There is an option in your Android OS to change your system to a encrypted system.
Read this howto: http://www.droidorigin.com/encrypt-android-device/
A partial copy here below:
Data encryption on Android, may not be a complete solution for securing your device, but is definitely a big step to tackle data attacks. Also, Android natively supports only full-disk encryption, so you can’t just go on encrypting individual applications, or services.
How it helps? Suppose that you somehow lost your phone, or you handed it over to your colleagues/friends/family, your data will still be safe, and will not be accessible at all, until you enter your chosen password/key.
While encryption is supported on most Androids, decrypting it is not a very common practice offered by OEMs. Knowing that, at most situations, decryption could be carried out by simply erasing the complete storage.
You will need to have a security PIN or Password setup in order to proceed. When that is done, go to device Settings > Security > Encrypt phone/Encrypt tablet. Scroll downwards, and tap on ENCRYPT PHONE or ENCRYPT TABLET. The button may be greyed out, and it will ask you to connect to a power source (plug in your charger). Upon doing this, you will see a warning screen, so just tap on ENCRYPT PHONE or ENCRYPT TABLET once more.
Your phone/tablet shall restart instantly, and start the encryption process, also displaying the amount of time, that would be required to finish the process. The time may vary, for every device, depending upon the kind and size of data on your filesystem. While the process is being carried out, make sure that you do not mess around with your phone and also connect it to your wall charger. Powering it off, or battery outage may corrupt your data and make it irrecoverable.
When done, your device will reboot again, and this time into the OS. Once booted, the phone/tablet will require you to enter the correct security password/PIN/Pattern. Enter it, or failing to do so, will lock you off the device.
B. Using Third-Party Apps
A bunch of apps are already present on the Play Store, that offers easy encrypting of a particular set of data on your And roid devices.
» SSE – Universal Encryption App
SSE is an all-in-one encryption tool that not only lets you encrypt different filesystem partitions, but also individual files like documents. Apart from this, you can use the app to store your passwords under the vault, for secure access.
The tool makes use of the following encryption algorithms: AES (Rijndael) 256bit, RC6 256bit, Serpent 256bit, Blowfish 448bit, Twofish 256bit, GOST 256bit. In case you’re a technical person, you might want to have a look at Encryption Algorithms on Wikipedia. In simple words, the above mentioned ciphers have proved to work best with Android.
The app’s user-interface may not be that snappy, but then who cares when the job is getting well done.
» Crypto Ghost – File Encryption
Unlike the above, Crypto Ghost is only limited to file encryption, so that you can share files with privacy. One of the plus points? You will not have to worry about the private key that you used to encrypt, it will be automatically backed up, and saved for you. You can always use your email and password to retrieve the lost keys.
Crypto Ghost uses only a single encryption algorithm – GCM mode with 256-bit key length, since it only allows file encryption. It’s not necessary to follow complete device encryption, you can encrypt your sensitive files and share them over with friends. It may come in handy, if you are only interested in protecting a few amount of files.
While you can also search for other apps on the Play Store that may help you with encryption on your Android, but the above two, are the most renowned apps to help you deal with the situation.
Has encrypting been a helpful technique to safeguard your data? Let us know your own which method did you choose for encrypting your Android device, via the comments.