Entropy (randomness)

A private key is only secure if nobody can predict it. Wallets therefore start from a large random number, typically 128 or 256 bits of entropy, drawn from the device's secure random number generator, hardware noise or, for the cautious, physical dice. That entropy is then encoded as a seed phrase and expanded into keys. With 128 bits there are more possible keys than could ever be searched.

Weak entropy has caused real losses. Brain wallets derived from memorable phrases were swept by attackers who hashed dictionaries and song lyrics. In 2023 the Milk Sad disclosure showed that a command-line tool generated seeds from a random generator with only 32 bits of effective entropy, and funds in those wallets were stolen. Faulty random number generators in phones and browser wallets have exposed keys too.

Users rarely see entropy directly, which is why choosing reputable, audited wallets matters. Never create a seed phrase by choosing words yourself, using a website, or reusing a phrase someone else generated. Hardware wallets and dice-based generation are the main ways to reduce reliance on a single software source of randomness.