Alice claims to use a perfectly-secure encryption scheme to encrypt messages to Bob. However, Eve shows Alice that she can recover 90% of the bits of Alices key even after just seeing one encrypted message from Alice.

1. Explain how this is possible by constructing a perfectly-secure encryption scheme which has these properties.

2. Eve claims she can always recover 10% of the message from the encryptions. Prove that this means that the encryption scheme cannot be perfectly secure.