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In the open source (https://github.com/bitcoin/bitcoin/tree/master/src/crypto) there are these algrithms that as I know connected with gerenation the new keys and master key. So I try to understand what exactly each algorithm does and how they related in Bitcoin Core.

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They implement 3 distinct cryptographic schemes:

  • HMAC-SHA256 is a MAC (message authentication code, or a keyed hash function) based on SHA-256. It is used in the RFC6979 nonce generation function for deterministic ECDSA signing.
  • HMAC-SHA512 is a MAC based on SHA-512. It is used in the BIP32 key derivation logic.
  • HKDF-SHA256 is a (symmetric) key derivation function (KDF) based on HMAC-256. It is currently unused, but was added in anticipation of being used in the BIP324 (v2 P2P transport layer) implementation.
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HMAC in the name stands for "Hash-based Message Authentication Code" and the hmac_sha_512 is used to generate keys in hierarchic-deterministic BIP-0032 wallets, and to generate a master key from the seed phrase (BIP-0039), for example here.

HKDF in the name stands for "Hash-based Key-Derivation Function", and there's a comment in the code which describes it:

A rfc5869 HKDF implementation with HMAC_SHA256 and fixed key output length of 32 bytes (L=32)

If you look at rfc5869 specification, it uses some HMAC as a primitive in the key derivation scheme, and in hkdf_sha256 the hmac_sha_256 is the primitive i.e. hmac_sha_256 is used for hkdf_sha256. The hmac_sha_256 is also used in httprpc.cpp and torcontrol.cpp.

But what is hkdf_sha256 used for? It doesn't seem to be used anywhere.

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