(2025-03-10) Return of the Pen and Paper
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Those who have been following this phlog for a long time, know that pen and
paper cryptography is one of the topics left a bit behind the others. Well, 
I think it's time to return to it with several new ideas and re-evaluations 
of my old approaches. First, I'd like to mention that my main emphasis has 
shifted on the ease of operation and the minimum (if any) amount of 
intermediate steps necessary to be written down. Second, some of my earlier 
"no-no" techniques are now acceptable, but with some important modifications 
and precautions. Third, there are several new approaches that I hadn't 
considered before for some reason.

Let's take Playfair cipher, for example. It is pretty weak when used "as is"
and with a 5x5 character matrix. Let's improve it in several ways: extend it 
to 6x6, interleave the plaintext with completely random characters from the 
grid and change the "same row/same column" rule by swapping the resulting 
ciphertext digraph letters. Voila! We've made it much more resistant to the 
usual frequency analysis attacks. And since we're swapping the characters in 
some cases, you can't just remove the entire interleaved ciphertext because 
you don't know which character in each digraph is real and which one is a 
decoy. Add to this a reliable grid keying scheme and variable prefix length, 
and you'll get what I have called InterPlay-36 ([1]). All the technical 
description along with examples and a reference Python implementation is 
right there. You can also play with it in a JS-enabled browser using the Web 
version ([2]) which also has an option of outputting the keyed grid based on 
your passphrase. In fact, one of the best ways to train yourself on this 
cipher is to encrypt something in the website and try to decrypt it 
manually, and vice versa.

In some cases, however, Playfair still can be used "as is". For instance,
when encrypting short digital information, such as PINs and phone numbers, 
you can write all the digits from 0 to 9 in a random order into a 5x2 table 
(2 rows, 5 columns), append a zero to the plaintext if it has an odd number 
of digits, and use this table with the following Playfair-like rules for 
every digraph ab:

- if a is equal to b, replace both digits with the digit from the other row
on the same column;
- if a and b are on the same column, swap them;
- if a and b are on the same row, replace them with the ones to the immediate
right when encrypting and to the immediate left when decrypting (when the 
index is out of bounds, just wrap around the row);
- if a and b are on different rows and columns, replace them with the
corresponding opposite corners of an imaginary rectangle on the same row.

Just like with InterPlay-36, while you still might need to write down the 5x2
table somewhere, all the operations can and should be performed mentally and 
very quickly. I call this method Digifair for obvious reasons. Even before 
applying it, however, you can mask each digit of the plaintext with the 
following fractionation technique:

1. Choose a random digit from 0 to 9. 
2. Subtract your plaintext digit from it modulo 10. E.g. 4 - 7 mod 10 = 7.
3. Write both results as a new digraph instead of the initial plaintext digit.

To restore the initial digit from the digraph, just subtract the second digit
from the first one modulo 10 again. That easy.

Let's combine these two techniques in an example. Suppose we want to encrypt
a PIN 389211 with the key 6473820915. Let's write the key in a 5x2 table:

64738
20915

Then, let's fractionate and encrypt each digit (only the result of the
operation needs to be written down):

1. 3 => 74 => 37
2. 8 => 24 => 06
3. 9 => 56 => 28
4. 2 => 31 => 13
5. 1 => 43 => 78
6. 1 => 98 => 57

So, the encryption result is 370628137857. Note that this is not the only
valid ciphertext as this depends on the random choice on the fractionation 
stage.

Finally, to not make this post extremely long, I'm going to tell you about
another pen and paper technique that can be used as a pseudorandom number 
generator for any hand stream cipher that operates on decimal digits. It's 
based on the "subtract-with-carry" or "add-with-carry" algorithm. I'm going 
to use subtraction, although the addition-based approach would be identical 
here.

1. Write the initial key seed on the paper.
2. Start a new line underneath by subtracting the first digit from the last
one in the previous line modulo 10. Put a tick near the resulting digit if 
the result not modulo 10 would be less than 0.
3. Fill in the rest of the line by subtracting the digit to the top right
from the newly added digit modulo 10. If the digit has a tick, subtract 1 
more. Put a new tick near the resulting digit if the result not modulo 10 
would be less than 0.
4. Repeat steps 2 and 3 until you get the desired amount of pseudorandom
digits, not counting the original seed.

Example. Suppose your short-term key is 13378008135, then the next digits are
calculated like this (all operations are modulo 10):

* 5 - 1 = 4
* 4 - 3 = 1
* 1 - 3 = 8'
* 8 - 7 - 1 = 0
* 0 - 8 = 2'
* 2 - 0 - 1 = 1
* 1 - 0 = 1
* 1 - 8 = 3'
* 3 - 1 - 1 = 1
* 1 - 3 = 8'
* 8 - 5 - 1 = 2
* (now the original key is over, we continue on the calculated values) 2 - 4
= 8'
* 8 - 1 - 1 = 6
* 6 - 8 = 8'
* 8 - 0 - 1 = 7
* 7 - 2 = 5
* 5 - 1 = 4
* 4 - 1 = 3
* 3 - 3 = 0
* 0 - 1 = 9'
* and so on...

So, after discarding the original 13378008135 sequence, the first 20
keystream digits are calculated as 41802113182868754309.

Well, this is not everything that I wanted to tell you on this subject but I
surely hope this is a good start. Stay tuned!

--- Luxferre ---

[1]: https://codeberg.org/luxferre/InterPlay-36
[2]: https://pf.hoi.st