In Math We Trust

Every man and his dog will tell you to keep your Bitcoin seed phrase safe.

Store it off-site on a hardware wallet. YES. Storing on an exchange is a terrible idea.

Use a 24-word seed phrase. YES. 12 words are nowhere near as safe.

Don’t let anyone see it. NOT QUITE

I don’t expect you to believe me about the last statement. You shouldn’t.

For thousands of years, gold has been the best store of value. Why? Physics protects gold. It’s tough to fake and doesn’t rust or decay. Bitcoin is also tough to fake and doesn’t rust or decay. Every aspect of Bitcoin is protected by math. Math is invisible, weightless, and formless.

Math -v- Physics. No contest.

You know those movies where the hero slices the baddie in half with one sweep of their sword? For a moment, the villain doesn’t realise they are dead. Then they keel over. It's just a question of time.

You don’t have to be a math whizz to understand my explanation. Just get your Smart Phone out and follow along. I don’t expect you to believe me. I don’t want you to believe it. Just be a scientist.

In the following screenshots, I am using an iPhone calculator. Just turn your phone sideways to get the advanced calculator, and ensure you have cleared the memory with the AC button.

Type the number 3 and press the x! button. It‘s on the left, just above Rad.

The screen will display the number 6. Here’s what happened. You just used a built-in formula which says multiple three by two by one. 3 x 2 x 1 = 6.

If you want to check, clear the memory and do the same with 4. The answer is 24 because 4 x 3 x 2 x 1 = 24). This formula is called a factorial. It shows you the total number of combinations possible. If you have three widgets, there are six possible ways to arrange them. With four widgets, that jumps to 24.

With me so far?

Now clear the memory and type 23 and press the x! button. The result is so big it just tells you how many zeroes are on the end. The e stands for exponent and the number after tells you how many zeros. For example, e13 is a trillion. This number is e22. You can read about e here.

Now multiply that result by 8. Again a vast number with lots of zeros. Now the exponent is 23.

So what have we done? Your 24-word seed phrase comprises twenty-three words selected from the BIP-39 list of 2,048. The last word is a checksum. It makes sure you haven’t entered any word incorrectly. There are only eight possible checksums for every seed phrase of twenty-three words. So that is why we got the factorial of twenty-three and multiplied the result by eight.

It’s a huge number. Can’t a computer find the right combination by going through all the possibilities?

Let’s see. I’m saying that it would take a million years to crack.

So now divide the result on your screen by one million. Notice it’s the same number but e17, not e23 because it's a million times smaller.

Now divide that by 365 to see how many calculations you must do daily.

Now divide again by 24 to get the number of calculations every hour.

Divide it again by 60 to get the calculations every minute.

Divide it again by 60 to get the calculations required every second.

The result tells you your computer will need to check 6.5 billion possibilities every second of every hour of every day of every year for a million years — no time off for breaks.

(The same computer would only need to check ten possibilities a second to brute force a 12-word seed phrase in a year at most. That’s why 24-words are better.)

The mythical computer may get lucky and find the answer in the first 1%. That still takes 10,000 years. Even more random, and it hits the jackpot in the first 0.01%—still a hundred years. Even luckier, and the answer is in the first 0.001% or ten years. How much energy do you think it will take, by the way?

Today there is no such computer. I don’t think a quantum computer will be able to do it faster. There is no shortcut for brute force attacks like this. You have to try every combination. It’s the same as bitcoin mining. You will see ignorant articles saying miners must solve incredibly complex math problems. Nonsense. It’s a bingo card. The first one to shout ‘house’ wins.

Would you care if your seed phrase was cracked in a million years? Probably not. What about a hundred years? Or ten years. You can always move funds from one wallet to another yearly, and the poor little computer would have to start again.

With me so far?

To recap.

There are billions of trillions of combinations. No computer could check all possibilities in any time frame that matters.

So what has that got to do with your seed phrase?

Back on earth, you store your seed phrase at home, right? It’s convenient. You know it’s dumb. But you want it close to you. It feels safer. If you lost access to your wallet, you know you can enter your seed phrase and be back up and running in a few minutes.

Here are three common ways you might have to rebuild your wallet.

1. You do a software update, and something goes horribly wrong. You know there is a message which says, ‘make sure you have your seed phrase before doing this update’? That's for a reason. It happens. It happened to me. That’s why I wrote this.

2. You entered your hardware wallet passphrase three times wrong. You are locked out. The only way, and I mean the only way, to recover your wallet is with your seed phrase. Which is where?

3. The wallet broke. Either something physical or something electronic doesn’t work. Again it happened to me.

Here are three common ways to lose your seed phrase. There are more.

Lost, mislaid, damaged

Here are three less common ways:

Fire, flood, theft.

There are plenty of other ways to lose access. Forever.

Back to math.

Here is the implication. You can safely write your seed phrase alphabetically. You can even print the alphabetical list on a steel plate if you want to. The printer won’t be able to crack it.

If you are paranoid, you can print the sequence but not the words on a steel plate. It will just be a list of numbers from 1–24.

OK, why would you do that? Because now you really can store your seed phrase somewhere safe but not at home. If you ever need to use it, you can use the alphabetical list, which you can keep at home, in your wallet, or wherever convenient.

There is one last question you will have. “If a computer might take a million years to crack the seed phrase, how will little old me reshuffle the words back in the correct order?”

Great question. It turns out that what a computer can’t do, you can very easily. How come?

I will go off on a tangent, but bear with me. Ask yourself this question. Why do humans have brains? It’s probably a question you have never asked. We have brains, don’t we? Yes, but why?

Here’s a clue.

Think about all the different kinds of life forms on the planet. Imagine a football stadium. On one side, there are representatives of all the life forms which don’t have a brain. Let’s not get too esoteric. I mean, they don’t have neurons. Things like grass, trees, flowers, bacteria, viruses.

On the other, the ones with brains. Bees, cows, birds, ants, and us. What's the difference? You don’t need a brain if you don’t move voluntarily. Moving through three-dimensional space requires a brain and a memory system to recall previous routes. It’s a very complex thing to learn, as any robot designer or parent will tell you. That memory system is grounded in images, sounds, smells, tastes, and touch. Those images then form the basis of language. All language is metaphorical. This brings us back through a million years of evolution to you and your seed phrase.

Because the words are written down (ideally on a stainless steel plate), you can relax. It is unnecessary to memorise them (although that can be fun). You have the exact spelling. You need a simple way to reshuffle them back to the right order. If you can imagine walking through your home, you can do this. How easy is that?

Now in the worst-case scenario, you must go to your safe place. But that’s just annoying. Your current strategy is based on hope. If it fails, it is disastrous.

In Math We Trust. This little formula (23!) * 8 is a miracle.

I founded BinkBonkBank, a website whose purpose is to help plebs self-custody safely. https://www.binkbonkbank.com.