Ask HN: Cloud Email with Strong Privacy

HELP! A client of mine is looking for an easy-to-use cloud-based email solution with strong privacy protection.

They've got four requirements:

1) no cleartext is stored in the cloud

The only way to read the mail is to enter a secret at the beginning of each session.

2) email is encrypted instantly upon receipt by the service

e.g. an SMTP daemon is running that encrypts each email using a public key and stores only the encrypted copy

3) email can only be read by the person who holds the secret

4) the mailbox should be easily accessible using a client application

And one non-requirement:

The solution doesn't have to protect plaintext emails from intercept in transit.

I'm not talking about encrypting emails between parties; I'm just talking about storing them securely while preserving ease of access