Final answer:
An ideal MAC scheme should be resistant to forgery without the secret key, protect the key from discovery through MAC functions, and be collision-resistant to ensure unique MACs for different messages, thus ensuring the integrity and authenticity of communications.
Step-by-step explanation:
The property of an ideal Message Authentication Code (MAC) scheme includes several critical attributes that are essential for ensuring data integrity and authenticity. An ideal MAC provides that it should be computationally infeasible to generate a valid MAC without knowing the secret key. This means that even if an attacker has access to several message-MAC pairs, they shouldn't be able to forge a MAC for a new message.
Another important property is that it should be computationally infeasible for an attacker to recover the secret key from access to the MAC function. This implies strong resistance against cryptographic attacks, such as known plaintext, chosen plaintext, or chosen ciphertext attacks. In addition, the MAC should be collision-resistant, meaning it should be hard to find two different messages that produce the same MAC. Essentially, the uniqueness of the MAC per message is maintained.
Overall, these properties help ensure the security of a communication system by making it difficult for malicious parties to tamper with or forge messages without detection.