Public Key

How public keys work

The cryptographic foundation:

• Public key is mathematically derived from a private key using elliptic curve cryptography.
• One-way derivation — private to public is easy; reverse is computationally infeasible.
• Wallet address is typically derived from public key (with hashing and encoding).
• Used for verification of signatures created by the private key.

Anyone can verify a signature using the public key without knowing the private key.

Public key vs. address

A subtle distinction:

• Public key — cryptographic object derived from private key.
• Address — human-readable identifier derived from public key (typically through hashing).
• Different formats — public keys are longer; addresses are typically shorter.

For Bitcoin and Ethereum, what users see and share is the address, not the public key directly.

Why public keys matter

Several roles:

• Signature verification — anyone can verify your transactions are legitimate.
• Address derivation — provides privacy until you actually transact.
• Encryption — sensitive data can be encrypted to a public key (less common in crypto than in PGP-style systems).

The public key system is what makes self-custody crypto possible.

When public keys are exposed

A subtle privacy point:

• Address is shared publicly to receive funds.
• Public key is only revealed when you actually transact (the public key is needed to verify the signature).
• For Bitcoin specifically, this matters — pre-transaction, only address is known; post-transaction, public key is exposed.

This affects long-term privacy and quantum-computing concerns. Some Bitcoin best practices recommend not reusing addresses partly because of this.

Public key cryptography

The fundamental technology:

• Asymmetric encryption — different keys for different operations.
• Standard since 1970s — RSA, then elliptic curve variants.
• Foundation for HTTPS, SSH, GPG, and crypto wallets.
• Mathematical guarantees are quantum-vulnerable for current schemes.

Quantum resistance is an active research area; future cryptography may need updating to handle quantum computers.

Public-key infrastructure

In broader IT:

• Certificates verify ownership of public keys.
• Certificate authorities issue and verify certificates.
• TLS/HTTPS uses public-key crypto for secure communication.
• PGP/GPG uses for email encryption.

Crypto's use of public-key cryptography is one specific application of broader cryptographic infrastructure.

Address derivation

Different chains use different methods:

• Bitcoin — RIPEMD-160(SHA-256(public key)) plus encoding.
• Ethereum — last 20 bytes of Keccak-256(public key).
• Different encoding formats — Base58 for Bitcoin, hex for Ethereum, others.

These produce different-looking addresses despite similar underlying cryptography.

What individuals should know

For most crypto users:

• You see addresses, not public keys — that's normal.
• Address sharing is safe — receiving address can be public.
• Don't share private keys — that's the security-critical object.

For privacy-conscious users:

• Address reuse exposes more on-chain history than necessary.
• Hierarchical deterministic wallets automatically generate new addresses.
• Bitcoin specifically benefits from address rotation.

Public keys are foundational cryptographic objects underlying all crypto. For most users, they operate invisibly through address abstraction. Understanding their role provides better mental model for how crypto self-custody actually works.