Math in… Password Protection

When you send a password or credit card number across the internet, your computer encrypts it into a secret code so that only the intended recipient can read it. But how can a message be decrypted by its intended recipient without decryption instructions that the wrong person might intercept and use?

In public key cryptography, the receiver tells the sender (and everyone else!) how to encrypt a message so that only the receiver will know how to decrypt it. This requires decryption to be tricky enough that even knowing how to encrypt won’t help too much. Public key cryptosystems are based on trapdoor functions: operations that are easy to do but hard to undo.

For example, multiplying numbers is straightforward,

6223198477 * 219998344367 = ?

but factoring a number is much trickier.

28816009319611941822107 = ? * ?

Numbers with hundreds of digits can take billions of years to factor, which is what keeps the RSA cryptosystem secure — for now!