Our modern, interconnected world runs on the invisible machinery of cryptography – the mathematical science behind safeguarding information. Every time we enter credit card details during an online purchase, cryptographic protocols secure them from cybercriminals. Banks depend on encryption to ensure the integrity of financial transactions, so no one can manipulate your coffee purchase of £2.50 into an absurd £2.5 million. Even mobile networks utilize encryption to prevent devices from interfering with each other’s signals.

The clever application of mathematical concepts has long underpinned cryptographic security, but the advent of quantum computing may soon outpace current methods. What strategies can be deployed to prepare for this quantum leap and maintain the integrity of our digital lives?

These urgent concerns were at the forefront of discussions during the Quantum Computing: Applications and Challenges event, hosted by the Newton Gateway to Mathematics. This conference formed part of a broader initiative held at the Isaac Newton Institute for Mathematical Sciences in Cambridge.

Quantum risks ahead

At the heart of online security lies a system known as public-key cryptography. (You can explore a basic overview of this concept here.) Today’s cryptographic standards remain robust, even against the mightiest traditional computers, due to constant updates that account for improved hardware. The RSA algorithm, for instance, is based on the difficulty of breaking down very large numbers into their prime factors. In 2007, to maintain security, recommendations shifted from using 300-digit numbers to those exceeding 600 digits, in response to growing computational capabilities.

However, quantum computing could render these techniques obsolete, warned Zygmunt Lozinski from IBM Research during his talk. “Imagine a fully functioning quantum computer—how would that reshape the security of our networks?”

Unlike classical machines, quantum computers process information in fundamentally different ways, enabling radically new methods for solving complex mathematical problems. In 1994, American mathematician Peter Shor developed an algorithm capable—at least theoretically—of dismantling the RSA system. “It’s still baffling how he did it,” said Lozinski. “He proposed that with a quantum computer, which was purely hypothetical back then, RSA could be cracked rapidly.”

While such quantum machines aren’t yet operational at that scale, the urgency to adapt our cybersecurity infrastructure is real. “Revamping systems and networks takes decades,” Lozinski emphasized. Moreover, information circulating on today’s networks is already vulnerable.

Even encrypted data can be intercepted now and stored until quantum decryption becomes viable—a tactic known as a harvest now – decrypt later attack. Lozinski illustrated this with examples like encrypted pharmaceutical data or engine designs, which might be worth fortunes if decrypted in the future by competitors.

While some data is intentionally public, we rely on cryptographic protections to ensure its authenticity. “If your property is listed in a digital registry secured by public-key encryption,” Lozinski said, “and someone alters that record, it’s catastrophic for you. Now imagine that happening on a large scale—it could disrupt entire infrastructures globally.”

Yet, there is hope. Mathematics may once again provide a path forward—this time in a form that even quantum computers may not be able to penetrate.

The promise of lattice-based cryptography

Systems like RSA and elliptic curve cryptography rely on what are called one-way functions: problems that are easy to compute but extremely difficult to reverse. RSA, for instance, encrypts data by multiplying two large primes—simple one way, but unraveling the result back into those primes is nearly impossible without special information.

To defend against quantum threats, we require a mathematical challenge that resists even quantum algorithms. The most promising direction currently involves lattices.

In a simple sense, a two-dimensional lattice resembles a grid of points on an endless sheet. In the mathematical realm, lattices expand into hundreds or even thousands of dimensions. (You can read about the basics of lattices here and explore higher dimensions here.) Lozinski likened this cryptographic method to searching for a needle in a haystack. The encrypted message gets embedded within a high-dimensional lattice—the “haystack”—making it incredibly difficult to locate without a special key. (More on lattice-based encryption can be found here.)

Lattice-based encryption is currently one of the most promising post-quantum solutions. Of the four algorithms being standardized by NIST (the U.S. National Institute of Standards and Technology), three are based on lattice techniques. (For technical documentation, visit NIST’s site, which also offers an accessible summary.) “Still, there are no absolute assurances,” cautioned Petros Wallden from the University of Edinburgh’s Quantum Software Lab. “Like classical methods, post-quantum systems must withstand rigorous testing.”

Building resilience through cryptographic adaptability

Our trust in traditional cryptographic methods like RSA grew because they were relentlessly challenged by experts. Despite increased computing capabilities, those systems held strong under scrutiny. “Achieving that same confidence in post-quantum encryption requires a similarly aggressive review by the cryptanalysis community,” Wallden stated during the event. “We need specialists who understand both quantum algorithms and advanced encryption.”

Yet such interdisciplinary experts remain rare. Many attendees hoped that this event—and the broader programme—would help attract more talent into the field. Not only is the work intellectually stimulating, but it also plays a vital role in shaping society’s digital future.

However, identifying suitable cryptographic solutions is only part of the equation. Updating global digital infrastructure is a long and intricate process. While the U.S. leads with strategic initiatives like those at NIST, European nations are preparing to begin similar efforts around 2026. In the UK, both Lozinski and Wallden are contributing to this transformation.

“Thankfully, there won’t be a single catastrophic ‘Q-Day’ when everything collapses,” Lozinski noted. Quantum computers capable of breaching today’s encryption may emerge over decades, and initially they’ll likely be reserved for specialized scientific tasks—like simulating chemical reactions in battery development or modeling protein folding. Still, it’s widely believed that quantum-capable codebreakers will appear eventually. “We need governments and industry to act now—before it’s too late.”

Lozinski stressed the importance of what he called cryptographic agility: “Think of it like changing the batteries in a flashlight or switching out headphones—we need modular, replaceable encryption tools built into our digital systems.” The shift to post-quantum cryptography marks not just a technical upgrade, but a change in mindset. As he put it, “The era of ‘set it and forget it’ encryption is over.”

About this article

This article draws on insights shared by Zygmunt Lozinski and Petros Wallden during the Quantum Computing: Applications and Challenges event. The session was part of the Quantum Information, Quantum Groups, and Operator Algebras programme hosted by the Isaac Newton Institute for Mathematical Sciences in Cambridge.

Zygmunt Lozinski is a Senior Technical Staff Member at IBM Research, where he is leading initiatives to secure global networks against quantum threats.

Petros Wallden serves as an associate professor within the Quantum Software Laboratory at the University of Edinburgh.

Rachel Thomas holds the position of Editor at Plus magazine.

This piece was developed through our partnership with the Isaac Newton Institute for Mathematical Sciences (INI), as well as the Newton Gateway to Mathematics.

Situated alongside us on the mathematics campus of the University of Cambridge, the INI is a globally recognized hub for mathematical research. The Newton Gateway functions as the outreach and application branch of the INI, fostering interaction between mathematicians and those who utilize mathematical methods.