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Is there any difference between disk encryption and encrypted file container in terms of security? Which one is better?

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It depends on what you need to secure, and who should have access to it. In some circumstances, implementing both is reasonable.

Full disk encryption (FDE) is generally more secure if only one method can be chosen. If the entire volume is encrypted, an attacker cannot modify files. Without FDE, they could install a rootkit or a keylogger to steal the password for your encrypted container. Along those lines, an attacker will have no access to forensic artifacts in the environment, including such useful resources as: the pagefile, recently-used files lists, Windows registry, user authentication data, full/partial copies of files in slack space, and public/shared folders.

FDE has some limitations and operability concerns. Either the system must support automatic unlocking, or the users must have credentials which can unlock the boot volume. In addition, if the encryption header is corrupted, the entire volume will become inaccessible, and the computer will be unusable until it is reimaged. (Note that most FDE solutions store multiple copies of the header to reduce this risk.)

An encrypted container may support multiple unique users who are capable of unlocking it, e.g., Bitlocker-protected VHDX files. Each user must be enrolled by providing a password, token, certificate, and/or PIN. Access can be revoked by removing their key protector on the fly, which offers greater convenience and flexibility. Note that some container formats use a single keyfile, and each user merely protects their copy of the keyfile---in these cases, the container would need to be re-keyed or recreated to revoke access. If this concerns only your own personal data, this might not matter to you.

Both methods have several software options, and administrators can usually configure emergency recovery methods, as long as this is planned prior to encryption. Recovery agents are typically assigned smart cards, key fobs, or certificates which they can use to unlock managed devices. In an enterprise scenario, user enrollment and recovery planning are often as important as data protection.

In both cases, encrypted data cannot be compressed or deduplicated. These space-saving technologies will not work once the data is encrypted. While you can compress/dedupe data before encryption, you will usually see a significant reduction in deduplication savings. Since containers only encrypt files chosen by the user, they are more efficient with regard to disk utilization in the enterprise.

There is no technical limitation which prohibits you from using an encrypted container on an encrypted disk. In a high-security or high-stakes environment, using both types of encryption may be necessary.

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Based on the available algorithms, both types of encryption offer the same capabilities, so there is no difference in this regard.

The main difference stems from access control. Full Disk Encryption (assuming we are talking about your main disk containing your operating system) only protects your data as long as the system is not running. Once you have entered your passphrase (or other type of authentication) during system boot, the key is available in RAM and files will be decrypted transparently on access. That's great if you travel with your notebook turned off or if you are afraid someone steals your hard disks from your data-center, but that's about it. If an attacker gains access to your running system, full disk encryption doesn't protect your data.

With encrypted file containers you have the possibility of fine grained access control. If you do not need access to the encrypted files permanently, you can provided the credentials on demand and close the container when you are done. In addition, you can have multiple encrypted file containers on a single file system, so that you only have to open a limited set of files at a time. In a multi-user environment, every user can have his/her own containers as well.

That being said, I assumed that you are talking about full disk encryption of your main disk containing your operating system. If you are talking about a second disk or a removable device, the differences become even smaller, as you can mount and decrypt them on demand as well.

Last but not least you have modern disks that provide hardware based full disk encryption. Such disks provide the added security benefit, that the encryption key does not leave the disk and can therefore not leak via attacks against the RAM (e.g. cold-boot attacks). If this is relevant for you, depends on the actual threats you are facing.

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