I apologize for such a noobish question and am ashamed that I'm not getting this yet, but I can't seem to put together all of the pieces. I've read every question I can find on the subject, the Satoshi paper, and bitcointalk.
How exactly is a transaction signed?
How exactly is a transaction verified? I simply cannot understand how secure transactions signed with private keys that are presumably unknown to all else can be confirmed to be valid and correct without actually knowing the private key itself. Please show me in detail how this works.
I know this looks like a dupe, but I've read every related question, and I just can't get to that "ah ha" moment that puts it all together.