docs: update cryptography page with new signature schemes and address types

Author: b00f

content/protocol/blockchain/cryptography.md

@@ -3,28 +3,67 @@ title: Cryptography
 weight: 7
 ---
 
-The Pactus blockchain employs various advanced cryptographic algorithms, including hashing and signature schemes,
-to protect user data and transactions.
+The Pactus blockchain uses various cryptographic algorithms, including hashing and digital signature schemes,
+to protect user data and secure transactions.
 
 ## Hashing Algorithm
 
-Pactus uses a hashing algorithm called [Blake2b](https://www.blake2.net/).
-This algorithm is known for being a fast and secure way of creating unique digital fingerprints of data.
+Pactus uses the [Blake2b](https://www.blake2.net/) hashing algorithm.
+Blake2b is a fast and secure cryptographic hash function that produces unique digital fingerprints of data.
 
-## Digital Signature
+## Signature Schemes
 
-To ensure secure transactions, Pactus uses a signature scheme called
-[BLS](https://datatracker.ietf.org/doc/draft-irtf-cfrg-bls-signature/) (Boneh–Lynn–Shacham)
-threshold signature for cryptographic signing and verification.
+Pactus supports several signature schemes for different purposes.
 
-### Signature Aggregation
+### BLS Signatures
 
-One of the advantages of BLS signatures is signature aggregation. BLS individual signatures can be
-combined into one single aggregated signature, so that the overall size does not grow beyond one
-signature.
+[BLS](https://datatracker.ietf.org/doc/draft-irtf-cfrg-bls-signature/) (Boneh–Lynn–Shacham) is the primary signature scheme
+used by validators and BLS-based accounts.
+BLS is a threshold signature scheme with two notable properties:
 
-### Non-Malleability
+#### Signature Aggregation
 
-BLS signatures have an important property called non-malleability,
-which means that it is impossible to generate two valid signatures for the same message.
-In other words, each message has a unique signature, and signatures cannot be altered without invalidating the signature.
+BLS signatures can be aggregated — multiple individual signatures can be combined into a single signature
+without increasing the overall size. This is useful for consensus where many validators sign the same message.
+
+#### Non-Malleability
+
+BLS signatures are non-malleable: it is impossible to produce two different valid signatures for the same message.
+Each message has exactly one valid signature.
+
+### Ed25519 Signatures
+
+[Ed25519](https://www.rfc-editor.org/rfc/rfc8032.txt) is supported for account addresses
+(see [PIP-52](https://pips.pactus.org/PIPs/pip-52)).
+Ed25519 provides strong security, compact keys, and fast performance.
+Ed25519 account addresses start with `pc1r...`.
+
+### secp256k1 Signatures
+
+[secp256k1](https://www.secg.org/sec2-v2.pdf) (ECDSA) is supported for account addresses
+(see [PIP-53](https://pips.pactus.org/PIPs/pip-53)).
+This is the same curve used by Bitcoin, enabling compatibility with existing wallet tools.
+secp256k1 account addresses start with `pc1y...`.
+
+## Address Types
+
+Addresses in Pactus include a type that indicates their intended usage
+(see [PIP-8](https://pips.pactus.org/PIPs/pip-8)):
+
+| **Type** | **Usage**         | **Address Prefix** | **Derivation Path**             |
+| -------- | ----------------- | ------------------ | ------------------------------- |
+| 1        | Validator         | `pc1p...`          | `m/12381'/21888'/1'/index`      |
+| 2        | BLS Account       | `pc1z...`          | `m/12381'/21888'/2'/index`      |
+| 3        | Ed25519 Account   | `pc1r...`          | `m/44'/21888'/3'/index'`        |
+| 4        | secp256k1 Account | `pc1y...`          | `m/44'/21888'/4'/index'`        |
+
+## HD Key Derivation
+
+Pactus supports Hierarchical Deterministic (HD) key derivation for wallets.
+This allows a single master seed to generate a tree of keys in a predictable way.
+
+BLS HD derivation follows [PIP-11](https://pips.pactus.org/PIPs/pip-11),
+which defines a standard for BLS12-381 HD key chains based on
+[BIP-0032](https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki).
+Ed25519 and secp256k1 HD derivation follow
+[SLIP-10](https://github.com/satoshilabs/slips/blob/master/slip-0010.md).