You will need an internet-connected device (smartphone or laptop), but you don't need to download or sign up for anything. The answer key is publicly available on our website.
Interestingly enough, the odds of 3+ players having no smartphone among them are ~1% (by comparison, the odds of one player being illiterate are much higher), so unless you're playing the game in a remote location, you should be good to go.
That said, we have played a version with house rules that the judge is the ultimate authority -- i.e., he/she chooses the most convincing card, which immediately declares a winner, negating the need for an answer key. In this style, the gameplay becomes a lot like Apples To Apples or Cards Against Humanity; the upside is that plenty of people are familiar with that playing style, while the downside is that much of what makes Origin unique is lost. Still, it's a way to play if you're snowed in at a log cabin somewhere... though I might suggest burning the game for warmth rather than playing it at that point.