I'm a fan of paper cryptocurrency wallets. I'm not sure an explanation would do them justice. It could just be that I'm a mathematics major and keeping important information for solving math problems down on fancy pieces of paper just feels really natural to me. Maybe it's because I'm fascinated by the idea that a single key, written entirely off the grid, can become a manifestation of one's ability to spend from a particular source. Or maybe a part of me finds their tangible nature appealing -- although I think a paper wallet should be treated more like a cheque than a dollar bill, I still enjoy observing how different developers choose to represent the non-electronic incarnation of an address. I mean, consider the sheer variety out there. Some of these designs are gorgeous.

For a currency to exist almost entirely in the digital realm is not exclusive to cryptocurrency. Consider that banknotes and coins consist of a measly 11% of the United States total money supply, at most. All the rest exists in checking accounts, on credit, or otherwise in some imaginary form on a computer system. Cryptocurrency is not all that special by taking its form in the digital world -- but on the flip side, it wouldn't be that abnormal to see roughly 10% of cryptocurrency printed in physical, now would it?

So for the life of me, I couldn't tell you how the idea stuck. I remember downloading a few open source wallet generators and playing around with them. I couldn't even tell you which one it was in hindsight, but I distinctly remember a walkthrough describing the folding process for preventing candle-lighting. "It's not exactly origami," said the tutorial, "Just enough to ensure that the code can't be read through the paper when held up to a light."

Now I've seen a lot of people writing or filming tutorials on how to safely and securely produce a paper wallet for cryptocurrency.

I've also seen lots of people uploading tutorials on how to make origami wallets for their fiat currency.

Today, I'd like to introduce to you what I hope might be an ongoing series: the grand potential of origami paper cryptocurrency wallets. At last, a stylish and accessible method of granting somebody the physical embodiment of their own crypto-secured ledger currency.

(The crane is a double wallet for DOGE and Ethereum tokens. The rose is Bitcoin and Bitcoin cash)

I suppose it was the obvious choice, in hindsight. There have been plenty of people who've made money origami with banknotes from nations around the world. To make origami out of the data used to spend cryptocurrency struck me as almost inevitable.

I can see it already:

• Presented this way in a form of a bonus on behalf of your company.
• Or as a gift from older relatives on graduation day.
• A tasteful wedding present. For smaller values, a stocking stuffer.
• Or a polite replacement for gift cards, when an organization offers its apologies to dissatisfied customers.

In the case on the right, it could even be an inconspicuous fidget toy -- disguised through abstract algebra and unique geometry -- to smuggle nefariously large amounts of currency from organization to organization under the nose of a totalitarian government's scrutiny.

Allow me to illustrate: suppose you happened to live in a nation where your government just so happened to make sending and receiving cryptocurrencies disadvantageous. Or a nation where cryptocurrency might even be illegal to have. What would be a good way to store your currency in a nondescript, extremely secure, and completely effective way?

The Answer: Hexaflexagons

(For more comprehensive instructions, I recommend the video explanation made by PPO.)

Step 1: Before I even started folding, I had to get my physical iteration of my private key ready. My currency of choice for this wallet happened to be Monero. Now Monero carries a strong emphasis on security, privacy and the untraceable, which means procuring a paper wallet comes with a couple of interesting requirements.

The developers of the Monero paper wallet on Monero.how don't like the idea of users sending their private keys into the physical world directly. Instead, they prefer users generate a backup of their seed phrase for a valued address.

"For security reasons, we chose to create a paper wallet that requires us to write the seed onto it with a pen instead of printing the information directly onto the wallet. This is to avoid security threats from compromised printers and compromised smartphone QR readers. When you print something, there is a good chance that the images are being sent unencrypted across your network and stored unencrypted in the printer's memory even after the printing is complete. Because printer firmware tends not to be security hardened, it is not inconceivable that a virus could exist either now or in the future that would scan all print jobs for anything resembling a cryptocurrency key and transmit it to an attacker. We sleep better at night knowing that we used a pen."

