The attack on the RSA algorithm with the application of Euler's function

The security of present-day asymmetric encryption algorithms is based on certain limitations of modern mathematics. A wide range of applications of asymmetric cryptography in commonly and widely used network protocols poses a question as to what degree such solutions, in a situation where the security of the used algorithm is not given once and for all, are really safe? In the vast majority of instances, a discussion on security involves considerations on the problem of factorization. The attack, derived almost from the definition, is an attack that involves trying many different options to intercept the private key, indispensable for decryption of the encrypted message, on the basis of the intercepted public key. The present work discusses possibilities and the feasibility of an attack on the RSA algorithm using two given methods, factorization and the method that implements Euler's function. The paper presents an analysis of potential costs (time and computational) for both presented methods. The article also includes a discussion on strong and weak keys for the RSA encryption. The quality of the keys is discussed taking into account the aforementioned two algorithms carrying out an attack against the encryption algorithm.