Related keys with different roles
Public-key, or asymmetric, cryptography uses a pair of mathematically related keys. A public key may be disclosed to other participants, while its matching private key remains secret. With an appropriate scheme and parameters, deriving the private key from the public key should be computationally infeasible. This changes how parties establish protected communication without first sharing the same secret.
Public availability does not mean that an unverified key can be accepted indiscriminately. A public key still needs integrity protection and a trustworthy association with its intended owner. The private key requires confidentiality. These are different responsibilities, not two interchangeable copies of a password.
Encryption, signatures, and key establishment
In public-key encryption, a sender uses the recipient's public key to protect a message, and the corresponding private key enables decryption. In a digital-signature scheme, the signer uses a private key to produce a signature, and others use the matching public key to verify it. Confidentiality and verification of origin or integrity are different services.
Key agreement has another role: participants combine their own secret information with exchanged public information to establish shared keying material. Public-key cryptography encompasses these mechanisms, but not every algorithm supports every purpose. Nor should a key pair be assumed suitable for arbitrary reuse across protocols. Signing a message is not itself a service for hiding its contents.
Distribution still requires authentication
If an attacker substitutes their public key for the intended recipient's, a sender can protect information for the wrong party while every mathematical operation works correctly. Likewise, verifying a signature with some public key establishes a relationship to that key, not automatically to the person named beside it.
A certificate is one way to bind an identifier to a public key in a signed data structure. The verifier still needs a trustworthy basis for accepting that binding. FIPS 186-5 distinguishes mathematical signature verification from validation that also obtains assurances about identity, key validity, and possession of the associated private key. A plausible-looking certificate alone is not sufficient.
Working alongside symmetric cryptography
Symmetric cryptography uses shared secret keys and commonly protects bulk data. Hybrid designs combine it with public-key mechanisms: asymmetric operations support authentication or key establishment, while symmetric algorithms protect subsequent communication. The two approaches are usually complementary rather than one simply replacing the other.
TLS 1.3 illustrates this separation. Its handshake negotiates parameters, authenticates, and establishes shared keying material; its record layer protects traffic using symmetric authenticated encryption and traffic keys. The protocol also supports pre-shared-key authentication. Consequently, not every TLS connection requires certificates or directly encrypts a session key with a public key. Authentication, key establishment, and data protection must be identified separately in the actual protocol.