Tackles the Math Behind Digital Security

A new approach to an old problem

In the digital age, our online lives—from banking to private messaging—depend on invisible mathematical locks. One of the most important of these mathematical locks is based on a deceptively simple idea: factoring large numbers.

Factorization is the process of breaking down a number into smaller numbers that multiply together to give the original. For small numbers, this is easy. But when the numbers grow—into hundreds or even thousands of digits—the task becomes incredibly difficult. So difficult, in fact, that no one has yet found a fast and reliable way to do it.

This difficulty is the foundation of RSA encryption, one of the most widely used systems for securing digital communication. The assumption is simple: if factoring large numbers is hard, then breaking the encryption is hard too. But there is no formal proof that this problem is truly hard. It’s just that decades of effort have failed to crack it.

Collaboration with national and international experts

Markus Hittmeir in NORCE is setting out to challenge that assumption. With FRIPRO funding of NOK 9,4 million from the Norwegian Research Council, the project aims to explore new methods for integer factorization, particularly using deterministic techniques—approaches that follow a predictable path rather than relying on randomness.

The project involves collaboration with national and international experts, including Lilya Budaghyan from the University of Bergen, David Harvey from UNSW in Sydney and Pantelimon Stanica from the Naval Postgraduate School in California, and will run until September 2028.

– We’re trying to understand the true limits of these mathematical problems, says Hittmeir. If we can find more efficient algorithms, it could have a profound impact—not just on cryptography, but on how we think about complexity and computation itself.

Why it matters

But the project goes beyond just factorization. It also tackles other mathematical puzzles that play a role in cryptography, such as the subset-sum problem and the shortest vector problem. These are not just theoretical challenges—they have real-world applications in areas like resource allocation and post-quantum cryptography, which aims to protect data even in a future where quantum computers could break today’s encryption.

The stakes are high. If someone discovers a fast way to factor large numbers, many of today’s cryptographic systems could become obsolete overnight. That’s why researchers are racing not only to improve current methods but also to build new systems that can withstand future threats—including those posed by quantum computing.

In a world where digital security is more critical than ever, solving these mathematical mysteries could be the key to keeping our data safe.