Public key cryptosystems (also called asymmetric cryptosystems) are characterized by using different keys for encryption and decryption of information. Its main advantage is that they facilitate the process of distribution and exchange of keys among the participants of secure communication, which was a major problem of symmetric or private key cryptosystems.
Asymmetric algorithms generally employ much longer key lengths than symmetric ones, which use a single secret key. For example, while a 128-bit key is considered secure for symmetric algorithms, for most asymmetric algorithms (including RSA), keys of at least 1024 bits in length are currently recommended. In addition, the complexity of calculation involved in the algorithms of asymmetric cryptosystems makes them considerably slower than symmetric encryption algorithms. That is why in practice asymmetric methods are mainly used to encode the session key (symmetric) of each particular communication or transaction.
Cryptography based on public key cryptosystems is relatively recent, as the first asymmetric algorithms appear after 1975.
The cryptosystem of this most important and widespread class today is the RSA, which uses modular exponentiation to encrypt and decrypt and bases its security in the complexity of the problem of factoring large integers.