Tag: substitution

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”:

Polybius square

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

Bifid example plaintext conversion to numbers

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

Bifid digits single row

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

Bifid final decryption (To create 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:

Keyspace size k and unicity distance U

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”

Trifid polybius squares

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:

Trifid example plaintext conversion to numbers

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

Trifd digits single row

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

Bifid final decryption (To create 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:

Keyspace size k and unicity distance U

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:

The Bifid Cipher Explained

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 Trifid Cipher Explained

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

Cover of The Beale Papers (source Wikipedia)
  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:

Example “book” used as key for encryption in the “single letter scheme”

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.

A YouTube Video About the Book Cipher

The Book Cipher Explained

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:

Image of a „Syllabary square“ Source: Military Cryptanalytics – Part 1, Chapter XI,
April 1956, by Friedman and Callimahos

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:

Original Friedman scheme (for English)

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)

Digits and table changed (Scheme 3)

A YouTube Video About the Cipher

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

The Syllabary Cipher Explained

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.

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:

The generated Polybius square using the keyword “Keyword”

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:

Encryption of plaintext numbers using key numbers

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:

The Nihilist Cipher Explained

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:

A CrypTool 2 template showing the Nihilist cipher component

You can download CrypTool 2 from here.

Cryptography for everybody: I Created a Text-Based AES-Like Cipher – A Cipher Built Using Only Classical Ciphers

Can you build a cipher with the structure of the Advanced Encryption Standard (AES), our current standard modern symmetric cipher, but only use classical ciphers? I asked myself this question when I implemented AES in C# as a preparation for my upcoming AES videos on my YouTube channel in 2021.

AES’ structure (10 rounds for AES-128) consists of 4 different building blocks:
1) AddRoundKey,
2) SubBytes,
3) ShiftRows, and
4) MixColumns:

AES structure

The AddRoundKey building block adds a round key to the state array of 16 bytes (or plain and/or ciphertext) using XOR. The SubBytes building block substitutes each byte using AES’ S-Box, the ShiftRows building block performs a shift of the rows of the state array, and the MixColumns building block mixes the columns of the state array by multiplying each “vector” with an invertible matrix in the finite field GF(2^8).

When I implemented each of these four steps, I was reminded of some classical ciphers: AddRoundKey reminded me of an additive cipher, SubBytes reminded me of a simple substitution cipher, MixColumns reminded me of a transposition cipher, and the matrix multiplication finally reminded me of a Hill cipher.

Thus, I changed the inputs (plaintext and key) and the output (ciphertext) of the AES to simple text (just letters from A to Z), exchanged AddRoundKey with an additive cipher (using MOD 26), exchanged SubBytes by SubBigrams (a bigram substitution cipher), I kept ShiftRows as it was, and exchanged MixColumns with a 4×4 Hillcipher (also using MOD 26). The “TextAES” was born :-).

To also allow decryption, I computed the inverse S-Box (an inverse lookup table for the bigram substitution cipher) and an inverse matrix for the Hill cipher.

I kept the key expansion more or less as it was, but with text, and also used the bigram substitution and replaced its round constants by “AAAA”,”BAAA”,”CAAA”, etc.

Finally, I was convinced that you can create an AES-like cipher using only classical ciphers :-).

If you are interested in details of this self-made crazy cipher, have a look at the video I made about it:

I Created a Text-Based AES-Like Cipher

If you are interested in details of the real AES, you may also have a look at my other two videos about AES and AES key schedule:

AES – The Advanced Encryption Standard Explained
AES – Key Schedule/Key Expansion Explained

Also, if you want to play with my source code in C# of AES and TextAES, you can find it freely available on GitHub: https://github.com/n1k0m0/AES-and-Text-Based-AES

Finally, here is the original publication of AES:
Daemen, Joan, and Vincent Rijmen. The design of Rijndael. Vol. 2. New York: Springer-verlag, 2002.

Nils

Cryptography for everybody: Let’s Create Our Own Homophonic Substitution Cipher

In our newest video on “Cryptography for everybody”, we create a homophonic substitution cipher using CrypTool 2.


The “Substitution component” of CrypTool 2 allows to create substitution ciphers. For that, we implemented an easy-to-use syntax based on plaintext and ciphertext alphabets. An “alphabet” is just a string (some text), which consists of our “symbols”. A symbol can be one or more UTF-8 characters.

Example (simple shift cipher):
– Plaintext alphabet=”ABCDEFG…Z”
– Ciphertext alphabet=”BCDEFGH…A”

Providing these two alphabets to the substitution component would create a simple shift cipher, where each letter of the plaintext alphabet is shifted one to the left in our corresponding ciphertext alphabet. In the substitution component, letters are substituted based on their corresponding positions in the given alphabets. The first letter of the plaintext alphabet is substituted by the first letter of the ciphertext alphabet, the second by the second, etc.

But the substitution component is much more powerful. It allows also to create alphabets consisting of “words” and also allows alternative substitutions to create “homophones”.

Example (homophonic substitution cipher):
– Plaintext alphabet=”ABCDEFG…Z”
– Ciphertext alphabet=”[01|02][03|04]…[999|555]”

In this example, the letter A can be substituted by either 01 or 02. The brackets tell the substitution component that it should use everything inside the brackets as a single ciphertext symbol. The pipe symbol tells the component that we want to create alternatives. Using this syntax, we are able to create a homophonic substitution cipher, where one plaintext letter will be replaced by one of the defined homophones.

But we are not only limited to use simple two or three digit combinations. We can also create mappings like [MAXIMILIAN] in the plaintext alphabet and [1001] in the ciphertext alphabet. Doing so, we can create so-called nomenclators. How this can be done in CrypTool 2 is part of the linked YouTube video. So if you are interested in more details, you should have a look at this 🙂

If you are interested in downloading the newest version of CrypTool 2 (I always recommend the nightly build, since it contains the newest components) go to https://www.cryptool.org/en/ct2/downloads

Nils