Digital Signatures and Public-Key Infrastructure
A public key lets anyone encrypt to you and verify your signatures — but it raises a new question: how do you know a public key really belongs to who it claims? If an attacker can substitute their own public key for the bank's, all the cryptography in the world protects your connection to the attacker. Solving "whose key is this?" is what certificates, certificate authorities, and chains of trust exist for — the plumbing that makes public keys into verifiable identities.
A public key lets anyone verify your signatures — but how do you know a public key really belongs to who it claims? If an attacker substitutes their key for the bank's, all the cryptography protects your connection to the attacker. Certificates, CAs, and chains of trust solve 'whose key is this?'