Use the following information to answer questions

Although the key management problems associated with symmetric key cryptosystems (in which encryption and decryption use the same secret key) will disappear when public key cryptosystems are used, public key encryption is greatly slower than symmetric key encryption. Alice wants to send a 3,000,000 byte message to Bob.

1. To avoid slowing down the secure communication, Alice likes the speed of DES, but she hates the key management problems associated with DES. To solve this key management problem, Alice firstly uses her private key to scramble the DES encryption key; then she emailed the scrambled DES key to Bob. Then Bob can use Alices public key, which he knows, to descramble the received key; then Bob can get the original DES key; then Alice and Bob can enjoy using this DES key to do very fast encryption and decryption.

This idea sounds beautiful, but it has a security flaw. What is it? Please justify your answer.

2. please propose a method to fix the flaw you identified in the previous question.