Аннотация:Cryptography has been invented for thousands of years as an important tool to safely transfer sensitive messages. Nowadays, cryptography has already become an essential component of our society. The RSA cryptosystem, a widely used cryptosystem in our current online system, is a safe but time-consuming method. Eulers totient function, in the modular arithmetic that the RSA is based on, plays an important role and has strong potential to be applied with other cryptosystems to make innovations on the RSA. This paper will introduce the potential proposed risk of hacking the RSA cryptosystem using Eulers totient function, and how this function can be applied itself or with other ciphers to create more optimized algorithms and methods based on the RSA cryptosystem. The analyzed results show that the current innovations made to the RSA cryptosystems are rarely balanced on time complexity and security levels and need improvements under most circumstances.
