Overview
In Ethereum, a private key is 256 bits long (64 characters, 32 bytes), while the derived address is 160 bits (40 characters, 20 bytes). According to the Pigeonhole Principle, with enough private keys generated, collisions are inevitable. Theoretically, there are 2²⁵⁶ possible private keys mapping to 2¹⁶⁰ unique ETH addresses, meaning at least 2⁹⁶ private keys will share the same address.
Key Questions
- Ownership: If two private keys point to the same address, do both retain control over its funds?
- Security: Could a private key collision allow unauthorized access to assets?
Technical Explanation
Private Key Generation Limits
Ethereum’s private keys are generated within the bounds of the secp256k1 elliptic curve, defined by a constant N (hex: FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141). This restricts the total valid private keys to N - 1, reducing collision risks compared to the full 2²⁵⁶ space.
- Code Insight: Ethereum’s
go-ethereumenforces this viacrypto/secp256k1, rejecting out-of-range keys. - Implications: While multiple private keys could map to one address, practical generation methods minimize overlaps.
Address Collision Scenario
If two private keys (k and k’) satisfy k ≡ k’ mod N, they produce identical public keys and addresses. Both can sign transactions for the same address, but Ethereum’s decentralized nature makes such collisions astronomically rare.
FAQs
Q1: Can private keys collide?
A: Yes, but probabilistically negligible (~1 in 2¹²⁸ for SHA-256). Ethereum’s key-space restriction further mitigates this.
Q2: Are NEO’s private keys similarly constrained?
A: NEO’s key generation relies on .NET’s RandomNumberGenerator, which lacks explicit bounds checks. This increases theoretical collision risks compared to Ethereum’s secp256k1-bound keys.
Q3: Could a coordinated brute-force attack crack ETH addresses?
A: The computational cost (≈2¹²⁸ operations) and energy requirements render this infeasible with current technology.
Summary
- ETH Safeguards: Ethereum’s
secp256k1curve limits valid private keys, preventing shared-address scenarios. - NEO’s Approach: Uses broader randomization, potentially higher collision risks but still practically secure.
👉 Explore Ethereum’s cryptographic design
For deeper dives, see Ethereum’s S256() implementation or NEO’s wallet.cs.
Final Note: While theory suggests vulnerabilities, real-world blockchain security remains robust against private-key collisions. Always use trusted libraries for key generation.