Key Derivation

Mnemonics

Introduced in BIP39.

Mnemonics are 12-24 word phrase that is generated using entropy and is used to create master key of an account used during HD account creation. Words are generated from a list of 2048 words and are chosen using entropy generated during mnemonic creation.

Path for creating a 15 words, with each word of 11 bits due to number of words being 2048, i.e. $2^{11}$.

• create a large random number of depending upon number of words in mnemonic, with more words being more secure. To create a 15 word mnemonic, you need 165 bit random bit string called final entropy, 11*15=165.
• calculate checksum of entropy by hashing using SHA256 and take first CS bits of hash. Append this checksum to ENT to create final entropy. Divide it into chunks of 11 bits to create mnemonic word list.
  • Why division by 32? Because every 1 bit checksum for each 32 bit value results in a total 33 bit value divisible by 11 bits.

  CS = ENT / 32
  MS = (ENT + CS) / 11
  
  |  ENT  | CS | ENT+CS |  MS  |
  +-------+----+--------+------+
  |  128  |  4 |   132  |  12  |
  |  160  |  5 |   165  |  15  |
  |  192  |  6 |   198  |  18  |
  |  224  |  7 |   231  |  21  |
  |  256  |  8 |   264  |  24  |
  

• Mnemonic is then generated into a seed that can be used to create HD wallets using BIP32. PBKDF2 with SHA512 is used as hashing function for creating the seed.

Mnemonic seed to Master private key

BIP32 implements Hierarchical Derivation wallets that can be used to generate billions of addresses from a single master private key in an hierarchical manner.

• To calculate master private key from mnemonic seed: HMAC-SHA512("Bitcoin seed", mnemoic_seed). Produces a 64 byte output.
  • First 32 bytes are used as private key and latter 32 bytes are used as chaincode to extend the private key to generate children nodes.
• To derive public key from private key, Bitcoin uses secp256k1 EC and just perform y=xG.
• Child keys are derived from master private key by hashing extended private key with an index again and again.

Extended Keys