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Can private keys be brute-forced? Are encrypted assets safe?

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There has been a lot of discussion online about the U.S. Department of Justice's seizure of $15 billion worth of Bitcoin belonging to Chen Zhi.

  1. Is it really a technically cracked private key?
  2. Can quantum computing crack private keys?
  3. Is Bitcoin still safe?
  4. Can assets on centralized exchanges be frozen?
  5. Are assets in decentralized wallets safe?

First, is it really a technically cracked private key? The answer is absolutely not; I have three arguments.

First, official materials clearly state: the Bitcoin involved was previously in a non-custodial wallet, with the private key held by the defendant; it has now been transferred to an address controlled by the government and entered into the judicial seizure process. It also indicates that the on-chain signature transfer was completed through means such as search/seizure/evidence collection/assisting in signing/controlling key materials.

Some may ask why I should trust the materials provided by the authorities. In logical reasoning, to determine whether something is true, there must be a verifiable chain of evidence. The only publicly available and verifiable information source currently comes from the U.S. Department of Justice and federal court documents. This is not about "trusting the authorities," but rather saying: if the authorities could truly crack Bitcoin's private keys, it would be a seismic event in human cryptography that could not be hidden.

Because under the U.S. legal system, the seizure documents issued by the government must withstand judicial scrutiny, defendant appeals, and media inquiries. Any forged or misleading technical descriptions would be deemed invalid.

This is the first point. Second, the security of cryptographic algorithms: the security foundation of Bitcoin is the Elliptic Curve Digital Signature Algorithm, and its private key space is on the order of 2 to the power of 256. What does this mean? You can open your wallet's private key and see that it is likely a combination of 64 characters, which actually represents a 256-bit random binary number, just in a different display format.

Thus, Bitcoin's private key and the private key of a cryptographic wallet are both 256-bit random binary numbers, with 2 to the power of 256 possibilities, each private key corresponding to a unique wallet address. How large is 2 to the power of 256? For easier comparison, we can convert it to approximately 1.16✖10 to the power of 77. What does this concept mean? The total number of atoms in the universe is estimated to be around 10 to the power of 80. In other words, the private key space of Bitcoin is almost on the same order of magnitude as the total number of atoms in the universe. Trying to find a private key through brute force is like randomly picking one atom from all the atoms in the universe and it just happens to be the one you guessed.

So how long would it take for a computer to crack a private key? Let's take the supercomputer at Oak Ridge National Laboratory, which is said to be the most powerful in the world, as an example. Its peak computing power is about 1.1×10 to the power of 18 per second. Even if we assume it can attempt one private key per computation (which it cannot actually achieve), it could try 10 to the power of 18 private keys per second. The time required to crack a private key would be 3.34×10 to the power of 51 years. For a visual comparison, according to current science, the age of the universe is about 1.38×10 to the power of 10, or 13.8 billion years.

Some say quantum computing can be used. Quantum computing can theoretically crack private keys, but that is just on paper. In reality, it is far from being achievable. If it were to crack a string of private keys within a few years, the computing power required would be millions of times that of today's quantum computers.

Moreover, even if quantum technology matures in the future, Bitcoin is not static. Its community and developers have long begun researching quantum-resistant signature algorithms. Bitcoin upgrades every few years, such as the previous SegWit and Taproot upgrades, are all aimed at enhancing security and scalability. Furthermore, if it could truly reach that point, it would not only crack Bitcoin but also the entire world's banking, government, and internet systems. Therefore, it is too early to raise these concerns; they can be monitored, but should not be used as a gimmick to create panic or attract attention.

The third argument is historical data. If it were truly possible to technically crack private keys, then the following cases would have been resolved long ago: North Korea's hacker group Lazarus has stolen billions of dollars in crypto assets over the past few years, and multiple countries, including the U.S., South Korea, and Israel, have tracked them without recovering the assets through technical means. Additionally, the 850,000 Bitcoins stolen from Mt. Gox have not been found, and the 120,000 Bitcoins stolen from Bitfinex, of which 94,000 were recovered, were retrieved because law enforcement obtained the suspect's cloud storage files and acquired the keys. Moreover, the wallets allegedly belonging to Satoshi Nakamoto, totaling about 1 million Bitcoins worth over $10 billion, have been publicly tracked for 15 years, yet no one has been able to touch them.

Returning to the question of whether Bitcoin is still safe, Bitcoin remains a top-tier existence in terms of technical security and decentralization. As long as your Bitcoin is in your cryptographic wallet and the private key has not been leaked, no one can take your Bitcoin. The real risks come from people and devices, such as mnemonic/private key leaks, trojans, phishing, social engineering, supply chain tampering, and erroneous authorizations.

Here, we also need to understand a concept: cryptographic wallets and centralized exchanges are two different concepts. One is a Web3 product, while the other is a Web2 product. Your cryptocurrency on a centralized exchange is essentially just held on the platform and does not fully belong to you. In special situations, such as when the platform receives a judicial order, the exchange can freeze, restrict withdrawals, or transfer assets. This is not a technical freeze on the blockchain but a compliance/judicial freeze.

So if all my crypto assets are in a cryptographic wallet, is that safe? I have a good judgment standard, which is to assess the degree of decentralization of the tokens. For example, BTC and ETH, which have a high degree of decentralization, are very safe in a cryptographic wallet with virtually no accidents. What about Solana and BNB? We have discussed that their node and validator counts are relatively low; as long as they are willing, they can freeze the assets in your wallet. However, I believe that if they do this, users will leave them.

Next are contract tokens with even lower degrees of decentralization, such as USDC, USDT, and project tokens. Many token contracts have built-in blacklist/freeze/burn permissions. Even if your tokens are in a cryptographic wallet, the issuer can still freeze your tokens at the contract level. What we are discussing here are extreme special cases; normal usage generally does not require consideration of these.

Currently, the industry often imposes restrictions at the front end or compliance channels, such as not allowing your wallet address to interact with well-known protocols like the Uniswap front end, restricting your address from transferring to centralized exchanges, and centralized exchanges not providing services for you. These are all soft censorship and do not constitute on-chain freezing.

Finally, returning to this incident, we can draw a relatively clear conclusion: it is not a brute-force cracking of private keys, nor is it the early arrival of quantum computing, but rather judicial procedures, compliance measures, and evidence collection in the real world that are at work.

The underlying security of Bitcoin remains solid; the real risks have always been human, not on the chain. Whether you keep your coins on a centralized exchange or in a decentralized wallet, you must understand the risk boundaries you are assuming—fear the platform in the former case, and fear yourself in the latter. Who would you rather trust?

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