The unique model of this story appeared in Quanta Journal.
For hundreds of years, in case you needed to ship a secret message, there was mainly one solution to do it. You’d scramble the message utilizing a particular rule, recognized solely to you and your supposed viewers. This rule acted like the important thing to a lock. In case you had the important thing, you possibly can unscramble the message; in any other case, you’d want to select 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 techniques: How do you get that key into the precise arms whereas maintaining it out of the mistaken ones?
The counterintuitive resolution, often called public key cryptography, depends not on maintaining a key secret however quite on making it broadly out there. 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 by utilizing this mixture 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 substances 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 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 might be positive 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 maintaining 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 a substitute of utilizing chemical substances, public key cryptography makes use of mathematical puzzles referred to as trapdoor features. These features are simple to compute in a single path and very troublesome to reverse. However in addition they comprise “trapdoors,” items of knowledge that, if recognized, make the features trivially simple to compute in each instructions.
One frequent trapdoor perform entails multiplying two massive 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 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 personal key, which comprises the prime components—the mandatory trapdoors. With these numbers, it’s simple to decrypt the message. Hold these two prime components secret, and the message will keep secret.
