The unique model of this story appeared in Quanta Magazine.
For hundreds of years, for those who wished to ship a secret message, there was principally one technique to do it. You’d scramble the message utilizing a particular rule, recognized solely to you and your meant viewers. This rule acted like the important thing to a lock. For those who had the important thing, you might unscramble the message; in any other case, you’d want to select the lock. Some locks are so efficient they will by no means be picked, even with infinite time and assets. However even these schemes undergo from the identical Achilles’ heel that plagues all such encryption programs: How do you get that key into the correct fingers whereas protecting it out of the incorrect ones?
The counterintuitive answer, often called public key cryptography, depends not on protecting a key secret however slightly on making it extensively out there. The trick is to additionally use a second key that you simply 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 non-public—that somebody can each scramble and unscramble a message.
To know 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 straightforward for him to do: Natasha has printed a simple and well-known formulation 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 formulation for the second ingredient with anybody—not even Boris—she will 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 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 known as trapdoor functions. These capabilities are straightforward to compute in a single course and very troublesome to reverse. However additionally they include “trapdoors,” items of data that, if recognized, make the capabilities trivially straightforward to compute in each instructions.
One widespread trapdoor perform 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 further mathematical operations. This public key can now encrypt messages. To decrypt them, you’ll want the corresponding non-public key, which accommodates the prime components—the required trapdoors. With these numbers, it’s straightforward to decrypt the message. Maintain these two prime components secret, and the message will keep secret.