Item Level Security Based On Column

Hello,

I would like to secure items in a list based on a Person or Group column.  So "John Smith" can only access items where his name is in the Person or Group column "Assigned To".  

The list was created in SharePoint 2007 and we have migrated it to 2013.  The security is broken.  I need to retroactively secure about 1000 items.

Is there a way to do this?

Thanks in advance.