Close Menu
Technology Mag

    Subscribe to Updates

    Get the latest creative news from FooBar about art, design and business.

    What's Hot

    TikTok’s ‘ban’ problem could end soon with a new app and a sale

    July 6, 2025

    How to watch Summer Games Done Quick 2025

    July 6, 2025

    The Verge’s summer “in” and “out” list

    July 6, 2025
    Facebook X (Twitter) Instagram
    Subscribe
    Technology Mag
    Facebook X (Twitter) Instagram YouTube
    • Home
    • News
    • Business
    • Games
    • Gear
    • Reviews
    • Science
    • Security
    • Trending
    • Press Release
    Technology Mag
    Home » The Simple Math Behind Public Key Cryptography
    Security

    The Simple Math Behind Public Key Cryptography

    News RoomBy News RoomDecember 17, 20243 Mins Read
    Facebook Twitter Pinterest LinkedIn Reddit WhatsApp Email

    The original version of this story appeared in Quanta Magazine.

    For thousands of years, if you wanted to send a secret message, there was basically one way to do it. You’d scramble the message using a special rule, known only to you and your intended audience. This rule acted like the key to a lock. If you had the key, you could unscramble the message; otherwise, you’d need to pick the lock. Some locks are so effective they can never be picked, even with infinite time and resources. But even those schemes suffer from the same Achilles’ heel that plagues all such encryption systems: How do you get that key into the right hands while keeping it out of the wrong ones?

    The counterintuitive solution, known as public key cryptography, relies not on keeping a key secret but rather on making it widely available. The trick is to also use a second key that you never share with anyone, even the person you’re communicating with. It’s only by using this combination of two keys—one public, one private—that someone can both scramble and unscramble a message.

    To understand how this works, it’s easier to think of the “keys” not as objects that fit into a lock, but as two complementary ingredients in an invisible ink. The first ingredient makes messages disappear, and the second makes them reappear. If a spy named Boris wants to send his counterpart Natasha a secret message, he writes a message and then uses the first ingredient to render it invisible on the page. (This is easy for him to do: Natasha has published an easy and well-known formula for disappearing ink.) When Natasha receives the paper in the mail, she applies the second ingredient that makes Boris’ message reappear.

    In this scheme, anyone can make messages invisible, but only Natasha can make them visible again. And because she never shares the formula for the second ingredient with anyone—not even Boris—she can be sure the message hasn’t been deciphered along the way. When Boris wants to receive secret messages, he simply adopts the same procedure: He publishes an easy recipe for making messages disappear (that Natasha or anyone else can use), while keeping another one just for himself that makes them reappear.

    In public key cryptography, the “public” and “private” keys work just like the first and second ingredients in this special invisible ink: One encrypts messages, the other decrypts them. But instead of using chemicals, public key cryptography uses mathematical puzzles called trapdoor functions. These functions are easy to compute in one direction and extremely difficult to reverse. But they also contain “trapdoors,” pieces of information that, if known, make the functions trivially easy to compute in both directions.

    One common trapdoor function involves multiplying two large prime numbers, an easy operation to perform. But reversing it—that is, starting with the product and finding each prime factor—is computationally impractical. To make a public key, start with two large prime numbers. These are your trapdoors. Multiply the two numbers together, then perform some additional mathematical operations. This public key can now encrypt messages. To decrypt them, you’ll need the corresponding private key, which contains the prime factors—the necessary trapdoors. With those numbers, it’s easy to decrypt the message. Keep those two prime factors secret, and the message will stay secret.

    Share. Facebook Twitter Pinterest LinkedIn WhatsApp Reddit Email
    Previous ArticleThe Best Humidifiers for Home and Away
    Next Article The Honda Prelude returns as a sporty hybrid with a new drive mode

    Related Posts

    The Promise and Peril of Digital Security in the Age of Dictatorship

    July 5, 2025

    Identities of More Than 80 Americans Stolen for North Korean IT Worker Scams

    July 3, 2025

    A Group of Young Cybercriminals Poses the ‘Most Imminent Threat’ of Cyberattacks Right Now

    July 3, 2025

    How to Protest Safely in the Age of Surveillance

    July 3, 2025

    US Supreme Court Upholds Texas Porn ID Law

    July 3, 2025

    ICE Rolls Facial Recognition Tools Out to Officers’ Phones

    July 3, 2025
    Our Picks

    How to watch Summer Games Done Quick 2025

    July 6, 2025

    The Verge’s summer “in” and “out” list

    July 6, 2025

    GM’s Cruise Cars Are Back on the Road in Three US States—But Not for Ride-Hailing

    July 6, 2025

    Lenovo Chromebook Plus 14 review: the new king of Chromebooks

    July 6, 2025
    • Facebook
    • Twitter
    • Pinterest
    • Instagram
    • YouTube
    • Vimeo
    Don't Miss
    Gear

    How to Use Voice Typing on Your Phone

    By News RoomJuly 6, 2025

    Tap the small “i” icon on the left of the toolbar if you need more…

    How to Travel to the Most Remote Office on Earth

    July 6, 2025

    With RFK Jr. in Charge, Insurers Aren’t Saying If They’ll Cover Vaccines for Kids If Government Stops Recommending Them

    July 5, 2025

    I’m an Outdoor Writer. I’m Shopping These 55 Deals From REI’s 4th of July Sale

    July 5, 2025
    Facebook X (Twitter) Instagram Pinterest
    • Privacy Policy
    • Terms of use
    • Advertise
    • Contact
    © 2025 Technology Mag. All Rights Reserved.

    Type above and press Enter to search. Press Esc to cancel.