Private Key and Certificate protection on IOS
Yes, iOS has MDM functionality built in to it to enforce enrollment into a policy framework where the device has to obey profile restrictions.

Passphrase restrictions was one of the first things to be deployed - perhaps around iOS 4.

You can use Apple's Server.app to set up these profiles as well as Apple Configurator and many third party MDM solutions can help you configure the OS to secure and introduce certificates and public/private key chains of trust.

Apple documents this at a high level at http://www.apple.com/iphone/business/it/management.html and once you have read up on how configuration profiles work, feel free to ask another more narrow question if you run into any difficulties.