HKDF

HKDF is an HMAC based key derivation function that transforms any weak key material (e.g. Diffie Hellman exchanged shared secrets) into a cryptographically strong key material (e.g. for subsequent use in encryption, integrity and/or authentication) and described in RFC 5869. It extracts a pseudo random key (PRK) using an HMAC hash function (e.g. HMAC-SHA256) on an optional salt and any potentially weak input key material (IKM). It then generates similarly cryptographically strong output key material (OKM) of any desired length by repeatedly generating PRK-keyed hash-blocks and then appending them into the output key material, finally truncating to the desired length. For added security, the HMAC PRK keyed hash blocks are chained during their generation by prepending the previous hash block to an incrementing 8-bit counter with an optional context string in the middle before being HMACed to generate the current hash block.

Note: HKDF does not amplify entropy but does allow a large source of weaker entropy to be utilised more evenly and effectively.

HKDF has two primary and potentially independent uses:

1./ To "extract" (condense/blend) entropy from a larger random source to provide a more uniformly unbiased and higher entropy but smaller output. e.g. an encryption key. This is done by utilising the diffusion properties of cryptographic MACs.

2./ To "expand" the generated output or an already reasonably random input such as an existing shared key into a larger cryptographically independent output, thereby producing multiple keys deterministicly from that initial shared key, so that the same process may produce those same secret keys safely on multiple devices as long as the same inputs are utilised.

These two functions may also be combined and used to form a PRNG to improve a RNGs (Random Number Generators) potentially biased output as well as protect it from analysis and help defend the random number generation from malicious inputs.

Example: Python Implementation of HKDF

   #!/usr/bin/env python3
   import hashlib
   import hmac
   from math import ceil
   
   hash_len = 32
   def hmac_sha256(key, data):
       return hmac.new(key, data, hashlib.sha256).digest()
   
   def hkdf(length, ikm, salt=b"", info=b""):
       prk = hmac_sha256(salt, ikm)
       t = b""
       okm = b""
       for i in range(ceil(length / hash_len)):
           t = hmac_sha256(prk, t + info + bytes([1+i]))
           okm += t
       return okm[:length]

References

• RFC 5869: HMAC-based Extract-and-Expand Key Derivation Function (HKDF)