The Times Australia
The Times World News

.
The Times Real Estate

.

Mind-bending maths could stop quantum hackers, but few understand it

  • Written by Nalini Joshi, Professor of Mathematics, University of Sydney
Mind-bending maths could stop quantum hackers, but few understand it

Imagine the tap of a card that bought you a cup of coffee this morning also let a hacker halfway across the world access your bank account and buy themselves whatever they liked. Now imagine it wasn’t a one-off glitch, but it happened all the time: imagine the locks that secure our electronic data suddenly stopped working.

This is not a science fiction scenario. It may well become a reality when sufficiently powerful quantum computers come online. These devices will use the strange properties of the quantum world to untangle secrets that would take ordinary computers more than a lifetime to decipher.

We don’t know when this will happen. However, many people and organisations are already concerned about so-called “harvest now, decrypt later[1]” attacks, in which cybercriminals or other adversaries steal encrypted data now and store it away for the day when they can decrypt it with a quantum computer.

As the advent of quantum computers grows closer, cryptographers are trying to devise new mathematical schemes to secure data against their hypothetical attacks. The mathematics involved is highly complex – but the survival of our digital world may depend on it.

‘Quantum-proof’ encryption

The task of cracking much current online security boils down to the mathematical problem of finding two numbers that, when multiplied together, produce a third number. You can think of this third number as a key that unlocks the secret information. As this number gets bigger, the amount of time it takes an ordinary computer to solve the problem becomes longer than our lifetimes.

Future quantum computers, however, should be able to crack these codes much more quickly. So the race is on to find new encryption algorithms that can stand up to a quantum attack.

The US National Institute of Standards and Technology has been calling for[2] proposed “quantum-proof” encryption algorithms for years, but so far few have withstood scrutiny. (One proposed algorithm, called Supersingular Isogeny Key Encapsulation[3], was dramatically broken[4] in 2022 with the aid of Australian mathematical software called Magma, developed at the University of Sydney.)

Photo of the elaborate copper pipe cooling system of a quantum computer.
As quantum computers advance, encryption methods will need to keep up. Hans Pennink / AP[5]

The race has been hotting up this year. In February, Apple updated[6] the security system for the iMessage platform to protect data that may be harvested for a post-quantum future.

Two weeks ago, scientists in China announced they had installed[7] a new “encryption shield” to protect the Origin Wukong[8] quantum computer from quantum attacks.

Around the same time, cryptographer Yilei Chen announced[9] he had found a way quantum computers could attack an important class of algorithms based on the mathematics of lattices, which were considered some of the hardest to break. Lattice-based methods are part of Apple’s new iMessage security, as well as two of the three frontrunners[10] for a standard post-quantum encryption algorithm.

What is a lattice-based algorithm?

A lattice is an arrangement of points in a repeating structure, like the corners of tiles in a bathroom or the atoms in a diamond crystal. The tiles are two dimensional and the atoms in diamond are three dimensional, but mathematically we can make lattices with many more dimensions.

Most lattice-based cryptography is based on a seemingly simple question: if you hide a secret point in such a lattice, how long will it take someone else to find the secret location starting from some other point? This game of hide and seek can underpin many ways to make data more secure.

A variant of the lattice problem called “learning with errors” is considered to be too hard to break even on a quantum computer. As the size of the lattice grows, the amount of time it takes to solve is believed to increase exponentially, even for a quantum computer.

Read more: Has a mathematician solved the 'invariant subspace problem'? And what does that even mean?[11]

The lattice problem – like the problem of finding the factors of a large number on which so much current encryption depends – is closely related to a deep open problem in mathematics called the “hidden subgroup problem[12]”.

Yilei Chen’s approach suggested quantum computers may be able to solve lattice-based problems more quickly under certain conditions. Experts scrambled to check his results – and rapidly found an error[13]. After the error was discovered, Chen published an updated version of his paper describing the flaw.

Despite this discovery, Chen’s paper has made many cryptographers less confident in the security of lattice-based methods. Some are still assessing[14] whether Chen’s ideas can be extended to new pathways for attacking these methods.

More mathematics required

Chen’s paper set off a storm in the small community of cryptographers who are equipped to understand it. However, it received almost no attention in the wider world – perhaps because so few people understand this kind of work or its implications.

Last year, when the Australian government published a national quantum strategy[15] to make the country “a leader of the global quantum industry” where “quantum technologies are integral to a prosperous, fair and inclusive Australia”, there was an important omission: it didn’t mention mathematics at all.

