How hard is it to crack a private key?

Even though modern encryption methods are very secure in theory, in real life, the biggest risks often come from how private keys are handled, not from someone actually breaking the encryption. Common mistakes include creating keys using weak random number sources, saving keys without encryption or strong passwords, getting hacked by malware, or having keys stolen through phishing scams. So, how hard is it to break a private key? Let’s find out.

Breaking vs Stealing

It’s critical to understand the two primary ways your private key can be compromised:

• Breaking a Private Key: This involves a hacker using immense computing power or advanced mathematics to guess your key – a complex, highly improbable task akin to cracking an extremely long and intricate password.
• Stealing a Private Key: Far more common, this happens when someone gains direct access to your key due to poor security practices or deception. Imagine leaving your house key under the doormat or being tricked into handing it over.

Most breaches occur through theft, often via malware or phishing scams that exploit user errors.

Your Private Key should ideally never be exposed to an internet-connected device – a hardware wallet is a good first step to guard against this common threat

What Exactly Is a Private Key?

At its simplest, a private key is just a very large, random number. [1]For things like Bitcoin, it’s essentially a number picked from an enormous range – imagine picking a number between 1 and 2256. The key to its security is that this number must be truly random and impossible to guess or predict. Computers use special processes to ensure this randomness, turning unpredictable data into your unique key.

Risks to key security

2 primary risks:

• Internal Risk: If a private key is generated poorly (e.g., using a weak random number generator), it could be easier to guess. Using reputable wallets eliminates this risk.
• External Risk: Advanced technologies, such as quantum computers, could theoretically pose a future threat by guessing keys faster, though this is not currently feasible.

How hard is it to crack a private key?

Complex Mathematics:

Bitcoin uses Elliptic Curve Cryptography (ECC) with the secp256k1 curve, which requires solving a highly complex mathematical problem called the discrete logarithm problem. A 256-bit ECC key has 2^256 possible combinations—a number vastly larger than the grains of sand on Earth.

Unimaginable Timeframes:

Even if a supercomputer could test a trillion keys per second, cracking a 256-bit ECC key would take roughly 10^65 years. For context, the universe is only about 13.8 billion (1.38×10^10) years old, making such an attack infeasible.

Are Quantum Computers a Threat?

Bitcoin’s cryptographic systems – ECDSA for digital signatures and SHA-256 for mining and address generation – are secure against today’s quantum computers. Here’s the breakdown of concerns about quantum computers breaking Bitcoin’s security:

• Current Quantum Limitations[1]: As of now, quantum computers (e.g., systems with ~100–200 qubits from companies like Google or IBM) are far too weak to threaten Bitcoin. Breaking ECDSA would require a quantum computer with approximately 2,500–3,000 logical qubits, which, factoring in error correction, could translate to millions of physical qubits – decades beyond current technology.
•  SHA-256 Resilience[2]: Quantum computers using Grover’s algorithm could theoretically reduce the time to attack SHA-256, but it would still require ~2^128 operations, demanding thousands of logical qubits and impractical timeframes. SHA-256 remains highly secure.
• Specific Vulnerabilities: Quantum computers could theoretically target public keys if they are exposed on the blockchain. This risk applies to:
  • Reused Addresses: Reusing a Bitcoin address may expose its public key, creating a potential vulnerability if quantum computers advance significantly.
  • Older P2PKH Transactions: Pay-to-Public-Key-Hash (P2PKH) addresses (starting with “1”) reveal the public key when funds are spent, offering a brief window for attack.
  • These cases are limited, as modern wallets encourage single-use addresses, and newer formats reduce public key exposure.
• Future-Proofing: The Bitcoin community is proactively addressing quantum risks by exploring Post-Quantum Cryptography (PQC)[3], such as lattice-based algorithms. Proposals like Schnorr signatures (BIP-340) and potential PQC integration are under discussion, with upgrades likely in the 2030s to ensure long-term security.

(Source: How long would it take a large computer to crack a private key?)

This 5-minute video on 256-bit encryption is well worth a watch:

Recommendations for creating and protecting private keys

To keep private keys safe, both individuals and organizations should follow some basic best practices. These fall into three main areas: key creation, storage, and backup.

Key generation

• Use trusted and open-source tools to create your private keys. Avoid unknown or unverified software.
• Make sure the system uses a strong source of randomness (such as /dev/random, a Hardware Security Module (HSM), or a Trusted Platform Module (TPM)).
• Bitcoin uses the secp256k1 ECC algorithm, which is secure when properly implemented. Future PQC algorithms may be adopted as quantum threats evolve.

Address generation

• Taproot (P2TR): Starting with “bc1p,” these offer the best security and privacy. Public keys are typically revealed only when spending funds, minimizing exposure, and Taproot’s design enhances quantum resistance.
• Native SegWit (P2WPKH): Starting with “bc1q,” these are also highly secure, revealing public keys only during spending, making them a strong alternative to Taproot.
• Older P2PKH Addresses: Starting with “1,” these are less efficient and lack modern security improvements. While public keys are also revealed only when spending (not when receiving), the format is more susceptible to script-level limitations and lacks malleability protections, making it a weaker choice going forward.

Key storage

• Never store your private key as plain text on a device that could be accessed by others.
• Use hardware wallets or secure hardware devices like HSMs to keep keys safe.
• Protect the key with a strong password, and use two-factor authentication (2FA).

Key Backup

• Always have at least one backup copy of your private key, stored in a separate and secure location away from the main system.
• If you use multisig (multiple private keys to approve a transaction), make sure to back up each key individually. This reduces the risk of losing access to all funds if one part is lost.

Does Multisig or MuSig improve security?

Multisig (Multiple Signatures) requires more than one key to sign a transaction before it is accepted. This method offers several key benefits:

• Better security: Even if one key is stolen, the attacker can’t access your funds without the others.
• Shared responsibility: The keys can be split between different people or devices, reducing the impact of a single point of failure.

MuSig (Multi-signature Aggregation) is a more advanced and efficient version of multisig, used in systems like Bitcoin with Taproot. Its advantages include:

• Smaller transaction size: It combines multiple signatures into one, saving space and reducing transaction fees.
• More privacy: To outsiders, a MuSig transaction looks just like a normal transaction from one person, helping protect privacy.
• Stronger security in some cases: If implemented properly, MuSig helps prevent certain attacks like rogue key attacks, which traditional multisig is more vulnerable to.

MuSig increases the overall security of the system by requiring multiple keys to work together while reducing the risk of a “SPOF” (“Single-Point-of-Failure”).

Need further guidance?

Our in-house Cybersecurity team at BitcoinVN offers 1:1 consulting sessions designed to help you take full control of your digital assets – securely and confidently.

Whether you’re just getting started with self-custody, exploring advanced setups like MuSig, or want to harden your operational security, our experts will guide you step-by-step toward true self-sovereignty. No fluff, no shortcuts – just practical, Bitcoin-native security tailored to your needs.

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