm, emphasizing that, computing joins mathematics to guarantee the impracticality in decrypting a public key, thus guaranteeing the security and integrity of information in the digital world.