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

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.

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

Secure communications largely rely on numeric keys generated by multiplying two enormous prime numbers together, and it is computationally impractical to determine these primes by trying to divide by every possible one. While Shor's algorithm can provide better guesses for this brute-force approach, it relies on a number that is difficult to determine on classical computers but much easier to calculate using the simultaneous computations enabled by quantum superposition.

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.

Quantum computers use qubits to solve problems much faster than classical machines

Unlike regular computers, where each bit is either 0 or 1, quantum computers use qubits, which can simultaneously be both—allowing for massive parallel processing power. Google’s quantum processor once solved a problem in seconds that would have taken a supercomputer 47 years.

Noise and instability made quantum computing seem out of reach for decades

Recent advances in error suppression, mitigation, and correction are allowing quantum computers to perform practical tasks that challenge classical machines. IBM’s 2016 launch of its first cloud-accessible quantum computer attracted over 22,000 users in its first month alone.

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.

View how AES—the global standard for symmetric encryption—works

Established by the National Institute of Standards and Technology in 2001, the Advanced Encryption Standard transforms plaintext into ciphertext using multiple rounds of processing, including substitution, transposition, and mixing. Larger keys undergo more rounds to produce 16-byte blocks of scrambled data, with 256-bit AES keys taking 3.31 × 10⁵⁶ years to decrypt via brute force.

Quantum physics explained in 22 minutes

Brian Cox, Royal Society Professor for Public Engagement in Science, discusses the fundamental principles of quantum mechanics, emphasizing their importance in understanding the nature of reality and their practical applications in emerging technologies like quantum computers.

A visual guide to how bitcoin transactions work and rely on cryptography

The "crypto-" in cryptocurrencies like bitcoin refers to the mathematical functions that generate pairs of public and private keys and encrypt data in blocks. When combined, these systems secure transactions on the network, verify digital asset and token transfers, and contribute to end-user anonymity.

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.

Watch a cybersecurity expert answers questions about hacking

From firewalls and VPNs to ransomware and viruses, IBM Distinguished Engineer Jeff Crume has seen many changes in cybersecurity during his 40 years of IT experience. In this video, he explores some of the most significant hacking events in history and provides advice on protecting yourself online.

Visualize how data becomes organized through a variety of sorting algorithms

This interactive shows how different algorithms shift elements in a randomized set to order them from smallest to largest. By comparing the different procedures and their corresponding functions, users can explore how runtimes vary across algorithms that complete the same task.

Passkeys, a new authentication method, aim to replace traditional passwords

Passkeys use cryptography keys to secure logins without passwords, resisting phishing and risks from data breaches. The FIDO Alliance developed passkeys as a combination of public and private keys for authentication.

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.

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.

The US Navy used The 'Harvard Calculator' to solve advanced physics problems

Designed in 1937 by Harvard graduate student Howard H. Aiken, the IBM Mark I was a groundbreaking machine used to solve ballistic trajectories and other mathematical problems whose solutions were needed for the design of the atomic bomb in World War II. The device was one of the first mechanical computers.

Explore this deep dive into how SSRIs work

This 101-style explainer on selective serotonin reuptake inhibitors explains how they work in the brain—complete with classroom-style whiteboard drawings. It covers common SSRIs, why someone might try this medication, and a deeper discussion about potential side effects.

National Security Agency whistleblower Edward Snowden once leaked documents suggesting Palantir had a role in alleged surveillance

After releasing documents detailing an NSA surveillance scheme named PRISM (which is also the name of a Palantir service), further documents show that Palantir's software enabled the expansion of the NSA's widest-reaching data programs, XKEYSCORE. Palantir has frequently denied claims of supporting government surveillance and has insisted that its software is designed to maintain "civil liberties," such as privacy.

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.

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.

Einstein warned the president that splitting atoms could lead to powerful bombs

In a 1939 letter to Franklin D. Roosevelt, Albert Einstein explained that nuclear fission could produce immense energy—and devastating weapons. The warning helped spur the Manhattan Project, a role Einstein later deeply regretted.

How the National Science Foundation supports the US economy

The NSF has filled funding gaps in the research and development of products developed in the private sector, particularly when the research requires more than three years to complete. These investments, including in startups such as Qualcomm and Symantec, have supported job creation, generated economic returns, and helped build the technologies many industries rely upon, such as the internet.

The foundation for computer viruses was published after its creator's death

In the late 1940s, Hungarian American mathematician, scientist, and engineer John von Neumann gave a series of lectures where he explained the theoretical framework for a computer program that could replicate itself—the von Neumann Universal Constructor. His lectures were later compiled and published in 1966, nine years after his death from cancer.

Watch a crystal undergo X-ray diffraction to determine its internal geometry

In the early days of X-ray crystallography, getting photos of a single sample could take dozens of hours, followed by months of mathematical analysis. Today, automation and computer software can complete such tasks in a few hours.

Visualize how CRISPR-Cas9—a type of immune system used by single-celled organisms to attack invasive viruses—targets and makes precise changes to a gene's DNA.

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

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.

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.

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.

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.

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.

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

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

When you complete a CAPTCHA on a website to prove you are human, you may be unknowingly training algorithms for self-driving cars, whose systems require training data to help identify crosswalks, bicycles, and other outdoor objects.

SpaceX's S-1 or 'prospectus' revealed many previously unknown details about the company, including its unprofitability despite doing $18.7B in revenue in 2025, exactly how many voting shares Elon Musk will have in the company (roughly 85%), and more.

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

Visualize the path of every solar eclipse from 1900 to 2099 and see what each looks like when observed from different locations on Earth.

Waves off the coast of Nazaré, Portugal, can reach over 100 feet and are caused by the area's deep underwater canyon geography

Fireworks make a loud booming sound after exploding due to air expanding faster than the speed of sound.

Some coin denominations have ridges etched on their sides, partly to prevent counterfeiting, in a practice called 'reeding.'

Warren Buffett's former professor Benjamin Graham is known as the 'father of value investing,' a strategy in which investors seek to buy stocks trading below their intrinsic worth.

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

Some renewable energy sources may weaken the resiliency of electric grids by removing outage buffers provided by coal- and natural gas-fired plants, which provide the system with more time to find a new power source if a plant goes down.

Trace how the Bill of Rights, inspired by centuries of political theory, took shape between 1774 and 1789.

In recent years a child anxiety expert has created and tested a novel phobia and anxiety treatment approach for children, focused on changing how parents respond to the fears.

During the French Revolution, a botanist's letter asking about "dear Rhus" (poison ivy) was intercepted, leading authorities to suspect he was conspiring with the Russians.

The first steps to rebuilding your credit score include getting to know exactly what's on your credit report and figuring out how far you are from the '700 club,' or 'good score' range.

The animatronic shark from Steven Spielberg's 'Jaws,' the first modern blockbuster, was a complex underwater apparatus called 'Bruce.'

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.