Tag: cipher

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 is a polyalphabetic substitution cipher, which needs two keywords. It was used by the Russian nihilists in the 19th century. To encrypt a text using the cipher, we have to perform the following three steps:

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.

I Implemented the “Mexican Army Cipher Disk” and also its Cryptanalysis in CrypTool 2

In the last view days, I implemented the Mexican Army Cipher Disk and its cryptanalysis in CrypTool 2. I also made a YouTube video about that (see below in this blog post).

The Constitutionalists in Mexico used the Mexican Army Cipher Disk at the beginning of the 20th century during the Mexican revolution. It is a homophonic substitution cipher, but rather weak. For encrypting a letter, you have either a 3-symbol or a 4-symbol homophone group, with a total of 100 homophones (01 to 00).

My self-created Mexican Army Cipher Disk

The groups are created using the disk device, which consists of 5 disks (see shown figure above):
• The outer disk contains the Latin alphabet
• Four inner disks contain 2 digits numbers
• Four inner disks can be turned

The key of the cipher is the rotation of the four inner disks and can be described in two ways:
1) The digit groups below the letter A : 01, 27, 53, 79
2) With four Latin letters ; each letter is the one above the first digit group of the corresponding disk: A, A, A, A

Build your own Mexican Army Cipher Disk

Now, if you want to also build your own cipher disk, you may use my self-created template here:

Mexican-Army-Cipher-DiskDownload

Since I used powerpoint to create the template, the angles are not 100% perfect, but it still works well. You need to print it five times and always cut a smaller disk out of each printout. To get more stability, you may also use some cardboard and glue the disks onto these before assembling the device. Finally, all the disks are placed on top of each other. I used a paper clip that I bent and put through all the slices.

Cryptanalysis

If we want to break the Mexican Army Cipher Disk, it is a rather easy task. By hand, we just search in each number group (01 to 26, 27 to 52, 53 to 78, and 79 to 00) for the most frequent homophone. This stands probably for the letter E. Move your disks to all found E positions and you should be able to decrypt your ciphertext.

If you don’t want to break it by hand, you can use CrypTool 2 and the “Mexican Army Cipher Disk Analyzer” component for automatic cryptanalysis. It performs a brute-force attack and searches through all disk settings. Here, with the help of a language model (e.g. English pentagrams) it scores each of the decrypted texts. The correct plaintext should be on the first position of the best list of the analyzer.

YouTube Video

I alse created a YouTube video about the Mexican Army Cipher Disk. You may watch it here:

My YouTube video about the Mexican Army Cipher Disk

Some References

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