Cryptanalysis: Nihilist Cipher

Notes on cracking Nihilist and Vignere ciphers by hand

What is a Nihilist cipher?

Recently for a challenge site I cracked a classical Nihilist cipher. These ciphers use an alphabet written into a 5 x 5 block. Addresses of each letter are used for the cipher, such as 11, 45, etc. Any order can be used, with no repetition. The alphabet usually starts with a keyword.

  1 2 3 4 5
1 E X A M P
2 L B C D F
3 G H I J K
4 N O Q R S
5 T U V W Y

A key is chosen, say obfuscate, which is coded using the addresses: 42 22 25 52 45 23 13 51 11. Then, the plain text is coded: LEAVE AT SUNDOWN becomes 21 11 13 53 11 13 51 45 52 41 24 42 54 41 (no spaces).

To generate the cipher text, the code of the key is added to the corresponding position in the text. The key is repeated as necessary. So, the cipher text for the above example is 63 33 38 105 56 36 64 96 63 83 46 67 106 86.

Vulnerabilities

To crack the cipher text turned out to be a lot of fun. I was provided the plain text for the first 15 characters or so, which made it a bit easier to generate the alphabet block. Some of the things I noticed on the way:

• Obviously, long cipher texts are better (won't elaborate on that)
• The length of the key is the first (most?) critical thing to find.
• The length of the key can be guessed by looking for low/high number patterns. By splitting the cipher text into blocks of the suspected key length, usually the trends of higher/lower key values will emerge after a few tries.
• For each number in the cipher text, say 89, there are only a limited combination of two digit numbers from 1, 2, 3, 4, 5 that will make that number. This narrows down choices significantly: 89 can be made only from 45 + 44
• "Extreme" numbers are helpful for the above point: low and high numbers have very limited options of what they can be.
• The numbers 22 and 110 are especially critical since they're undoubtedly the corners of the alphabet block. They indicate that the letter of the key is the same as the letter of the plaintext in those locations.
• A further way to narrow down the options is to write the minimum and maximum block addresses for each cipher text. For 76, for example, the minimum is 21, and the maximum is 55, a (large) range of 20 choices. Some numbers have smaller ranges and \"hint\" at solutions.
• A cipher key with numbers 2 or 0 as the second digit is interesting because they are limited to the first or last columns, respectively.

Surprisingly, I didn't program a solver, but went with the pen and paper approach. The solution had a nine-letter key. I suppose longer keys would make for easier cracking, but I'm not sure.

The Nihilist cipher, by the way, is a close relative of the Vigenere cipher, which does very much the same thing only using letters and a larger alphabet block.

Happy solving!