TL;DR: Android and iOS support full device encryption.
Android versions above 4.4 (your device will almost certainly be above version 4.4) have the option to enable full device encryption. Some devices even come with it enabled out of the box. Android uses dm-crypt encryption, and there's a guide on how to encrypt an Android device here.
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Start by heading into the Settings menu and tapping on “Security”. You
can start the process by tapping the “Encrypt phone” option.
The next screen will present a warning to let you know what to expect
once the process is finished. If you’re ready to proceed, hit the
“Encrypt phone” button.
One more warning will present itself which tells you not to interrupt
the process. Once you're ready tap the “Encrypt phone” button to
The phone will then reboot and start the encryption process. A
progress bar and estimated time till completion will show up, which
should at least provide an idea of how long the process will take.
Once it’s finished, the phone will reboot and you’re back in business.
If you set up a lock screen password, PIN, or pattern, you’ll have to
put it in now so the device will finish the boot process.
If you have an iPhone 3GS or later, an iPod touch 3rd generation or later, or any iPad then you can encrypt your device. Most modern Apple devices already use encryption by default. Apple devices use AES-256 encryption to encrypt devices (in 2012 the NSA approved AES-256 for storing top-secret data). Here is a guide on how to encrypt your Apple device.
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On devices running iOS 4–iOS 7, you can do this by going to the
General settings, and choosing Passcode (or iTouch & Passcode). As for
iOS 8-9, Passcode (or “Touch ID & Passcode”) has its own section in
the Settings app. Follow the prompts to create a passcode. You should
set the “Require passcode” option to “Immediately,” so that your
device isn't unlocked when you are not using it. Disable Simple
Passcode so that you can use a code that's longer than 4 digits.
If you choose a passcode that's all-numeric, you will still get a
numeric keypad when you need to unlock your phone, which may be easier
than typing a set of letters and symbols on a tiny virtual keyboard.
You should still try to keep your passcode long even though Apple's
hardware is designed to slow down password-cracking tools. Try
creating a passcode that is more than 6 digits.
Once you've set a passcode, scroll down to the bottom of the Passcode
settings page. You should see a message that says “Data protection
enabled.” This means that the device's encryption is now tied to your
passcode, and that most data on your phone will need that code to