Final answer:
A secret key cryptosystem cannot achieve nonrepudiation, which is the guarantee that a sender cannot deny having sent a message. This requires digital signatures and PKI, as opposed to symmetric encryption provided by secret key systems.
Step-by-step explanation:
The one thing that cannot be achieved by a secret key cryptosystem is D. Nonrepudiation. Secret key cryptosystems, also known as symmetric encryption, use the same key for both encryption and decryption. While they can achieve key distribution, confidentiality, and play a role in availability, they do not inherently provide nonrepudiation. Nonrepudiation is the assurance that someone cannot deny the validity of something. In the context of cryptography, it means that a sender cannot deny sending a message. This is typically achieved through digital signatures and public key infrastructure (PKI), where a unique public-private key pair is used to prove the origin of a message.