How predictable are you? Chances are, more than you think.
Random numbers play a key role in modern information security, for secure communication and for protecting secret data. Cryptographic protocols require random numbers to ensure security of the encryption. Random numbers are also an important resource for stochastic simulations used in many branches of science, as well as for games and gambling. For security applications (and also for gambling), the most important property of the random numbers is that they need to be unpredictable to any potential adversary who might try to gain access to the data. Designing a perfectly unpredictable process, however, is much harder than it might first appear.
In this project, you will develop a software game to illustrate this for human players.
Humans are very bad random number generators in general. To many people, this comes as a suprise. After all, how hard can it be to hit the keys on your keybord at random, for example? However, even when we try to be unpredictable, there are usually patterns and correlations in our behaviour, which can be exploited to predict what we will do next. The idea is to create a game where the player tries to be random, and the computer tries to predict the player's next move. Prediction will be based on stochastic mathematics, such as Markov chains built from previous user inputs. The quality of the randomness can also be estimated using mathematical tools such as the Wald-Wolfowitz run test, enabling you to build a score function for the game.
You will need to be creative, develop new code, and to understand the underlying mathematics. The game should be illustrative, rigorous, and importantly - fun to play :).
If the game turns out well, it can be used at popular science events, when discussing the ongoing research on quantum random number generation at the section for Quantum Physics and Information Technology of DTU Physics. The fact that true unpredictability is very hard to create motivates the development of random-number generators based on quantum physics. Quantum mechanics is in fact the only branch of physics where unpredictability can be guaranteed directly from the fundamental laws of nature.
You can take inspiration from the game here
, which was developed for an outreach event in Geneva, Switzerland (in French). Input: 'q', 'e', 'i', 'p', and arrow keys.
Potential extensions of the project include:
- Development of a physical interface / controller to play the game at outreach events.
- A study of quantum random number generators and how they compare with traditional approaches.