Politics: Do you not have secret vote in your elections?

They can also know demographic information about you and whether you're registered with a particular political party. With all that info, there's a good chance they can figure out HOW you're likely to vote...

Sounds very similar to how it works here in the U.K. You have to get your name checked off the list, but no one knows how I voted.

That depends on your state, it's not standardized.

We don't register with a party in my state, but during primaries, you choose which party's primary you wish to cast a ballot. Then, you sign in on that roll, so there would be a record.

Not in my state, we are all mail in vote and we do not have to register for a party to vote. I have never been to a polling place I've done all my voting and registering via mail. 

In my state you have to be registered as a democrat, republican, or independent. BUT, those registered as independent voters don't get to vote in the primaries. During the primaries you can only vote in elections that are about your party. Once it goes to the general election you are able to vote for whoever you want and independents can vote as well.

Ballots at my polling place are a fill in the box with a black pen. Then the ballot is fed through a "reader" machine that reads the pattern of black squares I made. I'm the only one to handle it at that time. I feed it through the reader. There is a person nearby to help if I have questions about which way to turn it. But they aren't near enough to really see my ballot. 

The ballot doesn't identify me personally but when I go to vote there is a big book of names of people who are registered to vote and are assigned to that polling place. You get assigned to a polling place by your address. Mine is a nearby church. Churches are popular around here because they typically aren't in use during the week so voting isn't disrupting other activities, they have room for the machines and plenty of parking.

So, my state knows what party I am registered with, where I am assigned to vote, my demographics so they can make a statistical guess... but they don't know for sure how I personally voted.

And Norway as well.

it is also illegal in several states to provide anyone, including the federal govt, the information they are asking for.. and there is no information on how it would be used, how it would be stored, kept secured, etc.

this is basically trump spending our money to prove a fraud that never happen.. just like he spent over $200,000 to figure out that the national park service was telling and showing the truth on his crowds at the swearing in..

When I vote it is just as described in the OP, except that the paper ballot doesn't go in a box per SE...it goes in a machine kind of like an electronic mailbox. I haven't registered with a specific party but do vote in the Caucus (which is by party but I don't recall having to show any party ID when I voted at the caucus, just went to the one that I wanted to). If they get any info on how I voted I suppose it could be from the machine, or they monitor online habits, etc. Who knows.

They know i voted
The know I've switched parties umpteen times for primaries
They know which parties primaries ive voted in ( our state has seperate booths for each party and you can only go to one for the primary not both )

But they can't really know exactly who I voted for.

We don't have primaries in the same way as the US, but we have a system where each riding / region chooses people to represent them at the leadership conventions for each party, both provincially & federally. So I see some similarities to the primary system. I say that because who is chosen to go to the conventions is determined by a vote, which includes deciding which candidate the riding is going to support. 

In that sense our system has differences & similarities. 

We have to sign the voter roll, but then I get a paper ballot that I fill out and feed into a scantron machine. If they can link me to my specific vote, that'd be some witchcraft right there.

This is also how it works in my NorCal county.