The unique model of this story appeared in Quanta Magazine.
For hundreds of years, if you happen to wished to ship a secret message, there was mainly one technique to do it. You’d scramble the message utilizing a particular rule, identified solely to you and your meant viewers. This rule acted like the important thing to a lock. In the event you had the important thing, you may 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 assets. However even these schemes endure from the identical Achilles’ heel that plagues all such encryption programs: How do you get that key into the precise palms whereas protecting it out of the improper ones?
The counterintuitive answer, generally known as public key cryptography, depends not on protecting a key secret however slightly on making it extensively accessible. The trick is to additionally use a second key that you simply by no means share with anybody, even the particular person you’re speaking with. It’s solely through the use of this mixture of two keys—one public, one non-public—that somebody can each scramble and unscramble a message.
To grasp how this works, it’s simpler to think about the “keys” not as objects that match right into a lock, however as two complementary components in an invisible ink. The primary ingredient makes messages disappear, and the second makes them reappear. If a spy named Boris desires 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 printed a simple 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 may be certain the message hasn’t been deciphered alongside the best way. When Boris desires to obtain secret messages, he merely adopts the identical process: He publishes a simple recipe for making messages disappear (that Natasha or anybody else can use), whereas protecting one other one only for himself that makes them reappear.
In public key cryptography, the “public” and “non-public” keys work similar to the primary and second components 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 course and very tough to reverse. However in addition they include “trapdoors,” items of data that, if identified, make the features trivially simple to compute in each instructions.
One widespread trapdoor operate entails multiplying two massive prime numbers, a simple 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 massive prime numbers. These are your trapdoors. Multiply the 2 numbers collectively, then carry out some extra mathematical operations. This public key can now encrypt messages. To decrypt them, you’ll want the corresponding non-public key, which accommodates the prime elements—the required trapdoors. With these numbers, it’s simple to decrypt the message. Preserve these two prime elements secret, and the message will keep secret.
