Key derivation function

A key derivation function transforms initial keying material, together with specified parameters and context, into one or more cryptographic keys. The output lengths and security requirements belong to the application. HKDF separates extraction of a pseudorandom key from expansion into the needed output material; the design and its assumptions are analysed in Krawczyk's primary paper.^[ref]

Derivation does not create secret information from nothing. For an original counting example, suppose a secret input is uniformly selected from only $2^{20}$ possibilities and every other derivation input is public and fixed. A deterministic function producing 256 output bits can then reach at most $2^{20}$ different outputs, not all $2^{256}$ strings independently. An adversary able to enumerate the original possibilities can enumerate the derived possibilities too. More output bytes alone do not raise the input's information entropy.

Context supports cryptographic domain separation. For a stipulated application, deriving a sending key with an unambiguous label send and a receiving key with receive assigns different intended roles to the outputs. Deriving both with exactly the same inputs and parameters instead reproduces exactly the same key. This deterministic equality is a functional property, not a failure to obtain fresh randomness during a repeated call. HKDF's info input is explicitly intended to bind output to application context.^[ref]

Parameter encodings must also distinguish intended inputs. Naive concatenation makes pairs ab, c and a, bc both encode as abc. A defined length-prefixed or otherwise unambiguous encoding avoids that collision of descriptions. Changing the encoding changes the KDF input even if a user informally regards the labels as equivalent.

A KDF therefore supplies a specified transformation and separation mechanism. Its security still depends on the initial material, the selected construction and the surrounding cryptographic protocol. It does not by itself authenticate the peer that supplied a shared secret.