Is this cascading encryption, and is my security weakened as a result?

Question

I'm trying to understand what is, and what is not, considered cascading encryption. All of the posts and conversations I've read over the past few days discourage the practice, including this article. Unfortunately, I don't really understand the variables in the equations. So, I haven't found anything that appears to address the setup, scenarios, and concerns I have in mind.

What I think I know:

1. AES is a cipher, and there are no known weaknesses in the cipher.

2. GPG is a crypto suite (a.k.a., "the implementation"?), and there are no known backdoors or weaknesses

3. OS X Disk Utility is (or could be considered) a crypto suite (a.k.a., "the implementation"?), and I ASSUME there are no known backdoors or weaknesses

4. OS X Filevault 2 is (or could be considered) a crypto suite (a.k.a., "the implementation"?), and I ASSUME there are no known backdoors or weaknesses

Initial Assumptions and Questions:

Assumptions:

1. No known backdoors or weaknesses in the ciphers or crypto suites

2. AES (at least 128) is used exclusively

3. Each encrypted "thing" (file, disk image, disk) is encrypted with a UNIQUE, random passphrase of sufficient length

4. Passphrases will not be leaked (by accident, rubber-hose, etc.)

5. Computer is not currently compromised (no monitoring, keyloggers, etc.)

Questions:

1. Any single "thing" (file, disk image, disk)

   1. encrypted with AES,
   2. via any of the crypto suites above,
   3. using a sufficiently long and random passphrase,
      provides "good" security, yes?

2. A GPG-encrypted file exists inside a Disk Utility-encrypted disk image. The disk image is not decrypted (not mounted). A copy of the disk image is stolen by someone who is equally knowledgeable as you in security matters. Is the file less secure inside the disk image than if it existed outside the disk image? Is it more secure? Why?

3. A GPG-encrypted file exists inside a Disk Utility-encrypted disk image. The disk image is not decrypted (not mounted). The disk image exists on an FileVault 2-encrypted disk. The computer is turned off and so the disk is not mounted. The computer is stolen by someone who is equally knowledgeable as you in security matters. Is the file less secure inside the disk image, on that encrypted disk, than if it existed outside the disk image and on an unencrypted disk? Is it more secure? Why?

I will likely ask follow up questions.

Answer 1

I would not consider your case to be a cascading encryption. The reason why is the fact you need multiple interventions before getting access to your file.

Here is what I would consider a cascading encryption (let's go crazy) : $$E(k_1,k_2,k_3,m) = \text{KEYAK}(k_1,\text{NORX}(k_2,\text{AES}(k_3,m)))$$ which you would decipher with : $$E^{-1}(k_1,k_2,k_3,m) = \text{AES}^{-1}(k_3,\text{NORX}^{-1}(k_2,\text{KEYAK}^{-1}(k_1,m)))$$ All operations are done in a single go. One should not need to enter keys one after the other.

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Considering your questions now.

1. As long as you use AES (supposed in the good mode of operation: i.e. not ECB) and under the assumption (3.) your files should be secure as long as the key is not leaked.
   
   In the case of GPG, I suppose you meant to use it in a asymmetric mode (the symmetric case fall under the previous assumption are it will generally use AES).
   For larges files GPG generally generate a random decryption key $K_D$, encrypt the files with AES and this key $K_D$, encrypt $K_D$ with the public key, therefore we are sort of back to point (1.) but with a asymmetric key.

2. I suppose your file to be already encrypted. If your disk image is encrypted therefore yes it will be more secure as just finding the file : you need to decipher the disk before getting access to the file... However, if your file is encrypted with the same algorithm as the one used to encrypt your file. If the first one is broken, expect the second to be the same (meet-in-the-middle... ).

3. Same idea as in 2...

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However what you should really consider is the fact that nowadays cryptography does not work that way. Assuming that the attacker has only access to the cipher text is assuming a very weak attacker.

Academics assume strong attackers : he has control over the plaintext, ciphertext and can ask for any part to be encrypted / decrypted. The only thing he does not have access is the key. The goal here is to retrieve the key. This is usually illustrated by the lunchtime attack.