Pet peeve: the blog post mentions _decimal_ and _denary_ several times, but in reality, there are no decimal numbers involved in any part of the computation.
This is a common mistake made by people who haven't fully internalized the distinction between numbers (which have no intrinsic representation) and _numerals_ which are the encodings of numbers.
When you are converting a permutation to its index, you are not converting to _decimal_, you are converting it to an integer. That integer has no intrinsic base. In Python (and the linked C++ code) that integer will be internally represented in binary (or a base that is a higher power of 2) and the corresponding decimal representation is generated only when printing.
So functions like decimalToFactoradic() should really be named integerToFactoradic(), etc.
Reminds me of the playing-card based encryption system designed by Bruce Schneier for the novel Cryptonomicon .
Nice! But why just hide one message if you can run an entire encryption algorithm with the deck? :)
Por que no los dos? One deck has the encrypted message, the other deck has the key.
Hey all, I found a cool way to convert text into a specific order of a deck of playing cards. I detailed the instructions of how it works in the blog post but a brief overview would be that it uses Lehmer codes which allow you to uniquely identify each permutation of a set i.e. each of the many many ways a deck of cards can be shuffled/arranged
TIL about Lehmer codes... and "poker encoding" ;)
(I just prefer poker to solitaire...)
Someone else mentioned that the orientation of the cards (up or down) and possibly even the front-back facingness of the card (facing up, facing down) would add another 2 possible bits to the available encoding space. (Of course, at that point you'd have to also encode which side of the whole deck is the "top"...)
My own thought was to add par2 to make it robust against small errors... at the cost of some transmission space!
> Of course, at that point you'd have to also encode which side of the whole deck is the "top"...)
An asymmetrical joker could indicate which short edge is "right way up", while also indicating which card is the first or last of the deck.
Yeah that would make an interesting addition. I was thinking about error correction so if you swapped two cards it would be okay but was struggling with how it would work, but I think it would be quite fun to add :)
> "...which side of the whole deck is the 'top'..."
A dark line drawn across the top of the deck would be enough. Though it would ruin the stealth factor of the cards.
Also, the pattern on the back of some playing decks isn't symmetrical, so that could be used as well.
Decode it both ways and see which isn't gibberish.
Good stuff. You could get much better bandwidth than this by tokenizing and using something like a Huffman or arithmetic code on token frequencies. As a simple example, if you set your tokens to be all English words - let's say there are between 500k and 1 million - that's about 9-10 bits per word. I am sure you could do much better than this as well
You can get much better than that by taking a well-known LLM model and encoding a series of offsets from the most likely sequence of tokens, especially if you are OK with the message being slightly different.
That sounds very interesting, I'll look into it thanks :)
A while ago I made an interactive demonstration of how encoding with factoradic works https://ilcavero.github.io/ seems like I found someone else who thought it was a fun thing to demo
Despite appearing to have perfectly ordinary structured static HTML content (aside from the fact that it spams things like <span style="font-weight:bold"> instead of using some basic CSS properly), without JavaScript I only see a solid-colour background.
Anyway, this doesn't offer a whole lot of storage:
$ python -c 'print(sum(__import__("math").log2(x) for x in range(1, 53)) // 8)'
28.028 bytes out of ~225 bits, sure. (I compute 228 bits, but precision gets funny with quantities so large. Interestingly, an emulated TI-86 and a real TI-89 Titanium returned different answers; the latter wasn't even divisible by 8!)
For movie-plot '52 pick-up' that's not so bad, especially if used to encode something like a key for the "Solitaire" cryptosystem, mentioned nearby, wherein the same deck can in turn be reconfigured and manipulated to generate an arbitrary-length keystream for application to a longer message transmitted under separate cover.
45 characters according to the blog post and this demo
45 code points in a custom 5-bit encoding representing 32 characters; 28 bytes (with 1 to 4 bits left over) of 8-bit ASCII.
7 characters of UTF-32
There are other five bit character sets as well, such as the 5-bit Baudot character set and the 5-bit Zork character set. You could also use variable bits characters, or other bases of numbers.
You can also use other decks, e.g. with tarot cards you will have 78 cards rather than only 52 cards, and can make a longer message.
Other comments on here had mention doing other things such as face-up vs face-down cards.
You should be able to get another 45 bits or so by also using the orientation of the cards (everything except non face card Diamonds).
The 2, 4, 8, and 10 of all suits are typically rotationally symmetrical.
Only if your deck has a rotationally symmetric back. A lot of decks are oriented with pictures or logos. Tarot decks almost always do to allow inverted readings (and you'd get a few more bits out from the major arcana).
You might squeeze a tag bit for the deck out of the 7◇, depending on the pack design.
>you might squeeze a tag bit for the deck out of the 7◇
awww, youuuuu!! hugz!
"The Seven of Diamonds meaning in a Tarot reading can show that you will be surrounded by love."
(i was looking it up to find what the different cards looked like and found that)
and yes "you and I might squeeze a bit" later
Good to see you're enjoying yourself, whoever you are.
is it just me or that comment unexpectedly lives up to your username
You could also add face up or down.
Encoding with common objects was (and maybe still is) actually used in practice by actual spies, see CIA shoelace code.
I've done Pontifex from Cryptonomicon on a Commodore 64 for fun. Bruce Schneier came up with it. https://imapenguin.com/2021/05/making-and-breaking-ciphers-o...
How about just assigning a number to every sentence in every language known to man, and using the absurdly huge number of deck combinations to identify them?
Impractical, but possible.
225 bits