The distinct version of this story ecombineed in Quanta Magazine.
For thousands of years, if you wanted to sfinish a secret message, there was fundamentalpartner one way to do it. You’d scramble the message using a one-of-a-kind rule, comprehendn only to you and your intfinished audience. This rule acted enjoy the key to a lock. If you had the key, you could unscramble the message; otherwise, you’d necessitate to pick the lock. Some locks are so effective they can never be picked, even with infinite time and resources. But even those schemes suffer from the same Achilles’ heel that afflictions all such encryption systems: How do you get that key into the right hands while protecting it out of the wrong ones?
The counterastute solution, comprehendn as unveil key cryptography, relies not on protecting a key secret but rather on making it expansively useable. The trick is to also engage a second key that you never split with anyone, even the person you’re communicating with. It’s only by using this combination of two keys—one unveil, one declareiveial—that someone can both scramble and unscramble a message.
To comprehfinish how this labors, it’s easier to leank of the “keys” not as objects that fit into a lock, but as two complementary ingredients in an inapparent ink. The first ingredient originates messages fade, and the second originates them reecombine. If a recommender named Boris wants to sfinish his counterpart Natasha a secret message, he writes a message and then engages the first ingredient to rfinisher it inapparent on the page. (This is effortless for him to do: Natasha has rerented an effortless and well-comprehendn createula for fadeing ink.) When Natasha gets the paper in the mail, she applies the second ingredient that originates Boris’ message reecombine.
In this scheme, anyone can originate messages inapparent, but only Natasha can originate them apparent aachieve. And becaengage she never splits the createula for the second ingredient with anyone—not even Boris—she can be declareive the message hasn’t been decodeed aextfinished the way. When Boris wants to get secret messages, he srecommend adselects the same procedure: He rerentes an effortless recipe for making messages fade (that Natasha or anyone else can engage), while protecting another one fair for himself that originates them reecombine.
In unveil key cryptography, the “unveil” and “declareiveial” keys labor fair enjoy the first and second ingredients in this one-of-a-kind inapparent ink: One encrypts messages, the other decrypts them. But instead of using chemicals, unveil key cryptography engages mathematical baffles called trapdoor functions. These functions are effortless to compute in one straightforwardion and excessively difficult to reverse. But they also grasp “trapdoors,” pieces of alertation that, if comprehendn, originate the functions trivipartner effortless to compute in both straightforwardions.
One standard trapdoor function joins multiplying two huge prime numbers, an effortless operation to carry out. But reversing it—that is, commenceing with the product and discovering each prime factor—is computationpartner imgenuineistic. To originate a unveil key, commence with two huge prime numbers. These are your trapdoors. Multiply the two numbers together, then carry out some insertitional mathematical operations. This unveil key can now encrypt messages. To decrypt them, you’ll necessitate the correacting declareiveial key, which grasps the prime factors—the essential trapdoors. With those numbers, it’s effortless to decrypt the message. Keep those two prime factors secret, and the message will stay secret.
