Every digital camera produces noisier images in dim light than bright light. Even many thousand dollar professional cameras. Cell phones are worse in this regard than real cameras (in general), and the higher megapixel cameras tend to be even worse.
Here's a very high level explanation of why: A digital image sensor is made up of a whole bunch of very tiny light sensors, called photo-sites. On the GS3, about 8 million of them. These photo-sites "collect" individual photons during the camera exposure. The fewer the photons, the weaker the signal the sensor generates, and the darker the image will be.
So if relatively few photons hit each photo-site, the camera has to amplify the signal coming from the sensor to make it bright enough to make a usable image. And when you amplify the signal, you also amplify the noise. So in dim light, the camera has to amplify the signal a lot, which makes the image noisier.
The more light, the more photons hit the sensor, and the better your image will be. How do we capture more photons? One way is to make the shutter speed longer, but beyond a certain point you'll get blurry images because you can't hold the camera still long enough.
Another way is to make each photo-site bigger (in diameter). The bigger the photo-site, the more surface area it has to absorb photons. To make photo-sites bigger, you either need to make the sensor bigger, or reduce the number of photo-sites. Cell phones don't have very much room for a big sensor. Consumers have been conditioned to equate more pixels with "better." So cell phone manufacturers cram a great many, very tiny, photo-sites into a very small sensor. That means that in low light the signal needs a lot of amplification (high ISO), which means a noisier image.
For the use most people make of cell phone pictures (posting on Facebook and other online sites), we'd probably be better off with fewer mega-pixels. But if you tried to sell a premium cell phone with a 4 MP camera today, you'd get laughed out of the marketplace.