Vice, Not Versa

It took me a while to understand that much of the internet's security rests on a mathematical imbalance. Our peace of mind hangs on the assumption that calculations which are relatively easy to perform in one direction remain extraordinarily difficult to reverse with today's computers.

Consider two prime numbers, 53 and 71. Multiplying them is straightforward:

53 × 71 = 3,763

Now consider the reverse. Suppose I gave you only 3,763 and asked you to find the two prime numbers that produced it. You could certainly work them out eventually, but unless you have an unusual fondness for prime numbers, you might be at it for a while. I know I would.

You could start testing possible divisors, trying different answers and brute-forcing your way to finding the right combination. With a number this small, it's tedious but manageable. Now imagine the original primes were hundreds of digits long. Any computer could multiply them almost instantly, but reversing the calculation would require an impractical amount of computation, even using the best conventional methods we know.

This concept helps us get closer to understanding the mathematical security behind RSA, one of the best-known public-key cryptographic systems. It's helpful to keep in mind that this security depends on what is computationally difficult for today's computers and algorithms. Change either one of those variables, and that assumption may no longer hold.

A conventional computer, whether it's your phone or an enormous data centre, processes information using bits, each representing a zero or a one. Everything from rendering a cat meme to running a language model ultimately comes down to operations involving those binary states.

Quantum computers work differently. Their basic units, called qubits, can exist in combinations of states known as superposition. They can also become entangled, allowing their states to be connected in unusual ways. By exploiting these properties, certain quantum algorithms can solve mathematical problems much more efficiently than conventional approaches.

In 1994, mathematician Peter Shor developed an algorithm showing that a sufficiently powerful quantum computer could factor enormous numbers dramatically faster than the best conventional methods known. His work also showed how quantum computers could threaten elliptic-curve cryptography, despite its different mathematics. There was just one problem: nobody had a quantum computer capable of doing it.

More than thirty years later, that remains a formidable engineering challenge. Quantum computers exist, but their qubits are extraordinarily delicate. Small disturbances introduce errors, and keeping them under control during complex calculations is difficult. No quantum computer has yet demonstrated the ability to break modern public-key cryptography at meaningful scales.

For now, we still have some time, although exactly how much is anyone's guess. Fortunately, cryptographers haven't been sitting around waiting for someone to crack the internet. Researchers have spent decades developing post-quantum cryptography, methods believed to remain secure even against quantum computers. The first major standards were finalized in 2024, and the transition is underway. There's good reason to start early, too. Encrypted information intercepted today could potentially be stored and decrypted years from now.

But while much of the world's attention has been entangled in quantum computing, something else has been happening in mathematics. AI is becoming increasingly capable of contributing to mathematical discovery, raising questions about what other computational shortcuts might eventually be found.

On October 6, 2026, OpenAI published new mathematical results developed with an advanced internal model, including proofs made available for independent verification. These weren't attacks on cryptography, but they demonstrated AI contributing to mathematical discovery rather than simply applying existing methods.

And this isn't entirely hypothetical. A few months earlier, in July 2026, Anthropic announced that its Claude Mythos Preview model had helped discover a mathematical weakness in HAWK, a proposed post-quantum digital signature system that had advanced to the third round of NIST's standardization process.

The discovery made certain attacks substantially more efficient than previously understood. On July 29, the HAWK team withdrew its proposal, acknowledging on its own website that the system was insecure and should not be used. The attack didn't compromise any finalized post-quantum standards, but AI had helped uncover a mathematical weakness serious enough to disqualify a promising cryptographic system.

The October announcement from OpenAI also caused quite a stir in the cryptocurrency community. Ethereum researcher Justin Drake warned on X that AI-assisted mathematical breakthroughs might eventually make it possible to recover private keys from public keys. He suggested that, in a particularly pessimistic scenario, such a breakthrough could emerge within months and encouraged cryptocurrency holders to consider what he called bunker mode.

Ethereum co-founder Vitalik Buterin was more cautious about immediate action, although he acknowledged the underlying concern. Neither was reporting an actual break of modern cryptography, but it was unusual to see people so familiar with these systems openly debating whether the timeline could be much shorter than expected.

Shor's discovery is a useful reminder that advances in algorithms can be just as consequential as advances in computing power. He worked out the mathematics decades before anyone could build the machines needed to exploit it.

Whether AI will uncover anything capable of undermining RSA or elliptic-curve cryptography remains an open question. But there's a practical concern here that goes beyond any single algorithm. Developing cryptographic standards takes years of research, scrutiny and testing, and replacing systems already in widespread use can take even longer. A mathematical breakthrough, meanwhile, can change the assumptions behind those systems almost overnight. I wonder whether our ability to discover new mathematical methods is beginning to move faster than our ability to adapt to them.

For now, our mathematical locks are holding up rather well. But with quantum computers getting better and AI developing a taste for mathematics, I wouldn't get too comfortable leaving the keys under the mat.