>>5322454As far as I know one of 3 things can happen:
1. You have a dynamic IP address. Your ISP issues your modem a lease on an IP address for a certain period of time, your modem has to communicate with your ISP for this. Many devices have things called Media Access Control addresses that are written to ROM on the device, this is a unique identifier for the device. A protocol called DHCP is used to issue a device with a MAC address a lease on an IP address, which is to say the DHCP server tells the device it can use a certain IP address for X amount of time. MAC addresses are unique identifiers and your ISP will know, and log, when your modem is assigned an IP address and when.
2. You have a static IP address. Your modem's IP address is hard-coded to the device, and set aside by your ISP for you. It will never change. Your ISP will know this is you, obviously.
3. You have a sticky IP address. Your IP address is tied to the MAC address of your router. As far as I know this is pretty much the same as the DHCP one except when your modem asks for an IP address it has that IP address set aside indefinitely for you. These can change, but don't in practice.
Since you pay your ISP for their services they have sufficient information to identify you from an IP address and timestamp at any time. I'm pretty sure they aren't allowed to sell this data, and I'm not sure how long records are kept for; but they will cooperate with the police.
