The unique model of this story appeared in Quanta Magazine.
For hundreds of years, in case you needed to ship a secret message, there was principally one strategy to do it. You’d scramble the message utilizing a particular rule, identified solely to you and your supposed viewers. This rule acted like the important thing to a lock. When you had the important thing, you can unscramble the message; in any other case, you’d want to choose the lock. Some locks are so efficient they’ll by no means be picked, even with infinite time and sources. However even these schemes undergo from the identical Achilles’ heel that plagues all such encryption programs: How do you get that key into the appropriate arms whereas holding it out of the improper ones?
The counterintuitive resolution, often known as public key cryptography, depends not on holding a key secret however reasonably on making it broadly out there. The trick is to additionally use a second key that you just by no means share with anybody, even the individual you’re speaking with. It’s solely through the use of this mix of two keys—one public, one personal—that somebody can each scramble and unscramble a message.
To grasp how this works, it’s simpler to consider the “keys” not as objects that match right into a lock, however as two complementary elements in an invisible ink. The primary ingredient makes messages disappear, and the second makes them reappear. If a spy named Boris needs to ship his counterpart Natasha a secret message, he writes a message after which makes use of the primary ingredient to render it invisible on the web page. (That is simple for him to do: Natasha has revealed a straightforward and well-known components for disappearing ink.) When Natasha receives the paper within the mail, she applies the second ingredient that makes Boris’ message reappear.
On this scheme, anybody could make messages invisible, however solely Natasha could make them seen once more. And since she by no means shares the components for the second ingredient with anybody—not even Boris—she might be certain the message hasn’t been deciphered alongside the way in which. When Boris needs to obtain secret messages, he merely adopts the identical process: He publishes a straightforward recipe for making messages disappear (that Natasha or anybody else can use), whereas holding one other one only for himself that makes them reappear.
In public key cryptography, the “public” and “personal” keys work identical to the primary and second elements on this particular invisible ink: One encrypts messages, the opposite decrypts them. However as a substitute of utilizing chemical compounds, public key cryptography makes use of mathematical puzzles referred to as trapdoor functions. These features are simple to compute in a single route and very tough to reverse. However in addition they comprise “trapdoors,” items of data that, if identified, make the features trivially simple to compute in each instructions.
One frequent trapdoor perform entails multiplying two giant prime numbers, a straightforward operation to carry out. However reversing it—that’s, beginning with the product and discovering every prime issue—is computationally impractical. To make a public key, begin with two giant prime numbers. These are your trapdoors. Multiply the 2 numbers collectively, then carry out some further mathematical operations. This public key can now encrypt messages. To decrypt them, you’ll want the corresponding personal key, which incorporates the prime elements—the mandatory trapdoors. With these numbers, it’s simple to decrypt the message. Maintain these two prime elements secret, and the message will keep secret.
