§ 02 · Cryptography · Overview
Cryptography
The math that lets strangers trust the same ledger
On this page 2 sections
Cryptography is what lets thousands of strangers agree on one ledger without trusting each other. Nobody has to take anyone’s word for anything: every claim comes with math anyone can check.
Pearl uses four kinds of it. Hashes fingerprint data. Merkle trees fold many fingerprints into one. Signatures prove who approved a payment. And, new in Pearl, a zero-knowledge proof in every block proves the mining work was done.
What’s in this group?
Read in order: each page builds on the one before.
| Page | What you’ll learn |
|---|---|
| Hash functions | SHA-256, SHA256d and BLAKE3: what they guarantee and where Pearl uses each. |
| Tagged hashes | How a label keeps hashes made for different jobs apart. |
| Merkle trees | One hash for a whole block, and a short proof for any transaction in it (7 hashes in a real 115-transaction block). |
| Elliptic curves | The one-way math from private key to public key, worked on a toy curve. |
| Schnorr signatures | How a 64-byte signature is made and checked, and why the nonce must never repeat. |
| XMSS | Pearl’s optional post-quantum signatures, built only from hashes. |
| Zero-knowledge proofs | What the ~60 KB certificate proves, how it’s built, and how fast it checks. |
What does Pearl change?
Less than you might think, and in a few precise places.
| Topic | Bitcoin | Pearl |
|---|---|---|
| Hashes | SHA-256, SHA256d, RIPEMD-160 | The same, plus BLAKE3 for mining |
| Proof of work | Block hash below the target | A BLAKE3 ticket below target × tile work, proved by a zero-knowledge certificate |
| Curve | secp256k1 | secp256k1, unchanged |
| Signatures | ECDSA and Schnorr | Schnorr only, plus optional XMSS |
| Tagged hashes | Seven BIP-340/341 tags | The same seven, no new ones |
In this group
- 02.01 Hash functions A fingerprint for any data, impossible to fake
- 02.02 Tagged hashes SHA-256 with a label on it, so no hash can be mistaken for another
- 02.03 Merkle trees One hash that vouches for thousands, and a short proof for any one of them
- 02.04 Elliptic curves Easy to multiply, impossible to divide
- 02.05 Schnorr signatures 64 bytes that prove you hold the key, for one exact message
- 02.06 XMSS Signatures made only of hashes, built to outlast quantum computers
- 02.07 Zero-knowledge proofs Proving the work was done without showing the work