RSA is a public-key algorithm built on a mathematically linked key pair. A hash function is a keyless procedure that turns any input into a fixed-length digest. They are different tools. They meet in digital signatures, where a message is hashed and encoded before RSA’s private-key operation is applied.
What RSA is
RSA is named after Rivest, Shamir and Adleman. NIST’s glossary describes it as a public-key algorithm used for digital-signature generation and verification and for key establishment. The PKCS #1 specification (RFC 8017, IETF, November 2016) also defines RSA encryption schemes, so RSA is not only a signature tool.
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“Public-key” means each party has two related keys. The public key can be shared, and the private key must stay secret. What the keys do depends on the scheme. In a signature scheme the private key signs and the public key verifies. In an encryption scheme the public key encrypts and the private key decrypts.
What hashing is
NIST defines a cryptographic hash function as one that takes a bit string of arbitrary length and returns a bit string of fixed length. The output is called a digest. A hash needs no secret key as a primitive, and anyone can compute it.
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Hashing is not encryption. A digest is not a ciphertext, and it is not meant to be reversed to recover the input. NIST lists three security properties:
- Collision resistance: it should be infeasible to find two different inputs with the same digest.
- Preimage resistance: given a digest, it should be infeasible to find an input that produces it.
- Second-preimage resistance: given one input, it should be infeasible to find a different input with the same digest.
Which property matters most depends on the use. Signatures rely heavily on collision resistance, because two messages sharing a digest would also share a signature.
RSA versus hashing at a glance
| Aspect | RSA | Hash function |
|---|---|---|
| Type | Public-key algorithm | Digest computation |
| Keys | Public/private key pair | None required |
| Output | Signature or ciphertext, depending on scheme | Fixed-length digest |
| Typical purpose | Signatures, key establishment, encryption schemes | Fingerprinting data; a component inside signatures |
| Provides confidentiality? | Only in an encryption scheme | No |
| Identifies the signer? | Yes, in a signature scheme, through the key pair | No, not on its own |
How RSA signatures use hashing
RSA operates on numbers of a fixed size tied to the key, not on arbitrary-length documents. A signature scheme therefore first processes the message with a hash function. It then applies an encoding method that formats the digest, and only then applies the RSA private-key operation. Verification uses the public key and checks that the result matches the expected encoded value for the received message.
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Random freezes, missing sound and display glitches usually trace back to one bad driver. Find and replace yours safely.Free scan · under a minuteTwo points follow. First, the hash supplies a compact fingerprint of the message. The RSA key operation is what ties that fingerprint to a particular key holder. A bare hash cannot tell you who created a message, because anyone can compute it. Second, signing is often described as “encrypting a hash with the private key”, but that shortcut hides the encoding step and the scheme-specific rules. Those rules are the part that matters for security and interoperability.
The two RSA signature schemes
RFC 8017 specifies two signature schemes with appendix:
RSASSA-PSS
RFC 8017 recommends PSS for new applications. FIPS 186-5 approves it, and requires an approved hash function or XOF (extendable-output function) for it.
RSASSA-PKCS1-v1_5
RFC 8017 retains this scheme for compatibility with existing systems. FIPS 186-5 also approves it, subject to additional constraints.
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In practice the choice comes down to whether you are building something new or must interoperate with existing deployments. Protocol and policy requirements, such as a standard or certificate profile you must follow, can decide it for you.
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Which hash goes with RSA?
No single hash fits every context. Use the hash that your protocol or policy specifies. Under FIPS 186-5, PSS needs an approved hash function or XOF, and RFC 8017 defines the scheme-specific details of how the hash is used. If you must comply with a specific standard, check its current text rather than relying on an older default.
Standards status
FIPS 186-5, the Digital Signature Standard, was published by NIST on February 3, 2023. Its abstract says it “specifies a suite of algorithms that can be used to generate a digital signature.” NIST’s publication page carries a May 12, 2025 note saying identified issues are intended for a future revision, and it links an errata spreadsheet. Check that page before relying on it for implementation.
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Common mix-ups
- “Does RSA encrypt or hash?” RSA does neither as a plain hash. It performs public-key operations, used in encryption schemes and signature schemes, and signature schemes call a hash function.
- “A hash proves who sent it.” It does not. Only the signature construction supplies that.
- “A hash hides the data.” A digest is not encryption and gives no confidentiality guarantee.
- “RSA signing and RSA encryption are the same thing.” They use distinct encodings and serve distinct purposes, even though both are defined in PKCS #1.
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