What is entropy in a wallet?
- Author
- CRYPTO PORT Editorial
- Published
- Updated
- Reading time
- 5 min
In short
Entropy measures how unpredictable the random value behind a key is. Wallets standardise on 128 bits or more, at which point brute force is out of reach. Seed something a human invented — a phrase, a date — and the funds are typically taken within hours.
Key points
- Unpredictability measured in bits
- 12 words carry 128 bits, 24 words carry 256
- Human-chosen strings have far less entropy than they look
- Poor randomness makes key length irrelevant
Definition
A logarithmic measure of unpredictability: the number of possible values a random secret could take. Each additional bit doubles the search space.
128 bits of entropy means about 3.4 × 10^38 candidates — beyond the reach of all the computing power on earth. In BIP39, 128 bits is 12 words and 256 bits is 24. The longer phrase is genuinely stronger, but since 128 bits is already unbreakable by search, the practical gap is narrow.
The real issue is the quality of the randomness. Wallets draw from the operating system's cryptographic generator, and hardware wallets use a dedicated source. Values that merely feel random — something you thought up — carry far less entropy. 'Brain wallets', which hashed a memorable phrase into a key, were emptied systematically by dictionary attacks.
If you want to supply entropy yourself, dice rolls are the known method: one six-sided die gives about 2.58 bits, so roughly 50 rolls reach 128 bits. Getting the procedure subtly wrong introduces bias, which is why delegating generation to a hardware wallet is usually the safer choice.
Watch out for
- · Keys derived from memorable phrases have been drained at scale in practice
- · Online random generators cannot prove they did not log what they produced
- · Second-hand or pre-opened hardware wallets may have had their randomness fixed in advance