RSA is one of the best-known public-key cryptographic systems and can be used to create digital signatures that help verify who signed data and whether that data was changed afterward. Instead of placing only a visible signature mark on a document, RSA uses mathematical operations involving a private key, a public key, a secure hash function, and a defined signature scheme. NIST continues to include RSA among standardized digital-signature techniques.
If you want to understand the steps visually, an rsa digital signature process diagram can help show how document hashing, private-key signing, and public-key verification connect. The basic idea is simple: the signer creates the signature with the private key, while the recipient verifies it using the corresponding public key.
What Is RSA in Digital Signatures?
RSA stands for Rivest-Shamir-Adleman, named after the researchers who introduced the cryptosystem. It is an asymmetric, or public-key, cryptographic system that uses mathematically related public and private keys.
For digital signatures, those two keys perform different roles.
Private and Public Keys Have Different Jobs
The signer keeps the private key secret and uses it as part of the signature-generation process.
The corresponding public key can be distributed to people or systems that need to verify signatures.
In simplified terms:
- Private key: Creates the signature.
- Public key: Verifies the signature.
- Hash function: Produces a compact representation of the data.
- Signature scheme: Defines how the hash and RSA operation are securely combined.
NIST defines signature generation as using a digital-signature algorithm together with a private key to generate a signature on data.
Why RSA Digital Signatures Use a Hash
RSA signing does not normally process an entire large document directly as though the document itself were the signature input.
Instead, a cryptographic hash function is applied as part of the signature scheme.
What Is a Document Hash?
A hash function takes data of practically any size and produces a fixed-size digest.
For example, the input might be:
- A PDF
- A contract
- An email
- A software package
- A transaction record
- A message
The hash acts like a compact cryptographic representation of that data.
If the signed content changes, even slightly, the hash used during verification will normally differ. This is one reason digital signatures can help detect unauthorized modification. NIST describes digital signatures as mechanisms for detecting data changes and authenticating the signatory.
How RSA Is Used for Digital Signature Step by Step
A practical RSA signing process can be divided into two major stages: signature generation and signature verification.
The following sequence explains what happens from the original document to the final verification result.
Step 1: Generate an RSA Key Pair
The process begins with an RSA key pair.
The pair consists of:
- A private key
- A corresponding public key
The private key must remain protected because anyone who obtains it could potentially create signatures that appear to originate from its legitimate owner.
The public key, on the other hand, is intended for verification and can be distributed through appropriate mechanisms, often together with a digital certificate.
Conceptually:
Signer owns → Private key
Verifier receives → Public key
Protecting the private key is therefore one of the most important parts of an RSA signing system.
Step 2: Hash the Document
Next, the signing system processes the document using the hash function specified by the signature scheme.
Imagine the original message is:
Approve purchase order #5832 for $20,000.
The system computes a digest representing that exact content.
Conceptually:
Original document → Hash function → Message digest
The digest is much smaller than the complete document and is used as an input to the RSA signature-encoding process.
Step 3: Encode the Hash for RSA Signing
This step is important because RSA digital signatures are more sophisticated than the common explanation of simply “encrypting a hash with a private key.”
Standard RSA signature schemes define specific encoding procedures.
RFC 8017 defines two major RSA signature schemes:
- RSASSA-PSS
- RSASSA-PKCS1-v1_5
The selected scheme prepares the hash and related information into the required encoded form before the private-key RSA operation occurs.
This structured encoding is essential to the security of the signature algorithm.
Step 4: Generate the Signature With the Private Key
After encoding, the RSA signing operation uses the signer’s private key to produce the digital signature value.
A simplified representation is:
Document → Hash → Signature encoding → RSA private-key operation → Digital signature
The resulting signature can then accompany the original document.
Importantly, the private key itself is not sent with the document.
Only the signature and the information needed for verification are made available.
What Happens During RSA Signature Verification?
Creating the signature is only half of the process.
A recipient needs a way to determine whether that signature is valid for the received data.
Step 5: The Recipient Gets the Document and Signature
The verifier receives:
- The document or message
- The RSA digital signature
- Access to the corresponding public key
Depending on the system, the public key may be contained in or associated with a digital certificate.
The verifier does not need the signer’s private key.
That private key should remain under the signer’s control.
Step 6: Hash the Received Document
The verification system computes a fresh hash from the document it actually received.
Conceptually:
Received document → Same hash algorithm → New digest
If the document has been changed since it was signed, the newly calculated digest will not correspond to the signed value expected by the RSA verification procedure.
This provides the integrity-checking component of the digital signature.
Step 7: Verify Using the Public Key
The system then uses the signer’s RSA public key and the appropriate RSA signature-verification algorithm.
The verification algorithm checks whether the supplied signature is valid for the newly calculated document hash under the selected RSA signature scheme.
The final outcome is essentially:
Valid
or:
Invalid
A valid result indicates that the signature mathematically verifies against that data and public key.
RSA Digital Signature Process in Simple Form
The entire process becomes easier to understand when the signing and verification sides are viewed together.
The signer and verifier perform related but different operations.
Signing Side
The process is:
- Prepare the document.
- Calculate its cryptographic hash.
- Apply the required RSA signature encoding.
- Use the private key to generate the signature.
- Send or store the document together with the signature.
In short:
Document → Hash → Encode → Private key operation → Signature
Verification Side
The recipient then:
- Receives the document.
- Receives the digital signature.
- Calculates the document hash.
- Uses the public key and matching signature scheme.
