TECHNICAL_DOC // CRYPTOGRAPHY / HMAC-SHA512
HMAC-
SHA512
SHA512
hmac-sha512/">HMAC-SHA512 is a keyed hash function that combines a secret key with
SHA-512 to produce a 512-bit authentication code. In Bitcoin, it is the core operation
of BIP32 hierarchical deterministic key derivation — turning a parent key and chain code
into child keys. The 512-bit output splits cleanly into two 256-bit values: the new key
material and the new chain code.
HMAC_CONSTRUCTION
HMAC ALGORITHM (RFC 2104)
HMAC(Key, Message):
ipad = 0x36 repeated to block size
opad = 0x5C repeated to block size
inner = SHA512((Key XOR ipad) || Message)
result = SHA512((Key XOR opad) || inner)
Output: 512 bits (64 bytes)
USED IN BIP32
BIP32 — MASTER KEY DERIVATION
Input seed: S (512 bits from BIP39 mnemonic)
I = HMAC-SHA512(Key="Bitcoin seed", Data=S)
→ 512 bits output
Left 256 bits: IL = Master Private Key
Right 256 bits: IR = Master Chain Code
If IL ≥ curve order n → seed is invalid (astronomically rare)
BIP32_CHILD_KEY_DERIVATION
Normal Child Key (Non-Hardened)
INDEX 0 – 2^31-1
Derives a child key that can also be derived from the parent's public key alone — useful for generating receive addresses without exposing private keys.
I = HMAC-SHA512(Key=parent_chain_code,
Data=parent_pubkey || ser32(index))
child_key = parse256(IL) + parent_key (mod n)
child_code = IR
Public key derivable from parent public key:
child_pubkey = IL×G + parent_pubkey
Hardened Child Key
INDEX 2^31 – 2^32-1
Uses the parent private key as input instead of the public key. Child key cannot be derived from parent public key — provides stronger isolation between branches.
I = HMAC-SHA512(Key=parent_chain_code,
Data=0x00 || parent_privkey || ser32(index))
child_key = parse256(IL) + parent_key (mod n)
child_code = IR
Notation: m/44'/0'/0' ← apostrophe indicates hardened
44' = index 0x8000002C = 2147483692
Hardened derivation is used at the account level in BIP44/84/86 to prevent a leaked child key from compromising sibling branches.
TERMINOLOGY_INDEX
HMAC
Hash-based Message Authentication Code. A keyed hash providing both data integrity and authentication.
Chain Code
A 32-byte value used as the key input to HMAC-SHA512 during BIP32 child key derivation.
Hardened Key
A BIP32 child key derived using the parent private key. Index ≥ 2^31. Cannot be derived from parent pubkey.
Non-Hardened Key
A BIP32 child key derived from the parent public key. Index < 2^31. Enables watch-only wallets.
BIP32
The standard for hierarchical deterministic key derivation using HMAC-SHA512.
xpub / xprv
Extended public/private key — a BIP32 key plus chain code encoded in Base58Check for sharing.