The Beale ciphers are some of the most well-known unsolved ciphertexts in the world. Out of the three ciphers published, one has been solved. The solved cipher is the second of the three texts and describes the context of the treasure hidden by Thomas Beale. It was encrypted by Beale using the Declaration of Independence and a homophonic cipher. The encrypted text consists of numbers ranging from 1 to 1005. Every number stands for a certain letter as well as several numbers standing for the same letter. For example:
A: 24, 27, 28, 36...
B: 9, 77, 90...
C: 21, 84, 92, 94...
…
This way, you could form the same word in many ways. In this case, ABC could be formed with 24, 9, 21 but also 36, 77, 92.
A homophonic cipher is when several letters, numbers or symbols stand for the same letter. The symbols that stand for the same letter are called homophones. A cipher that uses homophones is called a homophonic cipher. You don’t need a text (like the Declaration of Independence) for this cipher. Instead, you can just manually assign multiple symbols to a letter.
Homophonic ciphers have been around since the Middle Ages. Their goal was to beat frequency analysis and confuse cryptanalysts. The size of the alphabet used varied a lot. Some only had a few homophones because of the complexity of using more. This had the consequence of still being quite easy to solve. This is why most homophonic ciphers had 50 to 100 ciphertext letters. This meant you needed to use a combination of letters, numbers and symbols. Many of these ciphers then also had more homophones for more frequent letters such as E, T and A. This made frequency analysis even more useless and the cipher a lot harder to solve.
To detect a homophonic cipher, you often need to distinguish between a simple substitution cipher and a homophonic cipher. For this, there is one significant difference. Homophonic ciphers require a much larger ciphertext alphabet. While the simple substitution cipher only has 26 letters, a strong homophonic cipher can have more than 100. This makes it a lot easier to distinguish between the two. If your text has about 26 letters you can assume that it is a simple substitution cipher. If it has 50 or more, a homophonic cipher becomes a lot more likely.
Homophonic ciphers were extremely useful if you wanted to encrypt something in a safer way than just substituting the letters. However, they were very tedious and long. If you wanted to encrypt something important you would have to use many homophones. You would not be able to remember all these so you would have to write them down. If anyone got their hands on this paper, they could decipher all messages.
Overall, it was a big step toward making safer ciphers. Of course, nowadays with computers these are broken very easily but for that time it was a big milestone.