## The Bazeries Cipher Explained – A Classical Cipher Based on Substitution and Transposition

The Bazeries cipher was invented by and named after Étienne Bazeries, a French cryptographer. Bazeries was active between 1890 and the First World War.

Bazeries is probably most famously known for the “Bazeries Cylinder”, a cipher device similiar to the Jefferson Disk or the M-94 cipher. Bazeries was a good code breaker: He solved messages encrypted with the official French military transposition system (lead to improvements of the ciphers). He further exposed weaknesses in French cipher systems. He assisted in solving German military ciphers during World War I, after he retired from the army. And in the 1890s he broke the famous nomenclator system called the “Great Cipher”, created by the Rossignols in the 17th century.

### How Does the Cipher Work?

The cipher is a combination of substitution and transposition. For encryption, Bazeries only used a single number key, e.g. 123. In the following, we encrypt an example plaintext (“HELLOWORLD”).

We create two Polybius squares. In the first square, we put the Latin alphabet (I=J; filled from left to right and top to bottom row-wise). In the other square, we write a text representation of the number key, e.g. ONEHUNDREDTWENTYTHREE, followed by the remaining unused letters of the Latin alphabet. We fill the second square from top to bottom and left to right column-wise:

To encrypt a plaintext, we first substitute it using the two created Polybius squares. We look for the plaintext letter in the left square and use the corresponding letter of the right square for the ciphertext (For eample A->O, B->D, etc.). When we encrypt HELLOWORLD, we obtain BQEELYLWEI.

Then, we transpose the intermediate ciphertext using the digits of the number key. We split the text into blocks of sizes defined by the digits of the number key. Then, we reverse each of these blocks to create the final ciphertext:

So our final ciphertext here is BEQYLELWEI. Of course, the decryption is the inverse process of the above shown steps :-).

### Keyspace Size and Unicity Distance

Here, we compute the keyspace size as well as the unicity distance (https://en.wikipedia.org/wiki/Unicity_distance). In the original version, as written above, Bazeries created the second Polybius square using the same key as he used for transposition. So for e.g. a maximum number key length of four digits, we compute:

• For a 4-digit key, we have 10^4=10,000 different keys
• For a 3-digit key, we have 10^3=1,000 different keys
• For a 2-digit key, we have 10^2=100 different keys
• For a 1-digit key, we have 10^1=10 different keys

Then, we have to add all these number. Thus, we have a toal keyspace size of 11,110

If we consider that the encrypter uses an independent (other) key for the Polybius square creation, we would have to compute 26! ≈ 2^88.4 for the number of possible different Polybius squares. In this case, we have to compute for the “complex” Bazeries cipher 11,110 ∙ 2^88.4 which is about 2^101.8.

To compute the unicity distance (of the complex case), we have to divide the entropy of the keyspace with the redundancy of the language:

So we would need a ciphertext with a minimum length of 32 letters to obtain only one valid (and the correct) solution via cryptanalysis.

### A YouTube Video about the Bazeries Cipher

I also created a YouTube vide about the Bazeries cipher:

## The Four-Square Cipher Explained

This is the third cipher of Félix-Marie Delastelle, a French hobby cryptographer, which I implemented in CrypTool 2. Delastelle published the four-square cipher in his book “Traité Élémentaire de Cryptographie“. He wrote the book in 1901 but it was published after Delastelle’s death in 1902.

The four-square cipher is a bigraphic monoalphabetic substitution cipher. Bigraphic means, that it always encrypts two plaintext letters at the same time. The cipher uses four Polybius squares, two of which are created using keywords.

### Key Generation – Preparing the Four Polybius Squares

First, you have to prepare the four polybius squares. Let’s assume our keywords are “secret” and “keyword”:

Here, we created the second and third polybius squares using the previously chosen keywords. To create one of these polybius squares, the corresponding keyword is first written into the square from left to right and top to bottom. Here, if a letter occurs more than once, we omit it. In our example, we do not write the second “E” of “secret” again in the square. After writing the keyword, we fill the rest of the square with the remaining alphabet letters, which we did not already use for the keyword. After we created the second and third square, we fill the first and fourth square just with the alphabet. Since all the squares have only 25 positions, our alphabet consists of only 25 letters. Delastelle used “I” = “J” and did not include a “J” in his alphabet.

### How Encryption works

Now, we can encrypt a plaintext using our four polybius squares. Here, for example we want to encrypt “HELLOWORLD”. To do so, we search the letter “H” in the first square and the letter “E” in the fourth square:

We create a connected “rectangle” where “H” is the upper corner and “E” is the lower corner. Now, we find our ciphertext letters in the two other corners of the so-created rectangle. Here, we encrypt the “H” by “G” and the “E” by “Y”. We continue encrypting our plaintext using this method to obtain the complete ciphertext:

To decrypt a given ciphertext, we just reverse the process. We look up the ciphertext letters (pair-wise) in the second and third square and find our plaintext letters in the first and fourth square.

