Is it possible to break the RSA public-key cryptosystem which is commonly used in encryption/decryption operations of contemporary mediums of secure communication?

There are 2 specific attack implementations here, the first one is one of the simplest attack that can be performed on RSA (and also one of the extremely rare one to happen in the real world) is called as common modulus attack. In here RSA gets smashed (i.e. we get the plaintext M) by two different ciphertexts (C) that is acquired with the same modulus N of the same plaintext. You can get a more detailed explanation about this simple attack from this medium article, enjoy 😊

The other attack adopts a side channel attack mechanism to smash RSA, namely a power analysis attack is performed by exploiting the implementation of the RSA algorithm (not the algorithm itself but its implementation).