It really depends on what hosting service you are using and what capabilities you have. For something like that I would recommend using PHP and a database to hold user information. You could also make a database to hold the file names of each photo and whose photo it is.
For example... If you have a login where the user enters there name and a password or something to authorize themselves then you ca use php to find any photos in the database that are of that person and print them to the screen. I'm not sure how much experience you have but you can find tutorials all over the internet (php login script).
Depending on how many users you that are accessing you can either create seperate pages for each user and add login to each (for small amount) or the database will be your best friend
if your planning on having a lot of users.