Each private key has a corresponding public key. Generally the public key can be easily derived from the private key, but deriving the private key from the public key is computationally infeasible.
Private Key in SSH
In SSH, a private key is used for authenticating computers and users. A host key authenticates servers, and an identity key serves as an authentication credential for a user. Together they are called SSH keys.
SSH keys grant access to servers, similar to user names and passwords. Therefore, they should be part of identity and access management in enterprises. All cyber-security related laws and regulations also require managing SSH key based access.
It turns out that in many organizations SSH keys have not been properly managed, and they have literally millions of keys configured as authorized keys granting access to their servers. An assessment of risk and deployment of SSH key management tools is strongly recommended.