Question: To avoid slowing down the secure communication, Anna likes the speed of AES, but she hates the key management problems associated with AES. To solve

To avoid slowing down the secure communication, Anna likes the speed of AES, but she hates the key management problems associated with AES. To solve this key management problem, Anna first uses her private key to scramble the AES encryption key; then she emailed the scrambled AES key to Brian. Then Brian can use Anna's public key, which he knows, to descramble the received key; then Brian can get the original AES key; finally Anna and Brian can enjoy using this AES key to do very fast encryption and decryption.

What is the security flaw with this idea? Please justify your answer.

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