Module 2: Private Keys, Public Keys, and Bitcoin Addresses

2.1 Introduction

Bitcoin ownership is not stored inside the blockchain. Ownership is based entirely on who can produce valid cryptographic signatures proving they have control of unspent Bitcoin outputs (UTXOs).

The ability to create these signatures depends on private keys.

Understanding private keys, public keys, and addresses — and how they are mathematically linked — is essential for designing, securing, and reasoning about Bitcoin wallets.

2.2 What is a Private Key?

A private key in Bitcoin is simply a random 256-bit number. It is often represented in hexadecimal format — a string of 64 characters (0–9, a–f).

Example private key (in hex):

Private Key Example

Key facts:

Randomly generated.

Must be kept secret — whoever knows it controls the associated Bitcoin.

Cannot be feasibly guessed or brute-forced (the keyspace is astronomically large).

In Bitcoin:

Private key = ownership.

If a user loses their private key, they lose access to their Bitcoin permanently.

If a private key is exposed to an attacker, the attacker can spend the Bitcoin instantly.

2.3 From Private Key to Public Key

Using elliptic curve cryptography (specifically the secp256k1 curve), the private key can generate a public key.

The public key is derived through a one-way mathematical function:

Easy to compute public key from private key.

Practically impossible to compute private key from public key.

The public key acts like a "locking mechanism" — Bitcoin transactions lock coins to public keys (via scripts).

There are two common formats for public keys:

Compressed: 33 bytes (starting with 02 or 03)

Uncompressed: 65 bytes (rarely used today)

Example compressed public key:

Public Key Example

2.4 From Public Key to Bitcoin Address

To create a Bitcoin address from a public key:

Hash the public key using SHA-256, then RIPEMD-160.

Add version prefixes depending on the address type (Legacy, SegWit, Taproot).

Encode into a human-readable address format.

Different Bitcoin address types:

type	prefix	example format
Legacy (P2PKH)	Starts with 1	1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa
SegWit (P2SH)	Starts with 3	3J98t1WpEZ73CNmQviecrnyiWrnqRhWNLy
Native SegWit (Bech32)	Starts with bc1q	bc1qw508d6qe...
Taproot (Bech32m)	Starts with bc1p	bc1p5cyxnuxmeuwuvkwfem96l5xu6s7kz8mz0w5d3r7c0f3z95zmsxqjqs4kdk

The address is what the user shares publicly to receive Bitcoin. The private key remains secret and enables spending.

Flow Diagram:

Key Derivation Flow

2.5 Private Keys and Seed Phrases

Managing raw private keys directly is dangerous and error-prone for users.

Bitcoin wallets usually use a mnemonic seed phrase (based on BIP39 standard) to simplify key management.

12 or 24 English words

Encodes the random entropy that can derive private keys deterministically

Easy for humans to back up securely

Example 12-word seed phrase:

Seed Phrase Example

From this seed, the wallet can derive:

Master private keys

Public keys

Bitcoin addresses

Seed phrases are the root of all control in a Bitcoin wallet.

2.6 Critical Properties to Understand

property	why it matters
Private keys must be kept absolutely secret	Losing control means losing Bitcoin.
Public keys are safe to share (only indirectly through addresses)	No risk from sharing addresses.
Addresses are disposable	Users can generate unlimited addresses safely.
Seed phrases must be backed up securely	Loss of seed = permanent loss of Bitcoin.
Private keys are never stored on the blockchain	Only public information (addresses, scripts) is visible.

2.7 Product Implications for Wallet Builders

Backup UX:

The most important product journey is the backup flow. Force users to backup the seed phrase properly during onboarding. Offer reminders and backup verification challenges (e.g., "Enter word 6 of 12").

Key Storage:

Private keys should be encrypted on-device. Never transmit private keys over networks. If cloud backup is offered, encrypt the seed client-side before upload.

Recovery UX:

Wallet recovery is based entirely on entering the correct seed phrase. There is no server-side recovery unless you build a separate encrypted backup system.

Security Warnings:

Users must be warned:

Never share their seed phrase.

Never enter their seed phrase into any unknown app or website.

Future-Proofing Future-Proofing:

Use libraries that allow multiple address formats (Legacy, SegWit, Taproot) from the same key material.

2.8 Diagram: Full Chain of Control

Full Derivation Chain

##W## 2.9 PM Reflection Points

If you are building or managing a Bitcoin wallet product:

Every product decision around wallet creation, backup, and recovery must respect the sacredness of the private key and seed phrase.

Users are not just "creating accounts" — they are creating irreversible keys tied to real economic value.

Every seed lost is Bitcoin destroyed. Every seed leaked is Bitcoin stolen.

UX should guide users to act like custodians of serious money — because they are.

Product managers must design with the mentality that "every user is holding their own bank vault," not just "installing another app."

Module 2 Complete

We now have a solid, real understanding of how Bitcoin ownership works — how private keys, public keys, and addresses connect — and why wallets are critical key managers, not simple databases.