The Digital Signature Algorithm turns a document into a pair of integers that nobody can forge and nobody can quietly alter. This is what happens in the second after you click Sign, why one reused random number can undo all of it, and which algorithm actually signs your contracts today.
An image of a name proves nothing about who put it there or whether the page changed afterwards. A digital signature is a mathematical claim, and it either checks out or it doesn't.
Only the holder of one specific private key could have produced this pair of numbers. Verification uses the matching public key, which proves the link without ever revealing the private one.
Why it matters: identity rests on possession of a key, not on a picture of a name.The signature is computed over a hash of the document, not the document itself. Change a comma, change a date, change one invisible character — the hash changes completely and verification fails.
Why it matters: tampering is detected, not merely discouraged.Because only one key could have produced the signature, it is hard for the signer to credibly deny it — provided the key was genuinely under their control. That last condition is where real disputes are usually fought.
Worth knowing: the maths supports the argument; how much legal weight it carries still depends on the jurisdiction.DSA rests on the discrete logarithm problem: it is cheap to compute gx mod p, and currently infeasible to work backwards from the result to x. Everything below follows from that asymmetry.
Agree the public domain parameters, then draw a private key at random and derive the public one from it.
x never leaves the signer. y is published in the certificate.
Hash the message, draw a fresh secret k for this signature alone, and produce two integers.
The signature is the pair (r, s). Nothing else is sent.
Recompute a value from the public key and the document’s hash. If it lands on r, the signature holds.
No secret is needed to verify. That is the entire point.
Every letter in those equations has a job. Only two of them are secret, and the second one is secret for a single signature and then thrown away.
Carried inside the certificate. Anyone verifying a signature already holds every one of these, and knowing them gets you no closer to signing.
The large prime everything is computed modulo. Its size sets the difficulty of the underlying discrete logarithm problem.
A prime that divides p − 1. It fixes the size of the signature, which is why a DSA signature stays small while p grows.
A number whose powers cycle through a subgroup of order q. Shared openly, often across a whole organisation.
The only published value derived from the private key — and the one every verifier needs. Anyone can check with it; nobody can sign with it.
People say “DSA” loosely, and usually mean one of these four. They solve the same problem from different hard maths, and only three are still approved for new signatures.
| Algorithm | Hard problem | Typical key | Where you meet it | FIPS 186-5 status |
|---|---|---|---|---|
| RSAPKCS#1 | Integer factorisation | 3072-bit | PDF signatures, TLS certificates, most Class 3 signing certificates | Approved |
| DSAFIPS 186-4 | Discrete log, finite field | 3072-bit | Legacy PGP keys, older SSH hosts, historical government systems | Verify only |
| ECDSAP-256 and friends | Discrete log, elliptic curve | 256-bit | TLS, e-passports, most modern certificate chains | Approved |
| EdDSAEd25519, Ed448 | Twisted Edwards curve | 256-bit | SSH keys, code signing, newer protocol work | Approved |
Key sizes are not comparable across rows: a 256-bit elliptic-curve key is roughly the strength of a 3072-bit finite-field key. Smaller is not weaker here — it is different maths.
NIST published FIPS 186-5 in February 2023. It keeps DSA for verifying signatures that already exist, and removes it for generating new ones, citing security analysis of real implementations and the industry’s move to elliptic curves. FIPS 186-4 was withdrawn a year later, in February 2024.
So when a vendor says their product “uses DSA”, it is worth asking which one they mean. In practice, the signature on a contract today is produced by RSA or ECDSA — and which one is decided by the certificate and the authority that issued it, not by the platform sending the document.
Every signature needs a fresh, unpredictable k. Sign two different messages with the same key and the same k, and the two equations can be solved for x with ordinary algebra — no brute force, no supercomputer, no waiting.
This is not theoretical. Sony’s PlayStation 3 code-signing key was recovered in 2010 because the implementation used a constant instead of a random value. The key was extracted, and anything could then be signed as Sony.
The fix is standardised: RFC 6979 derives k deterministically from the private key and the message hash, so it is unpredictable to everyone else and never repeats for different messages. FIPS 186-5 specifies deterministic ECDSA for the same reason.
Which is why “we implemented the cryptography ourselves” is rarely the reassurance it is meant to be.You never choose an algorithm in Docsliy, and you shouldn’t have to. It is decided by the signature tier the transaction needs and the authority that issues the certificate.
For Aadhaar eSign, a Certifying Authority licensed by the CCA performs the authentication and applies the signature. We send a SHA-256 hash of the document — never the contract itself.
Aadhaar eSignA Class 3 Digital Signature Certificate keeps the private key on a token or HSM, so it cannot be copied off the machine. Required for MCA, GST, income-tax and tender filings.
CertificatesTimestamp, IP, device and authentication method are retained alongside the document. The cryptography proves the file is unchanged; the trail shows the circumstances it was signed in.
Trust & securityA cryptographically sound signature is not automatically the right one. Some markets require a qualified certificate, some require registration or stamping, and some exclude the instrument entirely.
Legality guideShort answers on what DSA actually is, where it still applies, and what replaced it.
Docsliy applies the signature tier the jurisdiction requires, through a certificate authority licensed to issue it, and keeps the evidence that goes with it. You send the contract.