Hi,
We currently don't have a mechanism to secure mobile geodatabases. We could consider one of the sqlite encryption options available, but they can incur a significant impact on performance (one popular option states "as little as 5-15% overhead"). Depending on what risks you trying to secure against, full device encryption might be a viable route and it does seem to be increasingly popular these days. However, I think device/hard-disk encryption inevitably still has an overhead; how much that actually is in practice and whether it is acceptable to your users in the field would require some testing.
If I find any more information, I'll let you know.
Cheers
Mike