Encryption is a fundamental element of today's world of technology. It is crucial in enhancing the security and privacy of data. In the realm of encryption and security, both private keys and public keys happen to be indispensable.

Public key and private key are part of a system known as public key cryptography or asymmetric cryptography. This system allows two parties to engage securely over an unsecured network. In this system, each party has a pair of keys - a public key and a private key.

Public keys are openly shared. They can be used by anyone to encrypt a message. Unlike public keys, private keys are kept private. Only the recipient of a private key can use it. The message encrypted with the public key can only be decryptedby the corresponding private key.

Cryptography is the practice and study of encryption and decryption. It incorporates creating cryptographic systems. Several procedures such as Hash Functions, Symmetric-key Cryptography, and more concretely, Public Key Cryptography or Asymmetric Cryptography have emerged from this field.

The security provided by this system is based on mathematical encryption algorithms and the difficulty of factoring large prime numbers. It is computationally impossible to calculate the private key check here based on the public key.

In asymmetric cryptography, the concept of public and private keys is applied extensively in multiple protocols, providing functions such as non-repudiation, authentication, and integrity.

In conclusion, public and private keys in encryption are fundamental to modern cryptography and, by extension, to online security. They help to ensure the secure transfer of information in a world where digital communication has become commonplace, ensuring that our private digital communications remain desirably confidential. Therefore, a profound understanding of these keys and their role in encryption and security can be extremely advantageous.