Now imagine a different card. You show it, and the only thing the man learns is “yes, over 18”. Nothing else. He can still be sure it is true.

That second card is the idea behind a zero-knowledge proof.

What is a zero-knowledge proof?

A zero-knowledge proof is a way to convince someone that a statement is true, without giving them any other information. Two sides take part:

• the prover: the person who knows something and wants to prove it;
• the verifier: the person who checks the proof.

At the end, the verifier is sure the statement is true. But the verifier has learned “zero” extra knowledge. That is where the strange name comes from.

The idea is older than Bitcoin. It was first described in 1985 by Shafi Goldwasser, Silvio Micali and Charles Rackoff, in a research paper from MIT and the University of Toronto. For a long time it stayed mostly in universities. Blockchains brought it into real products.

How can you prove something without showing it?

Here is a simple example that needs no maths.

Your friend is colour blind. You hold two balls, one red and one green. To your friend they look exactly the same. You want to prove that they really have different colours, but you do not want to tell him which one is red.

So you give him both balls. He hides them behind his back, and then he either swaps them or does not. He shows them to you again and asks: “Did I swap?”

Because you can see the colours, you always answer correctly. If the balls were really the same colour, you could only guess, and you would be right half of the time. After 20 rounds with no mistake, the chance that you were just lucky is less than one in a million. Your friend is now convinced. But he still does not know which ball is red.

Real zero-knowledge proofs use maths instead of balls, and they usually need only one message, not 20 rounds. The idea is the same.

The three promises of a good proof

Researchers describe a zero-knowledge proof with three properties:

1. Complete. If the statement is true, an honest prover can always convince the verifier.
2. Sound. If the statement is false, a cheater cannot convince the verifier, except with a tiny chance.
3. Zero-knowledge. The verifier learns nothing except that the statement is true.

If one of these is missing, it is not a real zero-knowledge proof.

Why does this matter for blockchains?

Most blockchains are public. As I wrote in Is Blockchain Private?, anyone can see the amounts and the history of every address. That makes the system honest, because everybody can check the rules. But it is bad for privacy.

Zero-knowledge proofs can give you both. The network can check that a payment follows the rules (“this person has enough money, and nobody spent the same coins twice”) without seeing the amount or the people.

Today they are used in a few main ways:

• Private payments. Zcash, launched in 2016, was one of the first blockchains to use zero-knowledge proofs so users could hide sender, receiver and amount.
• Scaling. Some networks bundle thousands of transactions outside the main chain and post one short proof that all of them were correct. This is cheaper than checking each one.
• Identity. The European Commission’s blueprint for an age verification app uses zero-knowledge proofs, so a website can learn “over 18” without learning who you are. You can read about it on the EU age verification portal.

What about Cardano?

Input Output, one of the companies that built Cardano, also developed Midnight, a partner blockchain focused on privacy. Its main network started in March 2026. Midnight uses zero-knowledge proofs so that apps can keep personal or business data private, but still prove that they followed the rules.

A simple example: a company could prove to a regulator that all its customers passed identity checks, without sending the regulator a copy of every passport. I find this one of the most interesting directions in the whole field, because it does not force us to choose between privacy and trust.

Cardano itself stays a public blockchain. Your ADA, your staking and your votes are still visible on a normal explorer.

What zero-knowledge proofs cannot do

It is easy to talk about this technology as if it were magic. It is not.

• It only protects what is inside the proof. If you show your face on a video call or log in with your email, the proof does not help.
• The source of the data still matters. For the age example, someone first has to check your real ID and give you the credential. That organisation knows who you are.
• It is hard to build. The maths is complex, and a small bug in the code can break the promises. Good projects publish their code and pay for independent reviews, but mistakes still happen.
• Proofs cost computing power. Making a proof can take seconds on a phone, sometimes more. This is getting better, but it is not free.
• Privacy tools worry governments. Some countries see private payments as a risk and limit them. The rules are still changing.

Why I care about this

Privacy is not about hiding something bad. It is about sharing only what is needed. The man at the concert door needs to know your age, not your address. A shop needs to know you paid, not how much you have left.

For most of the internet, the only way to prove something was to hand over the data and hope it stays safe. Zero-knowledge proofs give us another option. They will not fix every privacy problem, but I would rather have that option than not. If you want to read why I think no single company should hold all the keys, I wrote about it in What Decentralization Really Means.