How quantum computers can empower Shor's algorithm to break digital encryption

Explore a visual guide to how quantum computers can crack RSA encryption

In 1994, Peter Shor introduced an algorithm that showed a quantum computer could efficiently factor the product of two very large prime numbers, undermining the mathematics that makes RSA so secure. While using larger keys can delay the decryption time of quantum computers, this solution increases the time it takes to encrypt data, which may become impractical.

A mathematical breakdown of how RSA encryption uses prime numbers to encrypt data

This form of asymmetric cryptography uses mathematical functions that rely on the product of two large prime numbers. Because traditional computers struggle to factor such products, obtaining the private keys needed to decrypt messages becomes effectively impossible. This security can be reinforced with larger prime numbers, though this makes encryption more computationally taxing.

Quantum computers harness weird physics to explore unsolvable problems

Classical computers manipulate bits as either 0 or 1, but quantum computers use qubits to hold combinations of both, enabling new algorithms. This new approach could one day help with breakthroughs in medicine, chemistry, and AI.

The mathematics of quantum-based cryptography, and why existing data is already at risk

Seeing the potential of this technology, some governments and malicious actors are thought to have already started storing encrypted data, in the hopes that quantum computers within the next 10 to 20 years will be able to decrypt it. As of 2022, the National Institute of Standards and Technology had selected four algorithms for inclusion in a quantum-resistant encryption standard.

The Majorana 1 chip may provide quantum computing using geometry-based qubits

Traditional quantum computers are incredibly fragile, with encoded information easily disrupted and requiring significant error correction systems. Microsoft’s approach involves storing data on a surface, which is more stable, but involves an elusive particle first theorized in 1938.

Claude Shannon, for whom Anthropic's AI tools are named, proved the existence of an unbreakable cipher

In the one-time pad approach, the encryption key is randomly generated and of equal length to the plaintext. This randomness ensures that every possible plaintext is equally likely—RBBHN can mean HELLO, SOLVE, CODES, and so on, using a different key—while matching the message and key lengths prevents the appearance of patterns that can be exploited.

Watch how the Enigma machine encrypts messages and learn about its critical design flaw

Using settings selected from a series of rotors and a plugboard that let operators swap letters with any of their choosing, the machine lit up the output letter for each letter typed. While this system could generate messages requiring any of 150 quintillion potential keys, the machine's reflector never encrypted a letter as itself, providing an entry point for exploiting the system.

Google’s quantum computer completes a 10,000-year task in about 3 minutes

Google used its 53-qubit processor on an extremely difficult problem for traditional computers to simulate to showcase quantum supremacy. IBM later challenged Google’s claim by arguing that its Summit supercomputer could solve the same problem in just 2.5 days using a more efficient method.

Create your own cipher by combining mathematical operations and encryption protocols

This tool allows users to build an encryption workflow in which the output of one customizable function becomes the input to another, thereby creating undiscovered methods for obscuring information via a series of ciphers.

Visualize how passkeys, which rely on asymmetric cryptography to authenticate users, work

After using biometrics or a PIN to access the private key stored on a device, it is combined with a random number generated by the site to produce a cryptographic signature. This signature is verified using the site's public key, allowing a user to log in without entering a password. This reduces the risk of fraudulent messages—phishing attacks—and data breaches.

Understanding the Diffie-Hellman key exchange, an example of public key cryptography

Published in 1976 by Whitfield Diffie and Martin Hellman, the system involves two parties combining each of their unique private keys with a public key using a mathematical function. The combinations are exchanged and mixed to establish a common key that no third party can determine. The Diffie-Hellman system underlies many encryption protocols for internet traffic.

DNA computing allows for storage and processing of massive amounts of data

Although costly and less efficient for simpler tasks, as of 2025, DNA could hold 455 exabytes of data with near limitless parallel computation potential in small data centers. Every movie ever made would fit inside the volume of a single sugar cube.

Quantum mechanics-based technology may explain the Fermi paradox

It describes the discrepancy between the high likelihood of life beyond Earth given the vastness of the universe and the lack of evidence for such life, since extraterrestrial civilizations have not communicated with us. However, quantum communication—a more information-dense and effective method than classical means—requires massive receivers and very narrow signals, which would easily miss Earth, making a lack of signals expected.

The story of two female programmers running the simulations behind chaos theory's discovery

Margaret Hamilton and Ellen Fetter worked on MIT's 800-pound Royal McBee LGP-30 computer, which was fed binary code on paper tape to perform computations. Among the computations performed were those involving equations describing the motion of gas in a circulating fluid for Edward Lorenz, widely considered the father of chaos theory.

Traffic flow can be improved through research into card shuffling

Card-shuffling mathematics has been applied to solving problems in biology to estimate the evolutionary distance between organisms and in computer science to determine the optimal distribution of files and folders in databases.

The first algorithmic random number generator was developed in 1946

Although previous methods of randomness involved physical tools with limited outcomes, such as dice, or relied on chaotic variables for number generation, such as electronic noise, John Von Neumann's middle-square method turned the problem into a mathematical computation. It has since been replaced by methods that generate numbers from unique initial values, such as the time on a clock.

