There Is More Than One Way To Do It

March 31, 2025

Tim Towtdi says, In Code, as in Life, there is more than one way to do it!

Code first; then Life; Tim at the end.

Consider Julius Caesar’s method for secret writing, nowadays known as the Simple Caesar Cipher. Shift each letter of the alphabet by a certain number of positions. This procedure gives an encryption key for encoding a plain text message into a cipher-text and then decoding it to reveal the plain text.

When both the sender and the receiver of a message use the same key, they can transmit messages as cipher-texts that will appear difficult for anyone else to read who does not have the key.

Key 1, below, arranges letters of the English alphabet into pairs of rows such that letters in the second row shift just one position relative to those in the first row. ‘A’ in the second row slides over to sit beneath ‘B’ in the first, and so forth. What about the last letter, ‘Z’? It wraps around to the first position in the second row, beneath ‘A’.

Key 1:

A B C D E F G H I J K L M
Z A B C D E F G H I J K L

N O P Q R S T U V W X Y Z
M N O P Q R S T U V W X Y
		  

Encode each letter in the plain text by finding that letter in the first row of the key and replacing it with the one underneath it in the second. With Key 1, the plain-text message, HELLO WORLD would become the cipher-text, GDKKN VPQKC.

Decoding the cipher text uses the same key in reverse. Find each letter of the cipher text in the second row and replace it with the corresponding letter immediately above it in the first row.

This was the first technique I learned for secret writing. GDKKN VPQKC looks really mysterious, right? Alas, it would fool no one, because it is such an easy code to ‘crack’.

Simply shifting letters sideways gives only 25 different encryption keys for the 26 letters of the English alphabet, because the letters can be shifted only 25 times before they return to their starting position. Decode the cipher-text with each of the 25 shifted keys. One of them will reveal the original plain text.

But wait. There are more ways to make encryption keys for a Caesar Cipher: many, many more.

Suppose Julius were to shuffle the 26 letters like a deck of cards. Then, the number of available, distinct, different keys becomes very large. Key 2, below, gives just one such arrangement. The letters on the second row are shuffled rather than merely shifted:

Key 2:

A B C D E F G H I J K L M
T D V P L I X N O E U C Z

N O P Q R S T U V W X Y Z
J M Y F B A H R G K Q W S
		  

The number of different ways to arrange 26 letters is 403,291,461,126,605,635,584,000,000.

Imagine trying to decode a cipher text encoded with a shuffled key like that. How long would it take to try all possible keys?

If one were to examine 939 million of them in the span of a single second of time, doing so each second of every minute of every hour of every day since the Big Bang began the Universe, one would not be finished yet. It would take another million years or so at that rate to have tried them all.

Having so many different Caesar Cipher keys available would seem to make this secret writing system pretty secure. Unfortunately, no, because there is another way to decode a Caesar Cipher.

I won't go into it very much here. Basically, the approach involves analyzing the frequency of the different letters in the cipher text. We know that the twelve most-frequent English letters (in decreasing order) are: E T A O I N S H R D L and U.

Now, if the letter ‘L’ were to show up most frequently in a cipher text, and we know that ‘E’ is most frequent in plain text, then one could reasonably try ‘E’ in place of ‘L’, without needing to know anything about the encryption key.

Contestants on the TV game show, Wheel of Fortune, sometimes memorize ETAOIN SHRDLU as a kind of pronounceable clue to help them guess letters.

Counting letter frequencies can defeat a Caesar Cipher if the same key were used consistently to replace all of the letters in a plain-text. Tim Towtdi would have you look for other, different ways to produce cipher-texts which would be very difficult to decipher without knowing how they were encrypted.

We might guard against the letter-counting attack by using a series of different Caesar Cipher keys to encode a single message. That idea opens a big door. Let it be a story for another day.

Tim Towtdi is an acronym, of course. Yet I have imagined a face for wise, old Tim in my mind ever since I began to learn the Perl programming language.

Larry Wall, Perl's originator, frequently said, in his book about using the language, There is more than one way to do it.

His reason sounded unflattering. He said that programmers are lazy.

Actually, I believe Wall intended a permissive meaning. It should be OK to decline unnecessary work. Settle for a beneficial solution to a problem, even when someone else promotes a different approach.

Our champion Tim would no doubt say the same goes for a lot of things in life. If your way works (and does no harm), then go ahead! Do it your way and feel good about it.