I've read several posts where many people talk about what's happening in the market and with Binance. That's fine—creating content is important, although sometimes it can be tiring, imprecise, and repetitive.
However, I notice that many creators and users are confused or misinformed about how the mathematics behind Bitcoin actually works.
Today we're going to debunk the most common myth of all. We'll focus on what a private key actually looks like. To avoid mixing apples and oranges, we'll leave seed phrases aside, since that's a topic for another article :)
Point 1: The mistake of saying "It’s Impossible"
Many people blindly believe that it is "mathematically impossible" or "simply impossible" to crack the private key of a Bitcoin address, regardless of the method.
The reality: It’s not impossible! A Bitcoin address is based on public-key cryptography using the secp256k1 elliptic curve. For those who are more technical, this corresponds to the mathematical equation:
y² = x³ + 7 (mod p)
To avoid boring you with complex mathematics, I want to clarify that "hacking" in this context actually means "cracking" (breaking it through brute force). To understand this, let’s look at what a wallet looks like "behind the scenes" in two different scenarios. For this example, we’ll use a traditional address (Legacy P2PKH):
Example 1: A hypothetical "weak" key
• Address: 1GNmQzk1cU1FGwLht2CFDmSw96Nn65cmYW
• Private Key (Binary): 101010111100000100100011010001010110 (Only 36 bits)
• Private Key (Hexadecimal): ABC123456 (9 characters)
• Hash160 (Mathematical address): a8a7b25825ae01969065051044da18da09d6cd77
• Security: Exponentially low. Anyone with the right tool could crack it in a matter of seconds.
Example 2: A real Bitcoin key
• Address: 1M8Qk46ERsPrEtWLBRSET5NUH2Ck5wwREU
• Private Key (Binary): 100100011010001010110011110001001101010111100110111101111000000010010001101000101011001111000100110101011110011011110111100000001001000110100010101100111100010011010101111001101111011110000000100100011010001010110011110001001101010111100110111101111
A massive 256-bit number (a string made up of ones and zeros).
• Private Key (Hexadecimal): 0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef (64 characters)
• Hash160 (Mathematical address): dcc93f195534b4c1f4d9c829a6a6c6ebde55b2e8
• Security: Maximum. This is the famous standard 256-bit key.
WARNING: Do not use this test address or key, or any variants, with real money, or you will lose your money!
Point 2: Understanding how security works
In Example 1, an attacker with a decent graphics card (GPU) could set up a focused search range (for example, searching only between 0xABC1.... and 0xABC2....). This drastically reduces the search space and immediately exposes the funds.
Now let’s move on to Example 2. Suppose for a moment that an attacker with colossal computing power (farms full of ASICs or the latest GPUs) and lots of free time decides to scan the network. They use a fully optimized algorithm and, let’s say, have astronomical luck and persistence.
If by sheer chance the attacker manages to find the specific range where the target private key "lives," they could capture it, take full control of the wallet, sign transactions, and sweep all the funds in a matter of seconds.
So, yes! The theory shows that it can be done. In fact, there are some private organizations that help people who have lost their keys or passwords by providing information or hints (real clues) about their keys, giving them a huge chance of recovering their funds.
Point 3: Why does everyone say it’s impossible?
Because in practice it is computationally infeasible, which is not the same as impossible.
Articles on the internet that use the word "impossible" are confusing the terms. The right way to understand it is that with the technology humanity has today, it is ridiculously infeasible.
No one in their right mind would spend millions of dollars on supercomputers and monstrous electricity bills trying to guess a single random private key through brute force. The electricity would cost more than the treasure you’d find.
Is your address safe?
The honest answer is: It depends.
• It depends on whether your keys were generated with real, strong entropy (randomness) within the 256 bits.
• It depends on whether your keys are not in the hands of a third party (an exchange or custodial platform) that has absolute control over your wallet.
• It depends on whether you use paper wallets and only you know their physical location.
• It depends on whether you store your keys on an offline USB drive protected by a strong password.
And one detail many people forget: it depends on how often you update your addresses. When you move funds from an old address to a new one, you protect your security, since when you make a transaction, your public key is permanently recorded and exposed on the blockchain.
Despite the difficulty, groups of people and servers running around the clock are trying to obtain keys through brute force. They compare billions of keys per second to see if any match a real address on the blockchain that contains funds (inputs) they can drain.
Conclusion
Now that you have a clear picture of what lies behind a Bitcoin address, you know the truth: it’s not impossible, but it is computationally infeasible.
In my personal day-to-day life, I prefer to use paper wallets and run my own Bitcoin node when moving funds to maintain my anonymity as much as possible. After all, when you sign a transaction from an address that has been used, everything becomes public and traceable.
If you enjoyed this article, please feel free to follow me and leave your comments! Your support encourages me to keep writing and explaining complex topics in simple terms.
If you’d like a part two, let me know in the comments so I can prepare topics such as: What tools or programs are used to search for keys? What algorithms and metrics exist? Which programming languages are they developed in? What are PSBT files? What types of attacks exist on the blockchain network itself? And so on...
"As a final message, I assure you that most people who incorrectly spread this myth have not the slightest idea how the algorithm works internally, or how to develop their own kernels (optimized code) to make a search or attack on specific addresses feasible."
Note: The content presented is strictly educational. No one is encouraged to do anything improper, and readers are solely responsible for any actions they take using the information obtained in this article.
I’m all ears!