# Cryptography

## Overview

The signing curves, hashes, and ciphers Ethereum (and its ecosystem) runs on — audited
implementations, tree-shakable. Modules such as [`Secp256k1`](/api/Secp256k1),
[`P256`](/api/P256), and [`Hash`](/api/Hash) expose stateless functions that accept and return
`Hex` or `Bytes`. Heavy algorithms (BLS12-381, ML-DSA, some hashes) can be backed by pluggable
[engines](/guides/runtime/engines) such as WASM or native Node.js crypto.

```ts twoslash
import { Hash, Hex, Secp256k1 } from 'ox'

declare const privateKey: Hex.Hex

const payload = Hash.keccak256(Hex.fromString('agree to terms'))
// @log: '0x6f7a…b21c'

const signature = Secp256k1.sign({ payload, privateKey })
// @log: { r: '0x1c34…', s: '0x4f8d…', yParity: 0 }

const signer = Secp256k1.recoverAddress({ payload, signature })
// @log: '0x71bE63f3384f5fb98995898A86B02Fb2426c5788'
```

<Cards>
  <Card icon="lucide:layers" title="BLS Signatures & Aggregation" description="Sign, verify, and aggregate BLS12-381 signatures and public keys." to="/guides/crypto/bls" />

  <Card icon="lucide:signature" title="Convert Signature Formats" description="Move signatures between hex, bytes, DER, legacy, RPC, and tuple forms." to="/guides/crypto/signatures" />

  <Card icon="lucide:key-round" title="Ed25519 & X25519" description="Sign with Ed25519 and derive shared secrets with X25519." to="/guides/crypto/ed25519-x25519" />

  <Card icon="lucide:hash" title="Hash Data" description="keccak256, SHA-256, RIPEMD-160, HMAC, BLAKE3, and incremental hashing." to="/guides/crypto/hashing" />

  <Card icon="lucide:shield-check" title="Post-Quantum Signatures (ML-DSA)" description="Generate keys, sign, and verify with ML-DSA-44 (FIPS 204)." to="/guides/crypto/ml-dsa" />

  <Card icon="lucide:lock" title="Work with AES-GCM" description="Derive keys from passwords and encrypt arbitrary data." to="/guides/crypto/encryption" />

  <Card icon="lucide:fingerprint" title="Work with P256" description="Key pairs, signatures, recovery, and ECDH on the NIST P256 curve." to="/guides/crypto/p256" />

  <Card icon="lucide:key" title="Work with Secp256k1" description="Sign, verify, and recover on Ethereum's primary curve." to="/guides/crypto/secp256k1" />

  <Card icon="lucide:globe" title="Work with WebCryptoP256" description="Non-extractable P256 keys via the Web Crypto API." to="/guides/crypto/webcrypto-p256" />
</Cards>