# Randomness and entropy

A private key is only as safe as the randomness that made it. Learn what entropy means, how weak randomness led to real thefts, and how to stay safe.

Canonical page: https://mybitcoinexplorer.com/learn/randomness-and-entropy
Topic: Cryptography
Published: 2026-10-29
Updated: 2026-10-30


## Keys are random numbers
A [private key](https://mybitcoinexplorer.com/learn/private-keys) is just a number between 1 and about 1.16 × 10^77. Security comes entirely from the attacker not being able to guess it. That only works if it was picked **truly at random**.

## What is entropy?
> Diagram: Good: real randomness makes keys unguessable — Dice or hardware RNG → *128+ bits: of entropy → Seed words: 12 or 24 → Keys: unguessable

> Diagram: Bad: a phrase you thought of is quickly found — !Favourite quote: low entropy → Hash it → !Private key: swept by attackers

Entropy measures unpredictability, in bits. 128 bits of entropy means 2^128 equally likely possibilities, far too many to try.

| Source | Entropy | Safe? |
|---|---|---|
| 12-word seed from a good wallet | 128 bits | Yes |
| 24-word seed | 256 bits | Yes |
| A memorable phrase you thought of ("brain wallet") | Very low | No |
| A key from a buggy random generator | Unknown | No |

## Real failures
- **Brain wallets:** attackers run dictionaries, song lyrics and famous quotes through hash functions and sweep any funds instantly.
- **Weak generators:** some early wallet software reused [ECDSA signatures](https://mybitcoinexplorer.com/learn/ecdsa) nonces or produced predictable keys, and funds were stolen.

## Good practice
Let well-reviewed wallet software or a [hardware wallet](https://mybitcoinexplorer.com/learn/hardware-wallets) generate your [seed](https://mybitcoinexplorer.com/learn/seed-phrases-bip39). Never make one up, and never use a seed you've seen anywhere else.


## How much is 128 bits?
2^128 is about 3.4 × 10^38. If a billion computers each guessed a billion keys per second, checking every 128-bit possibility would still take more than ten trillion years.

## Checklist for a safe seed
- Generated by a reputable wallet or hardware device.
- Created on a device you trust, not a website.
- Never typed into a computer or phone after backup.
- Never chosen, edited or "improved" by you.


## Key takeaways

- Key security depends entirely on true randomness.
- 128 bits of entropy is far beyond brute force.
- Human-chosen phrases and buggy generators have led to real thefts.

## Common questions

### Can I roll dice to create a seed?

Yes, it's a known method if done carefully, with enough rolls and correct conversion. Most people should let a hardware wallet do it.

### How likely is it that someone else gets my key?

With proper randomness, the chance is so small it's not worth considering.

### Can I create my own seed words?

You shouldn't pick words yourself; humans are bad at randomness and the last word must include a checksum.

### Is 24 words safer than 12?

Both are far beyond brute force. 24 words adds margin but is not necessary for most people.

## Related lessons

- [Private keys](https://mybitcoinexplorer.com/learn/private-keys)
- [Seed phrases (BIP 39)](https://mybitcoinexplorer.com/learn/seed-phrases-bip39)
- [ECDSA signatures](https://mybitcoinexplorer.com/learn/ecdsa)
- [Hardware wallets](https://mybitcoinexplorer.com/learn/hardware-wallets)