-Monero.How

And this is fine advice, of course. The air gap is an important quality for ensuring the integrity of your private keys or seed phases. It's also good advice for anybody out there looking to print conventional wallets. If you must use a printer to produce your private key, make sure it's an older printer without memory. It's also important to ensure that the job is sent through a USB printer cable, not over an unsecured network.

But hey. If you can't hack paper and pencil, you sure as hell can't hack a typewriter. And this way, legibility is guaranteed while fingerprints are non-existent. As a plus, nobody could compare my handwriting in court.

Step 2: So now you got your seed words printed out onto paper. This means that if you really need to, you can export the values of your wallet by generating your private keys from a special set of dictionary words. Now it's time to start getting the paper ready for flexigon-folding.

The trick here is to make the paper an exact two-to-one ratio of squares. For me, that means folding it in half down the middle hamburger style, making two diagonal folds to gauge square distance, and tearing off the remaining portion along the longest edge.

Step 3: The next trick is to fold these two equally sized squares into progressively smaller and smaller subdivisions of squares. Start by folding the paper into squares both hamburger and hotdog style so the end result is each square on each side housing four equal subdivisions.

Once finished with this step, fold each subdivision in half, resulting in a paper with a grid of squares 4x8. Fold the final result inwards in half, hotdog style, from the top and bottom edges. On the back of the white portions, draw the following patterns with a ruler. Each line should have a slope of 1/2 or -1/2, and should be spaced two squares horizontally from its neighbor. It should end up looking like this:

Step 4: Next part's a little tricky. You're basically making folds along each diagonal line of both slope values that extend exactly the distance between slopes. Start by folding a lowermost corner along the first line closest to it so that its tip is just touching the second line. Repeat until you have creases along each of the diagonal lines you've drawn out.

Step 5: You should finish up with what appears to be some sort of band covered in odd little diamonds. Take this band and gently fold it around itself, weaving the first quarter of its length into the last quarter. Once locked in place, it might help to "rotate" this flat band you have, pinching in sections of the triangles around the outer edges.

Step 6: After having folded each of the triangular creases into the loop, try folding the next layer of triangles into the center. Simply grab at the outermost triangular points and fold them into the center. Then do it again. And again. And again. And again.

 

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The concept of hexaflexagons come with no shortage of interesting principles, tying abstract algebra to three-dimensional geometry. They were first discovered in 1939 when British Mathematician Arthur H. Stone found himself bored in class at Princeton. His American papers wouldn't fit into his British paper folders, so he cut off the ends and started playing with the loose strips. After his initial discovery, Bryant Tuckerman, Richard Feynman, and John Tukey joined in with a shared interest for them.

Naturally, the hexaflexagon comes with a couple of useless advantages in regards to cryptography. Since the inwards rotations follow a cycle of four before returning to their original orientation, this means that at least one triple set of triangular faces -- one face from each pyramid -- will always be concealed at any one time. The seed words cannot be read in their completion unless whoever possesses the hexaflexagon is willing to unfold portions of the seed, one at a time. i.e. The seed words cannot be stolen just from being photographed.

In a similar vein, you're always welcome to just fold the seed words inside of the hexaflexagon, keeping the seam sealed with an iridescent security label. But as much as I like shiny stickers, that's still probably not the most secure method of protecting your private information. As it stands, I think an inconspicuous paper toy with cryptic words typewritten along its surface is probably nondescript enough -- especially if you're the only one who knows which currency the seed words generate.

That being said: is it safe to say that yer boy here General Jack had a wonderful time flipping together Hexaflexagons to no end?

We can neither confirm nor deny these assertions. I'll allow for the results to speak for themselves.

For more on hexaflexagons, I strongly recommend both the respective Vihart videos associated with them. For more analysis of the mathematics present in the world of cryptography, I strongly recommend that you follow my wacky ramblings. Let me know if you enjoyed following along with this concept, or if you'd rather like seeing a cryptocurrency folded into some other odd abstraction of geometry.