Privacy and Integrity in Public Cryptography
Signing and encrypting together is not secure in this method, at least in the way most would perceive security. For example, Bob would likely interpret this message as being sent from Alice to Bob. However, Alice may have sent it to Charles who decrypted and re-encrypted the signed message under Bob's public-key. In order to do this securely, you need to add the sender's and receiver's identities inside (the signature with Alice's key should contain Bob's identity, and the encryption with Bob's key should contain Alice's identity). In addition, you need to use CCA-secure encryption. In short, this isn't so simple and you need to check the details in order to determine if it's secure. This topic is called "SignCryption" and you can look it up for more information.