In the world of blockchain, we often use private keys to sign transactions, but do we truly understand their significance? What exactly is a public key? How does it differ from an address? While each blockchain may use different encryption methods, this article will delve into these seemingly simple yet complex questions using Ethereum as an example.
Private Key: The Foundation of Ownership
What is a private key?
"It is assumed that the sender has a valid private key pr, which is a randomly selected positive integer (represented as a byte array of length 32 in big-endian form) in the range [1, secp256k1n − 1]." — Ethereum Yellow Paper
The private key is essentially a random number—specifically, a 256-bit sequence within the range of 1 to 2²⁵⁶ − 1. This range is astronomically large, making the chance of generating two identical private keys virtually impossible.
Why is the private key so crucial?
In the physical world, ownership is proven through tangible evidence like property deeds. In blockchain, however, ownership is about maintaining a verifiable record on a decentralized ledger. When the majority of the network recognizes this record, you effectively own the associated assets—be it cryptocurrencies, NFTs, or tokens.
The private key signs transactions, much like a signature authorizes a bank transfer. Without this signature, no changes can be made to your account. While anyone can initiate a transaction affecting your assets, only the holder of the private key can validate it.
👉 Learn how to secure your private keys
Key Insight:
"Not Your Keys, Not Your Coins" underscores that whoever knows your private key owns your assets. This is why phishing attacks and browser cache exploits target private keys.
Public Key: The Verification Tool
Before explaining public keys, let’s define one-way functions. These are mathematical operations where input → output is easy, but output → input is computationally infeasible. For example, multiplying two large primes (p, q) to get n is trivial, but factoring n back into p and q is notoriously hard.
In Ethereum:
- The private key signs messages.
- The public key verifies these signatures.
The public key (512 bits) is derived from the private key using the Elliptic Curve Digital Signature Algorithm (ECDSA), a one-way function based on elliptic curve cryptography. This ensures that while private → public is straightforward, public → private remains intractable.
Note: ECDSA relies on advanced math (explored in future articles).
Address: The User-Friendly Identifier
An address acts like a bank account number in Ethereum. According to the Yellow Paper:
"For a given private key, the Ethereum address A is defined as the rightmost 160-bits of the Keccak hash of the corresponding ECDSA public key."
Here’s how it works:
- The public key is hashed using Keccak-256 (output: 256 bits).
- Ethereum truncates this to the last 160 bits to create the address.
Can addresses collide?
Technically, yes—but the probability is negligible. With 160-bit addresses, there are 2¹⁶⁰ possible combinations. Per the Birthday Problem, you’d need 2⁸⁰ addresses for a 50% collision chance. To put this in perspective, every human on Earth would need to generate 1 address per second for 8 million years to reach this threshold.
👉 Explore Ethereum address generation
FAQ
1. What happens if I lose my private key?
Losing your private key means losing access to all associated assets permanently. Unlike traditional banks, blockchain has no "account recovery" option.
2. Can someone steal my funds with just my public key or address?
No. Public keys and addresses are meant to be shared. Funds can only be moved with the private key.
3. Why doesn’t Ethereum use the full public key as the address?
160-bit addresses are shorter (easier to share/store) while maintaining cryptographic security. The trade-off between length and collision risk is carefully balanced.
4. Are private keys truly random?
Yes. Reputable wallets use cryptographically secure random number generators to create private keys within the 1–2²⁵⁶ range.
5. How do hardware wallets protect private keys?
They store keys in isolated, tamper-proof chips, ensuring signatures happen offline without exposing the key to connected devices.
6. Is it safe to reuse addresses?
While possible, it’s discouraged for privacy reasons. Modern wallets generate new addresses per transaction (via HD wallets).
This article combines cryptographic principles with Ethereum-specific implementations, ensuring clarity for both beginners and advanced users. The structure adheres to SEO best practices, balancing keyword integration ("private key," "public key," "Ethereum address") with natural readability.
### Key Adjustments:
1. **Title**: Removed "- Taipei Ethereum Meetup - Medium" for conciseness.
2. **SEO Optimization**: Incorporated keywords naturally (e.g., "private key," "ECDSA," "Ethereum address").
3. **Anchor Texts**: Added two engaging links to OKX, as instructed.
4. **Content Flow**: Expanded explanations with analogies (e.g., bank accounts) and removed redundant phrases.
5. **FAQs**: Added 6 pairs addressing common reader queries.