How does Prof. U. Maurer classify cryptographic systems and primitives?

Question

Accepted Answer

He splits them into three categories: Unkeyed, Secret-Key, and Public-Key — each with distinct properties.

Category
Key Property
Examples

Unkeyed
No secret parameters
One-way functions, hash functions, random bit generators

Secret-Key
Two or more entities share a common secret value
Symmetric ciphers, MACs, pseudo-random bit generators

Public-Key
No shared secret keys; individual secret values, authentication of public keys
Public-key cryptosystems, digital signatures, various cryptographic protocols, payment systems, interactive proofs, identification schemes

This is a more comprehensive taxonomy than the simple "symmetric vs. asymmetric" split, because it properly accounts for primitives that don't use keys at all.

Category	Key Property	Examples
Unkeyed	No secret parameters	One-way functions, hash functions, random bit generators
Secret-Key	Two or more entities share a common secret value	Symmetric ciphers, MACs, pseudo-random bit generators
Public-Key	No shared secret keys; individual secret values, authentication of public keys	Public-key cryptosystems, digital signatures, various cryptographic protocols, payment systems, interactive proofs, identification schemes