Can blockchains save the internet?

Much of what you do on the internet — shopping, banking, logging into all kinds of accounts — is secured by public-key cryptography.

This was a major advance over single-key cryptography used in World War II Enigma machines and the toy decoder rings once found in cereal boxes. Both required sender and receiver to agree in advance on a key used to unscramble a secret message (eg, “shift every letter one to the left”).

Amazon does not want to send decoder rings to its 200 million Prime customers (or think up 200 million versions of “shift every letter one to the left”). So it uses public-key cryptography instead.

Public-key cryptography employs two mathematically related keys: a public key that anyone can use to scramble a message, and a private key that only the recipient holds to unscramble it.

The magic behind public/private keys is multiplication. Specifically, the fact that multiplying two large prime numbers (P * Q = N) is trivially easy for a computer, but reversing the process (factoring N back into P and Q) is practically impossible.

The holder of a private key doesn't have to factor N at all, because the key was created using P and Q, giving it a mathematical shortcut to unlock the encrypted message.

Anyone else has to find P and Q on their own.

Public-key encryption is effectively unbreakable because there’s no good way to do that.

The methods mathematicians have devised to factor numbers more quickly — algorithms that seek out underlying patterns and structure — are so inefficient they might as well be guessing. It would take a supercomputer trillions of years to “unmultiply” the prime numbers involved when you log on to Amazon.

Lately, though, the mathematicians have been getting better. Fast.

In May, for example, an OpenAI model overturned 80 years of assumptions about how geometric points can be arranged in space, disproving a famous conjecture by Paul Erdős. In August, a swarm of autonomous Claude subagents made advances in analytic number theory that appeared to compress years of mathematical labor into a single weekend.

In both cases, the AI mathematicians found underlying structure and patterns that human mathematicians had not.

So what happens if the AIs discover structures and patterns that make the factorization of large numbers radically more efficient?

It might break the internet. Large parts of internet security are based on the assumption that factorization is extremely slow and difficult. If that is no longer the case, hackers would be well on their way to building a decoder ring for all of your online transactions.

There’s no sign of this happening yet, and some mathematicians are skeptical it will anytime soon.

The problem, however, is that if it does happen, it will happen suddenly.

Quantum computers are the more famous threat to public-key cryptography. But there it’s mostly a question of hardware capability. Hardware improves slowly and publicly, so we should have ample warning before quantum breaks the internet.

AI, by contrast, might make a conceptual leap on factorization that seemingly comes out of nowhere.  

Factorization is not the only math safeguarding the internet. There's also elliptic curve math and lattice math, for example.

But what if AI breaks these defenses, as well?

It could happen. OpenAI recently announced, for example, that its unreleased Astra model discovered new structures in the lattice math used in post-quantum cryptography.

If AI math gods compromised those parts of public-key encryption, too, we might be down to our last line of defense: blockchains.

Can the devs do something?

So that’s the bad news: Both quantum computers and AI mathematicians can pull answers from mathematical structure in ways that classical computers and human mathematicians never could, thereby threatening public-key cryptography.

Here’s the good news: Not all cryptographic defenses rely on structured math. Hash-based cryptography, for example, turns data into unstructured noise, leaving hackers no equations to reverse engineer or patterns to decode.

“The point of hash functions,” Eli Ben-Sasson told me on a call, “is that they have no structure.”

(“No structure” being mathematician-shorthand, I think, for “no detectable structure.”) 

Ben-Sasson is the co-founder of StarkWare, which develops blockchain technology based on STARKs, the hash-based zero-knowledge proof system he co-invented in 2018. 

A hash function transforms data into a string of random-looking numbers, from which it’s virtually  impossible to work backward to the original data.

Ben-Sasson believes this makes zero-knowledge proofs running on blockchains the ultimate defense against quantum computers and god-like AIs. 

Standard web security uses public-key cryptography to establish a secure channel for, say, an online shopper to exchange data with Amazon. If the cryptography is compromised, all that data is at risk.

STARKs eliminate the channel, broadcasting instead a hash-based proof that anyone can verify. That proof can be broadcast — publicly — to establish that a private transaction is valid without revealing its contents. 

There is nothing to decrypt or steal — only mathematical evidence that the underlying computation is correct.

In short, STARKs replace secret-sharing with zero-knowledge verification.

Ben-Sasson of course thinks these proofs are best shared on Starknet, the layer-two blockchain developed by StarkWare, but the principle is broadly applicable: The STARK proof system is a general cryptographic primitive that can be used outside Starknet, the StarkWare website explains.

StarkWare Labs also publishes open-source research to help any blockchain become quantum and AI-resistant — including the original one. A StarkWare researcher recently published a paper on how to quantum-proof Bitcoin.

Still, StarkWare believes Starknet — because it was built on STARKs right from the start — is “uniquely positioned to become quantum-resistant.”

Helpfully, that should make it AI-resistant, too.

If AI mathematicians break public-key encryption, we might soon be doing our online shopping on a blockchain.

— Byron Gilliam