### Keyspace Size and Unicity Distance Computation

We compute the keyspace size by k = 25! * 25! = 2^167.36. This is, because we have to fill two polybius squares and a single polybius square has 25! possibilities to be filled with 25 letters.

We compute the unicity distance U by

Here, H(k) is the entropy of the keyspace and D is the redundancy of the language (here English). From the English Wikipedia: “In cryptography, unicity distance is the length of an original ciphertext needed to break the cipher by reducing the number of possible spurious keys to zero in a brute force attack”. In our case, we need more than 53 letters to be able to obtain only one valid plaintext.

### A YouTube Video about the Four-Square Cipher

I also created a YouTube video about the four-square cipher (and how you can use it in CrypTool 2). Watch it here:

## Discord Server for “Cryptography for Everybody” YouTube Channel and CrypTools

I have recently set up a brand new Discord server for the “Cryptography for everybody” YouTube channel and the CrypTool projects.

Thus, I would like to very cordially invite everyone who wants to discuss classical and modern cryptology, CrypTools, as well as crypto challenges in a friendly chat environment to join our new Discord community server here: https://discord.gg/8JeTZd8EpT

## The Bifid and Trifid Cipher Explained

I recently made two videos about two interesting classical ciphers invented by Félix Marie Delastelle. Delastelle wrote a book on cryptography in 1901. Unfortunately, he died before his book was published in 1902. In his book, he describes several ciphers he invented. This blog post is about two of them: the bifid cipher and the trifid cipher.

### The Bifid Cipher

The bifid cipher is a cipher which combines a Polybius square with transposition, and uses fractionation:

1. First, we use a keyword to create a 25-letter Polybius square
For example: “SECRET KEYWORD”:

2. Then, we encrypt the plaintext using the square, by writing the coordinates of the square below the plaintext. Example:

3. After that, we write the digits (transposed/fractionated) in a single row:

4. Finally, we decrypt the digits using the square to obtain the ciphertext:

The decryption is the reverse process. It is also possible to not encrypt the plaintext in one go. Instead, you can encrypt the ciphertext in blocks of n (n for example being 5).

The keyspace size and unicity distance (minimal number of letters needed in a ciphertext that allows having only a single valide solution) can be computed as follows:

### The Trifid Cipher

The trifid cipher was invented by Félix Marie Delastelle as an extension of the above shown bifid cipher.

1. First, we use a keyword to create three 9-letter Polybius squares. For example: “SECRET KEYWORD”

2. Then, we encrypt the plaintext using the squares, by writing the number of the used square number and the coordinates below the plaintext. Example:

3. After that, we write the digits (transposed/fractionated) in a single row

4. Finally, we decrypt the digits using the three squares:

The decryption is the reverse process. It is also possible to not encrypt the plaintext in one go. Instead, you can encrypt the ciphertext in blocks of n (n for example being 5).

The keyspace size and unicity distance (minimal number of letters needed in a ciphertext that allows having only a single valide solution) can be computed as follows:

### YouTube Videos about the Bifid and Trifid Ciphers

I made a YouTube video about the Bifid cipher. Here, you can also see how to use the bifid cipher component of CrypTool 2:

I also made a YouTube video about the Trifid cipher. Here, you can also see how to use the trifid cipher component of CrypTool 2:

## The Book Cipher Explained

A book cipher is a cipher where the plaintext letters (or words) are encrypted using a book (or other text document) as a kind of lookup table. Sender and receiver of encrypted messages can agree to use any book or other publication available to both of them. A book cipher has a considerable advantage for a spy in enemy territory since it does not raise suspicion (like e.g. a code book). The main strength of a book cipher is the key, because only being in possession of the original “book” allows the decryption.

# Famous Examples of Book Ciphers

1. The most famous book ciphers are probably the “Beale ciphers”
• The Beale ciphers are three encrypted documents
• Only one of the documents has been successfully deciphered (using the United States Declaration of Independence as key)
• The two other messages are still unsolved… (it is unclear, how these were encrypted)
2. The “Arnold Cipher” was a book cipher used by John André and Benedict Arnold in 1780 during the American Revolutionary War
• The book used as a key to the cipher was either “Commentaries on the Laws of by William Blackstone or Nathan Bailey’s Dictionary
• The cipher consisted of a series of three numbers separated by periods:
page number . Line number . word number
3. The “Cicada 3301 online puzzle” series also contained book ciphers

## The Book Cipher

First, the sender and the receiver have to agree on the (exact) same “book”. They also have to agree on an “encoding scheme”:
1. Encode single letters
2. Encode complete words

