For over 400 years,

the problem remained. How could Alice design a cipher

that hides her fingerprint, thus stopping the

leak of information? The answer is randomness. Imagine Alice rolled

a 26 sided die to generate a long

list of random shifts, and shared this with Bob

instead of a code word. Now, to encrypt

her message, Alice uses the list of

random shifts instead. It is important that

this list of shifts be as long as the message,

as to avoid any repetition. Then she sends it to Bob, who

decrypts the message using the same list of random

shifts she had given him. Now Eve will have a problem,

because the resulting encrypted message will have

two powerful properties. One, the shifts never fall

into a repetitive pattern. And two, the encrypted message

will have a uniform frequency distribution. Because there is no frequency

differential and therefore no leak, it is now

impossible for Eve to break the encryption. This is the strongest

possible method of encryption, and it emerged towards the

end of the 19th century. It is now known as

the one-time pad. In order to visualize the

strength of the one-time pad, we must understand the

combinatorial explosion which takes place. For example, the Caesar

Cipher shifted every letter by the same shift, which was

some number between 1 and 26. So if Alice was to

encrypt her name, it would result in one of

26 possible encryptions. A small number of possibilities,

easy to check them all, known as brute force search. Compare this to the one-time

pad, where each letter would be shifted by a different

number between 1 and 26. Now think about the number

of possible encryptions. It’s going to be 26 multiplied

by itself five times, which is almost 12 million. Sometimes it’s

hard to visualize, so imagine she wrote her

name on a single page, and on top of it stacked

every possible encryption. How high do you

think this would be? With almost 12 million

possible five-letter sequences, this stack of paper

would be enormous, over one kilometer high. When Alice encrypts her

name using the one-time pad, it is the same as picking

one of these pages at random. From the perspective of

Eve, the code breaker, every five letter

encrypted word she has is equally likely to

be any word in this stack. So this is perfect

secrecy in action.