Field Guide · term

Also known as: asymmetric cryptography, asymmetric encryption

Public-key cryptography (also asymmetric cryptography) uses a linked pair of keys: a public key that may be shared freely and a private key kept secret.1 Data encrypted with the public key can only be decrypted with the matching private key, so no shared secret has to be distributed in advance.

public key private key plaintext encrypt cipher decrypt plaintext
Two linked keys: the public key encrypts; only the private key decrypts.

How it works

The two keys are generated together and bound by a mathematical relationship — typically one based on a problem believed hard to reverse, such as integer factorisation (RSA) or the elliptic-curve discrete logarithm (ECC). The public key can be published openly; deriving the private key from it is computationally infeasible. The asymmetry is the whole point: the operation is easy in one direction (multiply two large primes, exponentiate a point) and believed intractable in the other (factor the product, take the discrete logarithm) for key sizes in current use.

This gives two complementary uses:

  • Encryption — anyone encrypts with the recipient’s public key, and only the holder of the matching private key can decrypt.
  • Digital signatures — the holder signs with the private key, and anyone can verify with the public key, proving authenticity and integrity.

Variants

Not every asymmetric scheme moves message bits directly. Key exchange protocols such as Diffie–Hellman let two parties who have never met derive a shared secret over a public channel, without either transmitting it: each combines their own private value with the other’s public value and arrives at the same result, which an eavesdropper who saw only the public values cannot compute.2 The main families in use are RSA (factorisation), the Diffie–Hellman / DSA family (discrete logarithm in a finite field), and elliptic-curve variants (ECDH, ECDSA), which reach the same security level with much smaller keys — an advantage on constrained radio hardware.

In practice

Because the heavy mathematics make asymmetric operations far slower than symmetric ones, real systems usually use public-key cryptography only to agree on or transport a short symmetric key, then switch to a fast symmetric cipher for the bulk data — the “hybrid” pattern behind TLS and most secure messaging. In land-mobile radio the same idea appears in modern key management: a public-key layer can authenticate radios and protect the delivery of traffic keys during over-the-air rekeying, so that a key loader need not physically touch every unit. As with all modern cryptography, its safety rests on Kerckhoffs’s principle: the algorithm is public and only the private key is secret.

Relevance to SDR

Public-key cryptography rarely appears in the over-the-air voice path of conventional trunked-radio protocols, which protect speech with fast symmetric ciphers instead. It is more likely to surface in key management and provisioning — distributing or rekeying the symmetric traffic keys tagged by their key ID / algorithm ID, and in device authentication — rather than in the per-call audio GopherTrunk demodulates. For the purposes of decoding received signals it is mostly background context, but it explains how the symmetric keys that do protect voice get delivered.

Sources

  1. Public-key cryptography — Wikipedia, for the public/private key-pair model and the key-distribution problem it solves. ↩

  2. Diffie–Hellman key exchange — Wikipedia, for deriving a shared secret over a public channel. ↩

See also