Entropy Meaning

Oct 24, 2023 | Updated Oct 24, 2023

The entropy of a variable is the measure of the ‘unpredictability’ of that variable. In hardware wallets, entropy refers to the large random number that ensures your crypto wallet is secure.

What is Entropy?

Entropy is simply a random number your crypto wallet generates to form the basis of your secret recovery phrase.

Isn’t the secret recovery phrase the one produced when initiating a wallet?

The secret recovery phrase is actually a direct translation of your entropy, which is a large random number. Your entropy and secret recovery phrase basically contain the same information, just in different formats– one simpler than the other. Your secret recovery phrase starts out as this large number known as entropy. Using the BIP-39 standards, which define how recovery phrases are generated, the entropy is converted into an easy-to-read phrase.

For instance, a 256-bit entropy translates into a 24-word recovery phrase, which is a more simplified version of the extremely long number. Then a 128-bit entropy would translate into a 12-word recovery phrase.

Since anyone with access to your entropy has access to your wallet, just like they would with its secret recovery phrase, the way it is generated is extremely important. To explain, the more random your entropy is, the more secure it is.

For example, if a bad actor can easily guess your entropy, then they can easily access your crypto wallet and digital assets.

How Does Entropy Work in Cryptocurrency Wallets?

Imagine an entropy lacking true randomness.. First, it would increase the probability of more than one wallet generating the same entropy, leading to the same recovery phrase for distinct users. Secondly, a weak entropy leaves a crypto wallet vulnerable to brute-force attacks regardless of how well a user has concealed their entropy.

The quality of entropy relies on its randomness. The idea is that an external entity re-generating your entropy should be statistically impossible. Thus, the greater the randomness of that code, the less likely someone could guess it.

In most crypto wallets, the entropy is generated by a random number generator (RNG). Simply put, the RNG generates the entropy, which is then translated into the secret recovery phrase using BIP-39. It is then used to derive unique private keys when a user is initiating a cryptocurrency wallet or creating an account.

To learn how Ledger uses entropy to generate secret recovery phrases, check out how Ledger ensures the quality of randomness.