There are, believe it or not, many among us who remain skeptical that blockchains like Bitcoin and Ethereum will ever have much of an impact on the mainstream tech world. When the conversation turns to issues related to privacy, their concerns generally come in one of two flavors: these systems are either too anonymous for apps that millions of people might end up using, or they are too traceable.

But the complex math underlying a cryptographic protocol called a zero-knowledge proof promises to upend today’s popular notions of blockchain privacy—and open the door to a range of new applications along the way.

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Bitcoin, Ethereum, and most other public blockchains are in fact pseudonymous, as opposed to truly anonymous; individuals transacting on the network are represented by publicly viewable strings of numbers and letters called addresses. (More here: “What Bitcoin Is, and Why It Matters”)

As long as no one connects your real name to your address, you can effectively hide your transactions. If your true identity does get connected to your address, though, suddenly anyone who might be interested can see every transaction you’ve ever made on the network.

Law enforcement organizations have cottoned onto this, and over the past few years they’ve honed their ability to follow the money on the Bitcoin and Ethereum blockchains, tracking down people who use the cryptocurrencies for illicit purposes. (More here: “Criminals Thought Bitcoin Was the Perfect Hiding Place, but They Thought Wrong”)

Enter zero-knowledge proofs, a technology so mind-bending it seems taken from the pages of a science fiction novel. Essentially, it is “a way to prove something to someone without revealing any of the information that goes into that proof,” says Emin Gün Sirer, a computer scientist at Cornell University. As a simple example, imagine that you must prove you are at least 18 years old. Instead of whipping out your ID, the math underlying zero-knowledge proofs can allow you to make someone 100 percent certain that you are older than 18 without revealing a shred of other information about yourself. Not your name, address, a photo—nothing.

The idea of zero-knowledge proofs has been known to cryptographers for two decades, but it wasn’t until last year that researchers figured out what could be the technique’s killer app: a Bitcoin-based cryptocurrency called Zcash. Zcash uses zero-knowledge proofs to guarantee that transactions are valid despite the fact that information about the sender, the recipient, and the amount transacted all remain hidden. The power of the idea has major banks interested. JPMorgan Chase recently worked with Zcash to add zero-knowledge functionality to its own private Ethereum-based blockchain.

Sirer says zero-knowledge proofs could open the door to many applications beyond finance, including ones we don’t yet know that we need. And since Ethereum recently added zero-knowledge functionality too, there’s reason to think we could soon start to learn what those are. (More here: “This Is the Reason Ethereum Exists”)

Ultimately, how far this technology can take us is still hard to say—the field’s top minds have only just begun to figure out how to put it to use. But there’s a very real possibility that it will one day extend into nearly every aspect of our online lives. We could be witnessing the beginning of a revolution in how we handle our most personal information.