The Vernam Cipher (also called the One-Time Pad) is the only cipher that is provably unbreakable.

Even a computer with infinite time and power cannot crack a message encrypted under this cipher. The Washington-Moscow hotline during the Cold War used the Vernam cipher, and spies have too.

The Vernam Cipher is fairly simple. Here’s how it works.We’ll use the following table to translate letters into numbers and vice versa in the encryption process:

To encrypt a message, we need a secret key of the same length. This secret key consists of a sequence of randomly selected letters / characters. For example, suppose that Alice wants to send Bob a seven-letter message–encrypted to conceal it from Eve the Eavesdropper. She first privately gives him a seven-character secret key that might look like this: “CBZUYEL.”

Now Alice wants to send Bob, say, the message “FAR CAR,” she encrypts it under their shared secret key as follows. She takes the first letter `F’ and “adds” it to the corresponding first letter `C’ in the secret key. She does this by finding the number corresponding to `F,’  namely 6, and the number corresponding to `C,’ namely 3, and adding them together to get 9. Then she maps this number back to a letter value; here, 9 gives the letter `I.’  Alice does this for every character in her message. If you work through it, you’ll see that:

FAR CAR +

CBZUYEL =

——————

ICQUAFC

There’s one small complication here. You may be wondering how `R’ + `Z’ is computed, since 18 + 26 = 44. When the sum of two characters is 27 or larger, we subtract 27 from it, i.e., “wrap around” the table. Thus, since `R’ + `Z’ = 18 + 26 = 44, we map it to 44 – 27 = 17, and  end up with Q.

This “wrapping around” is called modular arithmetic (also sometimes called “clock arithmetic”). It’s important in cryptography, and we use it in our first puzzle.

The Vernam cipher is unbreakable because the secret key is chosen at random. With the wraparound, this means that the encrypted message itself looks completely random to Eve. In our example, Eve doesn’t know the secret key CBZUYEL, so the encrypted message ICQUAFC is unintelligible to her.