You are the lead cybersecurity analyst at a multinational corporation that uses a hybrid encryption system to secure inter-departmental communications. The system uses RSA encryption for key exchange

AES-128 bits provides only ~64 bits of effective security against quantum attacks via Grover's algorithm, which is insufficient when RSA is already compromised, making this the weakest and least secure option.

AES-256 offers 128-bit post-quantum security which is strong, but when RSA is broken and the entire security burden shifts to AES, 256 bits is less preferable than 512 bits in a scenario explicitly prioritizing maximum security balance.

AES-192 provides an intermediate level of security (~96 bits post-quantum), but it neither maximizes security nor offers a compelling performance advantage over AES-256 or AES-512 given AES's linear O(n) complexity, making it a suboptimal choice in this threat model.

When RSA is compromised by a quantum algorithm reducing its complexity to O((log n)^2), the security of the hybrid system falls entirely on AES. A 512-bit AES key provides the highest resistance against both classical and quantum attacks (Grover's algorithm halves effective key strength, so 512 bits yields ~256-bit post-quantum security), making it the best choice when RSA can no longer be trusted for secure key exchange. Although AES-512 incurs higher computational cost, the O(n) linear complexity of AES means this overhead is manageable compared to the catastrophic security loss from a broken RSA layer.