Also, they need to know “what” is encoded:
1. Page
2. Line
3. Word

1. Single Letter Scheme:
In the following, we show an example of a book cipher with the “single letter scheme”. It uses this sample text as key:

To encrypt a plaintext, take a random word from the “book” above which starts with the plaintext letter you want to encrypt. Then, write the position of the word into the ciphertext. Go on, until you have encrypted the complete plaintext. In the following are two examples, how to encrypt plaintexts:

Example 1 (Write the offset of the word into the ciphertext):
H E L L O W O R L D –> 6 37 100 42 56 72 12 53 42 52

Example 2 (Write the line number and position of the word in the particular line into the ciphertext):
H E L L O W O R L D –> 09.04 04.08 12.03 05.08 05.09 08.06 06.03 07.07 12.03 06.09

Hint: With a real book, we could also prepend the page number.

2. Complete word scheme:
The “complete word scheme” is described in my YouTube video about the book cipher (see below). Also, I explain how to use a book cipher in CrypTool 2.

## Three Years “Cryptography for everybody” YouTube Channel

The “Cryptography for Everybody” YouTube channel, which is my YouTube channel about cryptography and cryptanalysis, is now three years old. On the October 8th, 2019 I started my channel as “CrypTool 2”, which I later rebranded to its current name. Early, I created my channel trailer, which image you can see here:

First idea of my channel was: Make videos about “CrypTool 2 Development”
– First series of the channel
– Today: Total of 10 development videos

My second idea was then: Make videos about CrypTool 2
– First video: “Break a Caesar Cipher” 🙂
– Today: Total of 40 videos about classical ciphers

Soon I got my next idea: Make a video series about cryptology
– First video: Part 1 (Cryptography – Terminology & Classical Ciphers)
– Today: Total of 25 videos about cryptology

Finally, I developed my YouTube channel to a channel about classic and modern cryptology (= cryptography and cryptanalysis). Here is an image of the new channel trailer with the rebranded design 🙂

A few facts of my YouTube channel:
Total Subscribers: 4,290 (2022-10-16)
Views: ≈ 280,000
Watch time: 16,910 ℎ𝑜𝑢𝑟𝑠 ≈ 705 𝑑𝑎𝑦𝑠 ≈1.93 𝑦𝑒𝑎𝑟𝑠 ≈2^19.95 𝑠𝑒𝑐𝑜𝑛𝑑𝑠

## A YouTube Video about the Three Years

I recorded a YouTube video and present much more history and channel facts. Watch it here 🙂

## The Syllabary Cipher Explained

In the linguistic study of written languages, a syllabary is a set of written symbols that represent the syllables or (more frequently) moras (basic timing unit in the phonology of some spoken languages) which make up words.

William F. Friedman and Lambros D. Callimahos present in “Military Cryptanalytics –  Part 1” a Syllabary cipher or Syllabary square on page 250. The American Cryptogram Association (ACA) also defines the Syllabary cipher as part of their list of ciphers:

Klaus Schmeh mentions a cipher he calls Crypto Number Table and also presents a challenge on his online blog. The crypto number table is in fact the Syllabary cipher.

## How does the Cipher Work?

The Syllabary cipher uses a 10×10 table that contains letters, syllables from a given language, and digits:

Basic ideas of the cipher are to suppress letter frequencies and to remove word patterns by different spellings of same plaintext words in the ciphertext.

To encrypt a plaintext, the text is replaced by digits  (coordinates) found on the top and left side of the table. Examples:

HELLO WORLD 1 → 53 65 65 74 06 77 65 31 12

You can find different ciphertexts encrypting the same plaintext:

SECRET  → 88 35 25 81 35 93
SECRET  →  89 25 83 93

To decrypt a ciphertext, you have to look up the plaintext element using the ciphertext symbol as coordinates.

## Keying Schemes

There are three different keying schemes (also defined by ACA):

1. Keep table and modify digits on top and on the left of the table (based on a digit key, e.g.  10293847568475610293)
2. Keep digits on top and left of the table but  reorder table (based on a keyword, e.g. 8SECRET1KEYWORD5)
3. Modify digits (based on a key) and reorder table (e.g. based on keyword)

## A YouTube Video About the Cipher

I created a YouTube video about the cipher that you can watch here:

## References

A blog post from Klaus Schmeh about the cipher: https://scienceblogs.de/klausis-krypto-kolumne/2018/09/01/can-you-break-the-crypto-number-table-challenge/

Friedman, William Frederick, and Lambros D. Callimahos. Military cryptanalytics. Vol. 2. Aegean Park Press, 1985.