Read more: What is quantum advantage? A quantum computing scientist explains an approaching milestone marking the arrival of extremely powerful computers[16]

Australia does have many leading experts in quantum computing and quantum information science. However, making the most of quantum computers – and defending against them – will require deep mathematical training to produce new knowledge and research.

References

  1. ^ harvest now, decrypt later (www.securityweek.com)
  2. ^ calling for (csrc.nist.gov)
  3. ^ Supersingular Isogeny Key Encapsulation (sike.org)
  4. ^ dramatically broken (mathematical-research-institute.sydney.edu.au)
  5. ^ Hans Pennink / AP (photos.aap.com.au)
  6. ^ updated (security.apple.com)
  7. ^ installed (www.scmp.com)
  8. ^ Origin Wukong (thequantuminsider.com)
  9. ^ announced (eprint.iacr.org)
  10. ^ two of the three frontrunners (csrc.nist.gov)
  11. ^ Has a mathematician solved the 'invariant subspace problem'? And what does that even mean? (theconversation.com)
  12. ^ hidden subgroup problem (www.ams.org)
  13. ^ found an error (crypto.stackexchange.com)
  14. ^ still assessing (crypto.stackexchange.com)
  15. ^ national quantum strategy (www.industry.gov.au)
  16. ^ What is quantum advantage? A quantum computing scientist explains an approaching milestone marking the arrival of extremely powerful computers (theconversation.com)

Read more https://theconversation.com/mind-bending-maths-could-stop-quantum-hackers-but-few-understand-it-228191

The Times Features

How to Protect Your Garden Trees from Wind Damage in Australia

In Australia's expansive landscape, garden trees hold noteworthy significance. They not only enhance the aesthetic appeal of our homes but also play an integral role in the local...

Brisbane Homeowners Warned: Non-Compliant Flexible Hoses Pose High Flood Risk

As a homeowner in Brisbane, when you think of the potential for flood damage to your home, you probably think of weather events. But you should know that there may be a tickin...

Argan Oil-Infused Moroccanoil Shampoo: Nourish and Revitalize Your Hair

Are you ready to transform your hair from dull and lifeless to vibrant and full of life? Look no further than the luxurious embrace of Argan Oil-Infused Moroccanoil Shampoo! In a...

Building A Strong Foundation For Any Structure

Building a home or commercial building can be very exciting. The possibilities are endless and the future is interesting. You can always change aspects of the building to meet the ...

The Role of a Family Dentist: Why Every Household Needs One

source A family dentist isn’t like your regular dentist who may specialise in a particular age group and whom you visit only when something goes wrong. A family dentist takes proa...

Benefits of Getting an Online Medical Certificate

Everyone has experienced it. Rather than taking a break, you drag yourself to the doctor's office, where you have to wait in lengthy lines, and then you have to hurry to get that...

Times Magazine

"Eternal Nurture" by Cara Barilla: A Timeless Collection of Wisdom and Healing

Renowned Sydney-born author and educator Cara Barilla has released her latest book, Eternal Nurture, a profound collection of inspirational quotes designed to support mindfulness, emotional healing, and personal growth. With a deep commitment to ...

How AI-Driven SEO Enhancements Can Improve Headless CMS Content Visibility

Whereas SEO (search engine optimization) is critical in the digital landscape for making connections to content, much of it is still done manually keyword research, metatags, final tweaks at publication requiring a human element that takes extensiv...

Crypto Expert John Fenga Reveals How Blockchain is Revolutionising Charity

One of the most persistent challenges in the charity sector is trust. Donors often wonder whether their contributions are being used effectively or if overhead costs consume a significant portion. Traditional fundraising methods can be opaque, with...

Navigating Parenting Arrangements in Australia: A Legal Guide for Parents

Understanding Parenting Arrangements in Australia. Child custody disputes are often one of the most emotionally charged aspects of separation or divorce. Parents naturally want what is best for their children, but the legal process of determining ...

Blocky Adventures: A Minecraft Movie Celebration for Your Wrist

The Minecraft movie is almost here—and it’s time to get excited! With the film set to hit theaters on April 4, 2025, fans have a brand-new reason to celebrate. To honor the upcoming blockbuster, watchfaces.co has released a special Minecraft-inspir...

The Ultimate Guide to Apple Watch Faces & Trending Wallpapers

In today’s digital world, personalization is everything. Your smartwatch isn’t just a timepiece—it’s an extension of your style. Thanks to innovative third-party developers, customizing your Apple Watch has reached new heights with stunning designs...

LayBy Shopping