There are more chess game variations than observable atoms in the universe

Mathematician Claude Shannon estimated there are 10 to the 120th power variations of chess games possible. Known as the "Shannon number," this is more than the estimated number of atoms in the cosmos.

Binary mathematics represented as switches allows silicon rocks to do math

Each switch is assigned a zero or a one based on whether it is open or closed, and logic gates are built from these switches that let the system perform mathematical operations. Modern software builds upon these operations to perform increasingly complex tasks.

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

Mathematical breakthroughs influenced Shakespeare’s stories

New ideas in math were transforming Europe at the time Shakespeare penned his plays, including newly popular conceptions of zero via philosophers Descartes and Leibniz.

A 14-year-old "human calculator" shatters six mathematical world records in one day

A teenage prodigy from Maharashtra, India named Aaryan Shukla set the record for the fastest time to mentally add 50 five-digit numbers. He did so in just 25.19 seconds–roughly equivalent to one addition every 0.5 seconds. The math whiz said he practices calculations for around five to six hours a day.

Moore's Law came from observing exponential computing growth in the 1960s

In 1965, Gordon Moore, cofounder of Intel Corporation, observed a four-year trend of constant growth rate in computing power. Hypothesizing the trend would continue, his observation became the benchmark that the computing industry has worked to maintain for 60 years.

Proof-of-work is the original way cryptocurrencies added new blocks to blockchains

It’s a competitive method requiring “miners” to solve cryptographic puzzles, often using equipment that consumes massive amounts of energy. Ethereum switched to proof-of-stake, a less energy-intensive method in which “validators” stake crypto to be randomly chosen to check transactions.

The fast Fourier transform breaks down wave signals into discrete components

The algorithm was initially discovered by German mathematician Carl Friedrich Gauss in 1805, but his notes were not found until after his death. Today, FFTs form the basis for most compression software in media and are essential to technologies such as radar, sonar, and telecommunications.

It took 70 years for computer scientists to determine how to cut a cake fairly

The cake-cutting problem explores how to divide something fairly, which is not solely about cutting evenly-sized pieces. A protocol that accounted for personal preferences (e.g., a corner piece) between just three people took 16 years to develop.

Explaining how open source systems like Linux can be secure, despite their public source code

While no computer system is immune to all cyberattacks and malware, the transparency of open-source technology means many thousands of developers can review and oversee the underlying code powering the software on an ongoing basis. This increases the likelihood of catching and patching vulnerabilities more quickly than smaller groups of cybercriminals looking to exploit them.

Watch how algorithms can be designed to train themselves and self-improve without human input, to the point where the optimized code is too complex for programmers to understand.

Radioactive elements can introduce software errors because the ionizing radiation they produce can detach electrons from atoms, and computer code relies on the distribution of electrons.

Elk Cloner, the first computer virus to spread in public, was written as a practical joke by Richard Skrenta, a Pittsburgh high school student.

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

Electrical grids worldwide must double their power delivery capacity by 2050 to meet surging demand from AI and electric vehicles.

According to the physics of black holes, our 4D reality may be a hologram—a projection of information coded on a 2D surface on the edge of the universe.

How fusion—which releases energy when two lighter atoms combine to form a heavier atom—differs from fission

Search a massive database of over 4 decades of clues from the TV quiz show 'Jeopardy!'

In 2025, four executives from large tech companies were given positions in the US Army Reserves—including Palantir Chief Technology Officer Shyam Sankar, which reinforced Palantir's ties with the US military and its role as a leading defense partner.

Art theft is the third-largest source of criminal revenues worldwide, thanks in part to the subjective nature of valuing a work of art.

Memecoins are a type of cryptocurrency—a form of digital currency with a wide variety of uses—created around popular 'memes,' or viral internet jokes.

Gerrymandering works through two techniques: cracking opposing voters across districts to dilute their power, and packing them into a few to waste their votes in lopsided majorities.

Learn how monoclonal antibodies, which mimic the body's antibodies, can fight diseases like Ebola.

The Nasdaq's 'Magnificent 7' companies are responsible for roughly 40% of the Nasdaq 100 index's gains, while the remaining 93 companies account for the other 60%.

Alzheimer's can lead to brain shrinkage, with an average of around 2% of volume reduction per year

Scientists can determine Earth's past climate conditions by analyzing air trapped in microscopic bubbles within ice cores—columns of compressed snow layers that build up over hundreds of thousands of years.

Fish populations in the Great Barrier Reef have increased after installing waterproof speakers on the ocean floor that played recordings of sounds from healthy coral reefs.

Calculate how much of your tax dollars go to each federal program based on your income, filing status, and number of children

The rivalry between Alexander Hamilton and Thomas Jefferson centered on federalism—the question of how much power the federal government should hold relative to the states.

Explore fun facts from the USPS, including unique post office buildings, a stamp that traveled past Pluto, and more.

US intelligence allegedly pursued more than 600 schemes to assassinate Cuban revolutionary Fidel Castro.

'Shogun,' a 1980s TV series, helped popularize sushi in the US by stimulating an American interest in Japanese culture.