Entropy

Also called: randomness, wallet entropy, seed entropy, bits of entropy, ENT.

Entropy is the randomness a wallet starts from: typically 128 to 256 random bits that a seed phrase encodes and every private key is derived from.

In a Bitcoin wallet, entropy is the random data the wallet is built from, measured in bits. The more unpredictable bits, the harder it is for anyone to guess the wallet.

How much entropy wallets use

BIP 39 lets a wallet start from 128, 160, 192, 224 or 256 bits of entropy (the BIP calls the length ENT). Those bits plus a short checksum become the 12 to 24 words of a seed phrase: 128 bits gives 12 words, 256 bits gives 24. BIP 32 accepts a seed of 128 to 512 bits and recommends 256.

128 bits is already enormous: 2^128 is about 3.4 × 10^38 possibilities. BIP 32 notes that breaking a secp256k1 public key is assumed to take about 2^128 operations, so a 12-word phrase already matches the security level of the keys themselves.

Where entropy comes from

Wallets normally use the operating system's random number generator or a hardware chip. Some people add their own dice rolls or coin flips. What matters is that the source is truly random. BIP 39 is explicit that it is not a way to turn human-chosen sentences ("brainwallets") into seeds, because people are bad at being random.

Related standards

• BIP 85 derives new entropy deterministically from an existing HD wallet, so one backup can produce child seed phrases, passwords or dice rolls.
• BIP 93 (codex32) proposes a checksummed format for backing up 128 to 512 bits of seed entropy, with optional Shamir secret sharing.

Entropy is the one part of a wallet that can't be recalculated. Lose it, and its seed phrase backup, and the private keys are gone for good.