## Halloween Update of “Cryptography for Everybody” YouTube Channel Header

I used the AI “Stable Diffusion” to create a few pumpkins and updated the YouTube channel header of “Cryptography for everybody”. The channel header is now changed on various occasions, such as Halloween, Christmas and Easter 🙂

You can watch my YouTube videos about cryptography and see the updated channel header here: https://www.youtube.com/c/CrypTool2
I also used the same header for the Facebook page of CrypTool 2: https://www.facebook.com/CrypTool2

## The Nihilist Cipher Explained

The Nihilist cipher, a polyalphabetic substitution cipher used by Russian nihilists in the 19th century, is explained in this blog article. The cipher involves two keywords and a series of steps including the creation of a Polybius square, conversion of a second keyword into numbers, and encryption of plaintext using these numbers. The process for decryption is also outlined, requiring the same keywords and Polybius square. This article not only explains the cipher’s methodology but also provides a visual and practical approach to understanding its encryption process.

Before I wrote this article, I implemented the cipher in CrypTool 2, where you can now use the Nihilist cipher component for encryption and decryption of text using the Nihilist cipher.

In the following, I show the process of encryption using the cipher:

Step 1: Choose a first keyword and generate a Polybius square:
In our example here, we choose “KEYWORD“. We fill the keyword letters into a Polybius square and fill the remaining part of the square with the rest of the alphabet in alphabetical order. Our alphabet has a total of 25 letters, where I=J. Also, if a letter occurs twice or more in the keyword, we remove all other occurences of the corresponding letter:

Step 2: Choose a second keyword and generate a list of numbers:
Using the previously generated Polybius square, we convert a second keyword to a list of numbers. For example, the keyword “SECRET” we convert to:
45 12 25 21 12 51
We do so, by looking up the letters in the square and taking the digits on the left of the square as the first digit of the number and the column digit on top of the letter’s column as the second digit of the number.

Step 3: Encrypt the plaintext using the numerical key:
In the last step, we encrypt our plaintext by writing the key numbers below plaintext numbers, which we also generated using the same Polybius square. We repeat writing the keyword numbers below the plaintext numbers until we reach the end of the plaintext. Then, we add the plaintext numbers and key numbers to obtain the ciphertext:

The receiver of the encrypted message has to perform steps 1 and 2 with the same keywords to also generate the same Polybius square and same key numbers. To decrypt the ciphertext, he has to subtract the key numbers from the ciphertext numbers and then look up the corresponding plaintext letters in the Polybius square.

## A YouTube video about the Nihilist cipher

I also created a YouTube video about the Nihilist cipher, which I uploaded to my YouTube Channel:

## A CrypTool 2 Component and Workspace

I created a CrypTool 2 component and template, which implements the Nihilist cipher. Besides the “original” cipher with a Polybius square of 25 letters, it also allows to encrypt using a square with 26 letters and 10 digits:

You can download CrypTool 2 from here.

## The Bacon Cipher Explained

Francis Bacon was the 1st Viscount St Alban and lived from the 22nd January 1561 until the 9th April 1626. He was an English philosopher and statesman. Also, Bacon is seen as one of the fathers of modern science.

Despite that, he invented the after him named “Bacon cipher”, which is actually not a cipher but a steganographic method. It was published after his death in the book “Of the Advancement and Proficience of Learning or the Partitions of Sciences IX Bookes” (Bacon , Francis (1640) translated by Gilbert Wats, Oxford University. On pages 257 up to 271, you can read the “original” description of Bacon’s cipher. A digitized version of the book can be found here: https://www.biodiversitylibrary.org/item/86617#page/384/mode/1up

## How Does the “Cipher” Work?

As mentioned above, the Bacon cipher is not a real cipher but it is a steganographic method. Bacon used it to hide secret texts within unsuspicious carrier texts. To do so, he used a “biliteral (hand-written) alphabet”.

His first step was to encode the plaintext using a code table:

For example, if you want to encode and then hide “HELLO WORLD”, you would do it like this:

First, you replace the “H” with “aabbb”, then you replace the “E” with “aabaa”, and so on:

Second, you hide the text using a bilateral alphabet. In our example here, the one alphabet uses bold letters and the other non-bold letters:

Here, you use the generated ab-pattern in the carrier text. We used non-bold letters for the “a”s and bold letters for the “b”s. The receiver has to reverse the order to obtain the hidden message. Clearly, we only transmit the carrier text and not the ab-pattern :-).

## Bacon’s Original Cipher Alphabets

Bacon used two different styles of hand-written alphabets. On the right side here, you can see a copy of the page of Bacon’s book showing these alphabets. As we can see, there are two styles for all uppercase and lowercase alphabet letters.

When Bacon wanted to hide his AB-pattern(s) in the text, he used the one alphabet style for “A”s and the other alphabet style for “B”s.

## A YouTube Video About the Bacon Cipher

I also made a video about the cipher and uploaded it to YouTube 🙂