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The “public/private key method” is more commonly called public-key cryptography or asymmetric cryptography. It uses a related pair of keys: a public key that can be shared and a private key that must be kept secret. Depending on the algorithm, the pair can be used for encryption, digital signatures, or key agreement—but those operations are not interchangeable.

How public-key cryptography works

Unlike symmetric cryptography, which uses the same secret key for an operation such as encrypting and decrypting data, public-key cryptography uses two mathematically related keys. The public key is associated with an entity and may be shared; the private key is associated with that entity and is not made public. NIST describes the public key as derived from the private key, while deriving the private key from the public key is computationally infeasible in the scheme description it provides.

NIST’s glossary definition describes separate keys used to exchange data, with one key used to encrypt or digitally sign and the other used to decrypt or verify. Which key does what depends on the purpose and algorithm.

What the keys do in different operations

Purpose Key operation What it provides
Encryption A sender encrypts data or a key using the recipient’s public key; the recipient uses the corresponding private key to decrypt it. Confidentiality: the intended recipient’s private key is needed to recover the protected material.
Digital signatures The signer uses a private key to create a signature; others use the corresponding public key to verify it. A way to check that a signature corresponds to the signer’s key and that the signed data has not changed. Verification is not decryption.
Key agreement Participants use an algorithm-specific exchange to compute a shared secret. A shared secret that can then be used in a secure communication scheme.

NIST’s public-key glossary entry describes these uses. Not every public-key algorithm or key pair supports every operation. For example, NIST’s FIPS 186-5 specifies that an RSA digital-signature private key computes a signature and the corresponding public key verifies it.

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How public-key encryption protects information

  1. The recipient shares a public key. The recipient keeps the corresponding private key secret.
  2. The sender protects information for that recipient. The sender encrypts data—or often a key used to protect data—with the recipient’s public key.
  3. The recipient uses the private key. The corresponding private key enables decryption of the protected material.

This direction is for confidentiality: using the recipient’s public key lets others protect material for the recipient, while possession of the corresponding private key allows the recipient to recover it. It is different from signing, where the private key creates a signature and the public key checks it.

How a public key verifies a digital signature

A signer creates a digital signature with a private key. A verifier uses the corresponding public key to check the signature against the signed data. A successful verification supports confidence that the signature was produced using the matching private key and that the data matches what was signed; it does not mean the verifier has decrypted the data. NIST’s FIPS 186-5 gives RSA as a specific example of this signing and verification relationship.

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Why a public key alone does not prove identity

A public key can be shared openly, but seeing a key does not by itself establish whose key it is. In real systems, a certificate or another trust mechanism can bind an identity to a public key. Without a way to establish that binding, a person could receive a key that belongs to someone else and mistake it for the intended party’s key. NIST’s glossary entry describes the public key’s association with an entity; the association still needs to be trusted in the context where the key is used.

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Why systems combine public-key and symmetric cryptography

Asymmetric algorithms are relatively slow and are not well suited to encrypting large messages directly. Practical systems therefore commonly use public-key techniques to protect or agree on a symmetric key, then use symmetric cryptography for bulk data. NIST’s introductory guide, SP 800-32, Introduction to Public Key Technology and the Federal PKI Infrastructure, discusses this role and characterizes asymmetric cryptography as a class of algorithms in which Alice has a private key and Bob and others have her public key.

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