Bitcoin Wallets: Using Math and Randomness Defensively - WiM Weekly

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Apr 04, 2025

A common question from Bitcoin Newcomers: What if someone hacks my Bitcoin wallet by guessing my seed phrase?

Valid question. After all, if someone were able to correctly guess your seed phrase, they could reconstruct your private keys and transfer your Bitcoin to an address they control. But once you understand how Bitcoin wallets function, and the sheer scale of randomness involved, you’ll see why this threat, in practical terms, is unfounded.

What Is a Seed Phrase?

At the core of your Bitcoin wallet is something called a seed phrase: a sequence of 12 or 24 words in a precise order. These 12 or 24 words are the human-readable version of a large binary number: 128 bits for a 12-word phrase, or 256 bits for a 24-word phrase (A 256-bit number is a number made up of 256 digits, where each digit is either a 0 or a 1).

Instead of displaying your seed phrase as a long string of 1s and 0s, your Bitcoin wallet maps that binary number onto 12 or 24 words pulled from a standardized list known as BIP39. 24 words are much easier to write down and/or remember than a string of 256 0’s and 1’s. The binary number and the list of 12 or 24 words represent the same thing, just expressed differently. The BIP39 standard was created specifically for the backup and recovery of Bitcoin wallets. No two words on the list share the same first four letters.

Bitcoin wallets use this binary number (remember this is the same as your 12 or 24 words) to derive your private keys, public keys, and Bitcoin addresses. If your wallet is lost or destroyed, you can enter your seed into a new device and your entire wallet will be regenerated (hence why seed phrase is often called a recovery phrase).

Why True Randomness Matters

The key to Bitcoin wallet security is entropy and randomness. Your seed must be generated in a way that maximizes unpredictability. This can be done physically (using coin flips or dice rolls) or digitally via a true random number generator (TRNG), which is built into most modern hardware wallets.

Do not create your seed phrase from familiar phrases, quotes, song lyrics, or Bible verses. These are highly predictable and easily indexed by bots scanning public data. Anything short of true randomness dramatically reduces the number of possible combinations, and with it, your security.

Can Someone Brute-Force a Seed Phrase?

Let’s explore the math.

Like we discussed above, Bitcoin seed phrases are built from a fixed list of 2,048 words (BIP39).

A 1-word seed has 2,048 combinations.
A 2-word seed: 2048² = ~4.2 million combinations (2,048 * 2,048)
A 3-word seed: ~8.6 billion combinations (2,048 * 2,048 *2,048)
A 12-word seed: 2048¹² = ~10³⁹ combinations.
A 24-word seed: ~10⁷⁷ combinations.

The number of combinations of a 24-word seed expressed in numeral form is:
115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936

To put this in perspective, it’s estimated that there are ~10⁸⁰ atoms in the observable universe. Someone hacking your Bitcoin wallet by guessing your seed phrase is like sending someone on a scavenger hunt to find a single atom in the entire universe. Good luck with that!

In the world of cryptography, randomness and large numbers are what protects you. Generate your seed phrase using true entropy, store it offline, and consider looking into multi-sig wallets if you’re holding a substantial amount of your net worth in Bitcoin (whatever “substantial” means to you in this context). In my opinion, a geographically distributed multi-sig wallet is best-in-class for Bitcoin custody.

When done properly, this simple list of words becomes the most secure and censorship-resistant way to store purchasing power in human history.

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WiM567 with Tom DiLorenzo

"The Fed was created in 1913. One of the first things it did was to print up enough money so that we could enter World War I. I doubt that we could have entered World War I, participated in World War I, without the Fed. And what a calamity that was. They had nothing whatsoever to do with us in this country. It led to Stalin taking over Russia, and Hitler later on. The Bolsheviks were an anti-war party during World War I. Woodrow Wilson, the president of the United States at the time, paid the Russian government, the Czar, to participate in World War I. Lenin himself once said, 'The war made our party.' Because that's how the Bolsheviks, the Communists, took over Russia. And it was Woodrow Wilson paying them. And the Fed allowed him to do it. Before that, whoever heard of a president of the United States giving a foreign government hundreds of thousands or millions of dollars to do anything? But with the Fed, they just print it up, and it's legalized counterfeiting."

Sound Money vs the State: How Inflation Fuels Corruption w/ Tom DiLorenzo (WiM567)

WiM568 with Dave Birnbaum

"I work in a space where we're bridging fiat to Bitcoin, so I see every day how fiat is reversible and very unstable. Bitcoin, by contrast, is very solid. The question is—how solid is that, really? I read an article by Patrick McKenzie, who says final settlement is a socio-legal construct—it doesn’t actually exist. That blew my mind. He basically sums it up by saying: if you and the United States government disagree on whether a transaction is final, you are wrong. In other words, the state can use its power to reverse a Bitcoin transaction—if the parties involved are known. If the parties are known, one or both can be coerced to reverse the transaction. It doesn’t have to happen on-chain—property can be confiscated. It really comes down to whether you're willing to be put in a cage over your transaction. So, I actually don’t think any non-private Bitcoin transaction is truly final."

The full episode with Dave Birnbaum and Robert Breedlove will go live today (4/4/25) at 3:00pm EST.

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Next Week:

4/8 with Geoff Woods

Geoff Woods is the #1 bestselling author of The AI-Driven Leader, host of the AI-Driven Leader podcast, and Founder of AI Leadership and The AI-Driven Leadership Collective, a network of executives collaborating to harness AI to build better businesses and better lives.

4/11 with CJ Konstantinos

CJ Konstantinos is the founder of “People’s Reserve” which is revolutionizing finance by building around Bitcoin equity as the most pristine form of collateral in the world.