Trap-Door Ciphers

But imagine the following situation. Suppose you have a special method of encoding and decoding that is ``one way'' in a sense. Imagine that the encoding is easy to do, but decoding is very difficult. Then anyone in the world can encode a message, but only one person can decode it. Such methods exist, and they are called ``one way ciphers'' or ``trap door ciphers''.

Here's how they work. For each cipher, there is a key for encoding and a different key for decoding. If you know the key for decoding, it is very easy to make the key for encoding, but it is almost impossible to do the opposite--to start with the encoding key and work out the decoding key.

So to communicate with your friend in Europe, each of you has a trap door cipher. You make up a decoding key $D_a$ and generate the corresponding encoding key $E_a$. Your friend does exactly the same thing, but he makes up a decoding key $D_b$ and generates the corresponding encoding key $E_b$. You tell him $E_a$ (but not $D_a$) and he tells you $E_b$ (but not $D_b$). Then you can send him messages by encoding using $E_b$ (which only he can decode) and vice-versa--he encodes messages to you using $E_a$ (which only you can decode, since you're the only person with access to $D_a$).

Now if you want to change to a new key, it is no big problem. Just make up new pairs and exchange the encoding keys. If the encoding keys are stolen, it's not a big deal. The person who steals them can only encode messages--they can't decode them. In fact, the encoding keys (sometimes called ``public keys'') could just be published in a well-known location. It's like saying, ``If you want to send me a private message, encode it using this key, and I will be the only person in the world who can read it.'' But be sure to keep the decoding key (the ``private key'') secret.