### A review about public cryptography protocols based on RSA or elliptic curves

We provide the basic deﬁnitions regarding computational complexity theory and review some basic cryptography protocols based on RSA or elliptic curves. These protocols summarize the history of the last ﬁfty years in cryptography and are actually ubiquitous in applications, as for example SSL (secure socket layers), smartcards, creation of a bitcoin wallet etc. Since it is known they are in the polynomial class for the Shor’s algorithm, the possible development of quantum computers, needed to run...