The unique model of this story appeared in Quanta Journal.
For hundreds of years, should you 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 supposed viewers. This rule acted like the important thing to a lock. For those who had the important thing, you possibly can unscramble the message; in any other case, you’d want to choose the lock. Some locks are so efficient they will 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 methods: How do you get that key into the proper fingers whereas holding it out of the mistaken ones?
The counterintuitive answer, generally known as public key cryptography, depends not on holding a key secret however somewhat on making it extensively accessible. 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 think about the “keys” not as objects that match right into a lock, however as two complementary substances 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 method 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 method for the second ingredient with anybody—not even Boris—she will be positive 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 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 substances on this particular invisible ink: One encrypts messages, the opposite decrypts them. However as an alternative of utilizing chemical substances, public key cryptography makes use of mathematical puzzles referred to as trapdoor capabilities. These capabilities are simple to compute in a single route and intensely troublesome to reverse. However in addition they include “trapdoors,” items of knowledge that, if identified, make the capabilities trivially simple to compute in each instructions.
One widespread trapdoor perform entails multiplying two giant 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 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 accommodates the prime components—the required trapdoors. With these numbers, it’s simple to decrypt the message. Preserve these two prime components secret, and the message will keep secret.