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

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.

The science of cryptography, including methods to encrypt data and how to break encryption

Monoalphabetic ciphers use a set of rules to replace each letter with another consistently, making them susceptible to brute force attacks that try every kind of replacement. While more complex ciphers can transform text in less obvious ways, because certain letters are used more often than others, an analysis of letter frequency may reveal patterns that help uncover the rules that make up a cipher.

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.

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.

The history and operation of SIGABA, the US counterpart of the Nazi Enigma machine

Developed by the US Army and US Navy, over 10,000 of these machines were deployed by the end of World War II to encrypt messages for the armed forces using three series of rotors. The device would continue to be used until the 1950s, while personal computers were shown to possess enough computing power to crack it by 2021.

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.

How end-to-end encryption protects messages, even from service providers

Using symmetric and asymmetric cryptography, data is encrypted on the sender's device before being transmitted across application servers that lack the key needed to decrypt it. The message is not decrypted until it reaches the recipient's device, which uses their private key to recover the plaintext. E2EE's effectiveness has led to its adoption by WhatsApp and Signal.

How the NSA has changed through history

The National Security Agency was born in the Cold War and then transformed by 9/11. This article answers all the basic questions you might have about the NSA, from what it does to how much data it collects to some of its useful intercepts.

The story of Kryptos, the long unsolved cryptographic sculpture outside the CIA's headquarters

Made by American artist Jim Sanborn, the sculpture features four copper plates engraved with messages written with the 26 letters of the Latin alphabet and question marks. The last of these plates was solved in 2025, but the piece remains of interest to cryptoanalysts.

How hash functions encrypt stored passwords and can be enhanced with 'salt'

Hash functions convert text into unique, random sets of characters, a process that is computationally expensive and time-consuming to undo. Because hashed outputs for many common passwords are publicly listed, some sites use a salt—additional characters appended to a password—before hashing to produce an output that is not known. When entering a password, it is salted and hashed, then checked against the database for a matching hash before permitting login.

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.

Venture firm a16z's crypto canon

Andreessen Horowitz (a16z) is a leading venture capital firm with deep expertise in cryptocurrency and blockchain technology. For 10 years, the firm has built its internal knowledge in the area, and archived a wide range of explainers exploring everything from fundamentals to emerging crypto trends, and much more.

View a timeline of AI deployments from 2017 to 2025

The development of transformer architecture and the release of GPTs across AI labs led to rapid changes in LLM scale and power. Companies like OpenAI, Google, Meta, Microsoft, and Anthropic have invested billions of dollars to develop reliable, versatile models.

The $1 bill hasn’t been redesigned in over 60 years

From a counterfeiting and forgery perspective, this makes the $1 bill one of the least secure American banknotes. In this video, the Wall Street Journal sits down with a leading currency expert to explore the techniques used to keep cash safe and figure out what's going on with the $1 bill.

NATO leads cyber war games in Estonia

Estonia is host to one of the world’s largest annual interactive cybersecurity drills. Russia is always considered the main threat, but this year, the war in Ukraine has only added to the stakes.

See how computer memory really works—from binary bits to modern RAM

The video explains how computers store information as 1s and 0s, how RAM functions as fast working memory, and why systems utilize different types of storage. The video demonstrates how this process enables computers to operate.

In 2019, Congress passed the Secure Act to reform key aspects of the US tax code

Key Secure Act provisions included raising the age at which mandatory distributions take effect (to increase saving), allowing larger catch-up contributions for older individuals, and allowing employers to directly match contributions in a Roth 401(k).

Go behind the scenes of Air Force One

ABC News takes viewers inside Air Force One, revealing how the president's plane operates as a secure command center in the sky. Explore the logistics and coordination that go into every presidential flight.

How we helped make Aedes aegypti mosquitoes such a problem

Mosquito genome sequencing data suggests that Aedes aegypti mosquitoes first started specializing on human blood around 5,000 years ago—when climates shifted and humans started domesticating plants in Africa and stored large amounts of water that may have attracted the bugs.

EOS and maximum length tokens tell an LLM when to stop generating a response

Tokens are words or subwords (e.g., prefixes) that a large language model processes to generate a response. During training, the model is taught that if it ever generates a special token called end-of-sequence, its response is complete.

How tPA, which helps dissolve blood clots, can lessen the severity of a stroke

One of the most exciting recent advances in treating stroke is a medication known as tissue plasminogen activator, or tPA. It is only effective for use in some ischemic strokes, and it must be delivered within 4.5 hours of symptom onset to have a chance at working.

There are 6 essential steps in cheesemaking

The six basic steps that are required to turn milk into cheese start with acidification and end with ripening (aka aging). This guide explains what happens at each step and how it contributes to the finished product.

The transatlantic cable allowed for communications between North America and Europe

It had significant impacts on just about every industry, including finance. Specifically, the transatlantic cable made it so that real-time financial transactions could take place across the Atlantic, and allowed for much faster sharing of information that increased global market accuracy.

View a breakdown of the mathematics behind the Standard Model

The Lagrangian version of the theory—related to the system's energy—presents a vast mathematical equation, with different components representing various force interactions and types of particles, including ghost particles to cancel out mathematical redundancies.

The US lags behind other developed countries in math and science scores

The Programme for International Student Assessment, administered every three years by the OECD to 15-year-olds, scores US students below the OECD average in math (465 vs. 472) and only slightly above average in science (499 vs. 485). These figures place US pupils in the lower half of developed nations.

The American Society of Civil Engineers' infrastructure report card gave the US a C in 2025, its highest grade since the project launched in 1998.

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.

While atoms are normally made of protons, neutrons, and electrons, exotic ones have been built with antimatter—alternate versions of normal matter that live for fractions of a second and are about a billion times as rare.

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

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

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.

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

The term 'algorithm' originated from the Latinized name of al-Khwārizmī, a 9th-century mathematician whose works introduced Arabic numerals and the decimal-based numeral system to Europe and whose treatise 'Al-Jabr' gave algebra its name.

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

While the first exchange-traded fund (a 'basket' of different assets that can be bought and sold on a stock exchange) in the US only launched in 1993, the global ETF market has grown to more than $10T in the short time since.

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.

The idea for the Federal Reserve was conceived in secret in 1910—with bankers donning duck hunt gear for disguise while traveling to a remote country club on Georgia's Jekyll Island

Ebola infects and disables immune cells, triggering a cascade of events that leads to small blood clots throughout the body, weakening blood vessels and interrupting blood flow to key organs.

The US Constitution is widely regarded as the longest-standing written national constitution still in force—see how it has influenced rights worldwide.

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.

For centuries, it was common to sleep in two shifts: a few hours at the beginning of the night, and a longer period beginning around midnight

Sony set the standard for cylinder-shaped batteries when it repurposed manufacturing equipment used to make rolls of magnetic recording tape.

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

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.

In 1984, Operation Smash Hit intentionally crashed a 239-ton train into a nuclear waste canister at 100 miles per hour to prove the canister's safety, which remained completely intact and lost just 0.29 of its 100 pounds of pressure.

The first image of a black hole was captured by creating an Earth-sized virtual observatory from a network of eight radio telescopes.

The word 'jazz' evolved from 'jasm,' 19th-century American slang for 'energy'

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.

In 1945, Surrealist artist Salvador Dalí and legendary animator Walt Disney began collaborating on a short film that was not completed until 2003, years after both men had died.

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