What is Entropy?
In cryptography, entropy is unpredictability — the measure of how many equally likely possibilities a secret could be. Every bit of entropy doubles the search space. A wallet’s security is decided at exactly one moment: when its randomness is generated.
- 128 bits of entropy = 2¹²⁸ ≈ 3.4 × 10³⁸ possibilities
- A 12-word seed phrase encodes 128 bits; a 24-word phrase encodes 256 bits
No supercomputer fleet can exhaust 128 bits by brute force. This is why the public BIP-39 wordlist doesn’t weaken wallets: knowing the dictionary doesn’t narrow down which 12 of 2,048 words were randomly chosen.
Where Entropy Comes From
Good wallets generate entropy from hardware sources that are physically unpredictable — chip noise, sensor jitter, user input timing — and often combine several sources. The danger zone is low-quality entropy:
- Wallets built by amateurs using standard random number seeds (repeated across devices)
- JavaScript
Math.random()— predictable, never cryptographic - Keys generated on compromised devices where an attacker can observe or influence the “randomness”
Famously, in 2023 an attacker swept funds from wallets created by a compromised library (libbitcoin) whose entropy was being silently recorded. The math was fine; the randomness was not.
Entropy vs Human-Chosen Secrets
Humans are terrible entropy sources. Song lyrics, birthdays, and “random-looking” phrases chosen by a person have a tiny effective keyspace and fall to dictionary-style attacks. That’s why brain wallets — passphrases converted into keys — are considered catastrophically insecure: attackers pre-compute keys from entire song corpora, books, and quote databases and sweep them continuously.
Rule of thumb: if you chose it, it’s not entropy. Let the wallet generate the randomness; your job is only to store the resulting phrase offline.