- Checks whether the signature is valid.
In short:
Document + Signature + Public key → Verification → Valid or Invalid
This separation between the private signing key and public verification key is central to RSA digital signatures.
What Does an RSA Digital Signature Provide?
RSA signatures are designed to provide more than a visible indication that somebody clicked a signing button.
When correctly implemented within an appropriate trust framework, digital signatures can support several security properties.
Data Integrity
Integrity means detecting whether the signed data has been changed.
Suppose a signed agreement originally contains:
Payment: $10,000
After signing, someone changes it to:
Payment: $100,000
The modified content produces a different hash, so signature verification should fail.
NIST identifies data integrity as one of the core services provided by properly implemented digital signatures.
Origin Authentication
Verification using the corresponding public key provides cryptographic evidence connecting the signature to the holder of the matching private key.
However, the public key itself must still be reliably associated with the claimed person or organization.
That is one reason digital certificates and public-key infrastructure are commonly used alongside digital signatures.
Support for Non-Repudiation
NIST also describes digital signatures as supporting signer non-repudiation when implemented with the necessary infrastructure and policy.
In practical terms, this can strengthen evidence about which cryptographic identity generated a particular signature.
It should not be interpreted as meaning cryptography alone resolves every legal dispute about a signature.
RSASSA-PSS vs. PKCS#1 v1.5
RSA is the underlying public-key algorithm, but practical systems use defined RSA signature schemes rather than applying raw RSA directly.
RFC 8017 specifies both RSASSA-PSS and RSASSA-PKCS1-v1_5.
RSASSA-PSS
PSS is a probabilistic RSA signature scheme.
It incorporates randomized salt into its encoding process, meaning repeated signatures of the same underlying message need not result in identical signature values.
RFC 8017 defines RSASSA-PSS as one of its supported RSA signature schemes, and modern protocols increasingly prefer PSS in contexts where RSA signatures are used.
RSASSA-PKCS1-v1_5
PKCS#1 v1.5 is an older standardized RSA signature scheme that remains present in many existing systems and protocols.
Unlike PSS, its signature encoding is deterministic for a given message, key, and hash algorithm.
RFC 8017 continues to specify the scheme for compatibility with existing applications.
Developers should use cryptographic libraries and protocol requirements rather than trying to design their own RSA padding or signature construction.
RSA Signature vs. RSA Encryption
Another common misunderstanding is assuming that RSA signing is simply RSA encryption performed backward.
That explanation may be convenient for beginners, but it is technically incomplete.
They Serve Different Purposes
RSA encryption is intended to protect confidentiality.
Digital signatures are intended to support authenticity and integrity.
A simplified comparison is:
- Encryption: Keeps information secret.
- Digital signature: Helps prove origin and detect modification.
RFC 8017 defines separate RSA encryption schemes and RSA signature schemes, while an RFC 8017 technical erratum specifically emphasizes that RSASSA-PSS is a signature scheme rather than an encryption/decryption operation.
So, avoid describing secure RSA signatures simply as “private-key encryption.”
Where Are RSA Digital Signatures Used?
RSA signatures can appear anywhere systems need cryptographic proof that data was signed by the holder of a private key and remained intact.
The exact implementation depends on the application.
Common Use Cases
Examples can include:
- Digitally signed documents
- Software signing
- Digital certificates
- Authentication protocols
- Secure communications
- Business records
- Electronic document workflows
NIST’s current Digital Signature Standard recognizes RSA alongside ECDSA and EdDSA as standardized digital-signature techniques.
Frequently Asked Questions
RSA can sound complicated because key generation, hashing, encoding, signing, and verification all happen behind the scenes. A few basic distinctions make the process easier to understand.
Does RSA Sign the Entire Document?
Not directly in the simplistic sense.
Standard RSA signature schemes first process the message through a hash function and then use defined encoding and RSA operations to create the signature. RFC 8017 specifies these processes formally.
Which Key Is Used for an RSA Digital Signature?
The private key is used to generate the signature.
The corresponding public key is used during verification.
Does RSA Encrypt the Document When Signing?
No.
A digital signature does not automatically provide confidentiality for the document. Signing and encryption serve different purposes.
If confidentiality is also required, a separate encryption mechanism may be needed.
What Happens If the Document Changes?
If signed content changes, the hash calculated during verification normally no longer corresponds to the original signed data.
As a result, signature verification should fail.
Is RSA Still Used for Digital Signatures?
Yes. RSA remains included in NIST’s current Digital Signature Standard, FIPS 186-5, alongside ECDSA and EdDSA.
Final Thoughts
So, how is RSA used for digital signature?
The process combines asymmetric cryptography with secure hashing and a standardized RSA signature scheme.
A simplified signing workflow is:
Document → Hash → Signature encoding → RSA private-key operation → Digital signature
Verification reverses the perspective rather than simply reversing encryption:
Received document → New hash + Signature + Public key → RSA verification → Valid or Invalid
The private key enables the signer to generate the signature, while the public key allows other systems to verify it without learning the private key.
Most importantly, modern RSA digital signatures should not be understood as merely “encrypting the document hash with the private key.” Real implementations use standardized constructions such as RSASSA-PSS or RSASSA-PKCS1-v1_5, which define how hashing, encoding, and RSA mathematical operations work together.
When implemented correctly, RSA digital signatures can help establish data integrity and authenticate the cryptographic origin of signed information. That is why RSA remains an important part of digital-signature systems even though most users never see the cryptographic steps happening behind the signing interface.