If 2 prime numbers are multiplied together, it is very hard to find these 2 prime numbers from their product. e.g. 41 AND 83 are prime numbers. Their product is 3403. Given this product it is hard for a human to find the 2 prime factors. (multipliers). Now, in this case because we are only using 2 digit prime numbers a computer could solve this almost immediately. But the problem gets exponentially more difficult as the prime factors get larger and some would take a computer years to solve. This is why many encryption systems use very large prime numbers as factors: Here is a link that explains how these prime factors are used to in Public Key Encryption methods. http://www.livinginternet.com/i/is_crypt_pkc_work.htm
I think it would work in a similar way to a 'Smart fridge' In order that you can communicate with said fridge you need to have it connected with the internet. Somewhere in the machines small print will be a clause that allows the manufacturer to harvest (no pun intended) your data and sell it to whomever they wish. The only way to stop the data would be to disconnect the machine from the net (or maybe communications is done by GPS?) However the machine may not work if it can not communicate.