Bitcoins/Litecoins/Virtual Currencies

Flobee said:

Probably need someone smarter than me to explain the relationship between entropy, random number generation, and a hardware wallet seed phrase in an easy to understand way haha. Cryptography is complicated.

I've enlisted the assistance of big number guesser himself though and he did a pretty good job

Spoiler: AI explanation

To explain how a seed phrase gets compromised in a situation like the one described, it helps to understand how **entropy**, **randomness**, and **seed generation** form the foundation of crypto security—and what happens when one link in that chain breaks.

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## 1. Entropy: The Pool of Possibilities

**Entropy** is a measure of unpredictability or "true randomness." In cryptography, high entropy means there are so many possible outcomes that it is mathematically impossible for anyone—or any supercomputer—to guess your secret.

* **High Entropy:** Imagine choosing a specific grain of sand from every beach on Earth. It is impossible for someone to guess which grain you picked because the pool of possibilities is staggering ($2^{256}$ potential seed combinations).
* **Low Entropy:** Imagine picking a number between 1 and 100. A computer can guess that in milliseconds because the pool of possibilities is tiny.

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## 2. Randomness (RNG): The Machine Drawing the Number

**Randomness** is the process used to pick a secret from that pool. To get high entropy, you need a **Cryptographically Secure Random Number Generator (CSPRNG)**. Hardware wallets usually use dedicated hardware chips (like thermal noise or radio noise sensors) to capture true physical chaos.

* **Cryptographic RNG:** Draws numbers in a way that is completely unpredictable, non-repeating, and impossible to reconstruct.
* **Standard/Default RNG (e.g., Python's standard `random` library):** Designed for things like video games, statistical simulations, or shuffling a digital deck of cards. It is a "pseudo-random" number generator. While it *looks* random to a human, it follows predictable mathematical algorithms. If an attacker knows the algorithm and a few clues, they can predict every number it will ever output.

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## 3. Seed Generation: Baking the Entropy into 12 or 24 Words

When you set up a hardware wallet, it goes through a specific sequence:

1. **Collects Entropy:** The wallet gathers raw bits of entropy (unpredictable 0s and 1s) using its hardware RNG.
2. **Generates a Seed:** It converts those random bits into a master private key.
3. **Translates to Words:** That long mathematical key is converted into your human-readable 12- or 24-word recovery phrase.

If the raw entropy collected in step 1 is truly random, your seed phrase is locked behind a door that no computer in the universe can break open.

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## 4. Bringing It All Together: What Happened in the Context

The scenario described highlights a critical point where this pipeline broke down:

```
[Hardware RNG Fails] ──> [Silent Fallback] ──> [Standard Python RNG Used] ──> [Low Entropy Seed Created]

```

1. **The Intended Design:** The wallet was supposed to use a custom, high-entropy random number function.
2. **The Software Glitch:** A naming conflict caused the code to silently fall back to Python’s default `random` module when the primary RNG failed.
3. **The Loss of Entropy:** Instead of drawing your seed from a pool of endless possibilities, the hardware wallet generated seeds from a small, mathematically predictable list produced by Python's standard RNG.
4. **The "Big Computer Guessers":** Because Python's default RNG isn't cryptographically secure, attackers running brute-force scripts don't have to search $2^{256}$ combinations. They only have to cycle through the predictable outputs of the weak algorithm to recreate the exact seed phrases generated by those affected wallets and drain the funds.

> **Key Takeaway:** Hardware wallet security relies entirely on high entropy. If the process for picking numbers drops from true cryptographic randomness to a simple software algorithm, even a 24-word seed phrase becomes easy for an attacker's automated script to guess.

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