Field Guide · term

Also known as: key, secret key

A cryptographic key is the secret value that controls how a cipher transforms data; with the correct key the transformation can be reversed, and without it the data should be infeasible to recover.1 In a sound system the key — not the algorithm — is the only secret.

key key space = 2^n cipher plaintext ciphertext
The key is the secret input to the cipher; its bit length sets the size of the key space.

How it works

A cipher is a fixed, often publicly documented algorithm; the key is the variable secret that selects one specific transformation out of an astronomically large family. Change the key and the same algorithm produces a completely different result.

The strength of a key is measured by its key space — the number of possible keys, set by the key length in bits. An n-bit key has 2ⁿ possibilities, so a 128-bit key has 2¹²⁸ of them, far beyond any feasible brute-force search.2 This is why key length matters: a longer key exponentially enlarges the search an attacker must perform. The bound is only an upper limit, though — it holds only if the effective key space really is that large. A cipher with a short key (DES’s 56 bits), predictable key generation, or a mathematical weakness that lets an attacker rule out most keys at once has a much smaller effective space than its nominal length suggests.

Variants

Keys take different forms in different systems:

Systems also distinguish a traffic key (the short-lived key that actually encrypts a call) from a key-encryption key (used only to wrap traffic keys for delivery), and they schedule periodic rekeying so that compromise of one key exposes only a limited window.

In practice

Because all the secrecy is concentrated in the key, key management — generating, distributing, storing, and retiring keys — is the hard operational core of any deployed cryptosystem. In land-mobile radio, keys are typically loaded into radios with a physical key loader / KFD and can be refreshed remotely by over-the-air rekeying; each key carries a key ID and algorithm ID so the receiver knows which key and cipher a given transmission used. By Kerckhoffs’s principle, a system should remain secure even if everything except the key is public — so protecting the key is the whole security argument.

Relevance to SDR

Whether GopherTrunk can recover encrypted voice comes down to one thing: the key. The decoder can identify an encrypted P25 or DMR call, read its key-identifier and algorithm fields, and follow the traffic, but the audio stays opaque without the secret key. That is the intended behaviour of a correctly designed symmetric cipher. It also clarifies the difference from reversible scrambling, which has no secret key and so can be undone by anyone who knows the public method.

Sources

  1. Key (cryptography) — Wikipedia, for the key as the secret parameter and the role of key length and key space. 

  2. Key size — Wikipedia, for how key length bounds brute-force effort and the notion of effective vs nominal key strength. 

See also