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An asymmetric-key algorithm uses a related pair of distinct keys: a public key that can be shared and a private key that is kept secret. Depending on the algorithm and protocol, the keys can support encryption and decryption, digital signatures, or key agreement. These are different operations, not one universal function.

What do the public and private keys do?

The public and private keys are mathematically related, but they have different roles. The public key may be distributed; its corresponding private key must remain secret. NIST’s glossary defines public-key cryptography as using two separate keys, one to encrypt or digitally sign data and another to decrypt it or verify the signature: NIST CSRC glossary: public key cryptography.

The particular operation depends on the algorithm. A public key is not automatically able to encrypt arbitrary data, and not every asymmetric algorithm provides encryption. NIST also describes public-key uses that include computing a shared secret: NIST CSRC glossary: public key.

How are encryption, signatures, and key agreement different?

Operation Typical key roles Goal
Public-key encryption Encrypt with the recipient’s public key; decrypt with the corresponding private key Confidentiality for the protected material
Digital signature Generate a signature with the private key; verify it with the corresponding public key Authenticity and integrity, not confidentiality
Key agreement Use related key material within an agreed protocol to compute a shared secret Establish shared secret material

The table describes common roles at a conceptual level; the exact operations depend on the algorithm and protocol.

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Encryption and decryption

For public-key encryption, a sender uses the recipient’s public key to protect material. The corresponding private key is used to decrypt it. The intended protection is confidentiality.

Signing and verification

A signer uses the private key to generate a digital signature. Other people can use the corresponding public key to verify it. A digital signature is not a message encrypted with the private key. NIST states that signatures provide authenticity and integrity protections, but not confidentiality: NIST SP 800-63-3.

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Key agreement

In key agreement, participants use related key material in a protocol to compute shared secret material. This is distinct from encrypting a message or signing it.

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