O uso da aritmética modular no desenvolvimento da criptografia RSA

Abstract

This work, entitled The use of modular arithmetic in the development of RSA Cryptography, aims to study the fundamentals behind RSA Cryptography, namely, modular arithmetic, your characteristics and properties. Initially, some basic properties of integers are studied to, then, to define the congruence between two integers given a third integer and present your basic properties. In sequence, the concept of inverse module n is presented and conceptualized, in addition to specifying your properties and condition of existence; Furthermore, relationships between inverses and some theorems widely used in RSA Cryptography are also established, such as the Chinese Remainder Theorem and Fermat’s Little Theorem. Having done all this theoretical foundation, RSA Cryptography is presented and defined, in addition to showing how and why RSA Cryptography works, using modular congruence for such purposes; Within this, a simple example of coding and decoding in RSA Cryptography is presented. Finally, some considerations are made about RSA Encryption, y effectiveness and the difficulty for an unauthorized person to decode a message, that is, to break the code, without possession of the private keys for decryption.