We propose a novel true random number generator using mouse movement and a one-dimensional chaotic map. We utilize the

Random number generators (RNGs) have been widely used in recently science and technology, such as simulation, sampling, numerical analysis, computer programming, decision making, recreation, cryptographic protocols, and cryptosystems [

However, it is widely known that TRNGs need a certain physical phenomena, like thermal noise [

Hu et al. [

Here we propose a simple algorithm of TRNGs based on user’s mouse movement and a one-dimensional chaotic map. We utilize the

In 2009, Aguirregabiria proposed a class of one-dimensional smooth map [

the Schwarzian derivative is negative in the whole interval. Schwarzian derivative is defined as

When map satisfies the three conditions above, we call the map “S-unimodal” [

Take

The curves of Lyapunov exponent.

Map (1) for

Map (4) for

And then, we use a modified class of one-dimensional maps in (

By simple calculation, one can find out that when

Here we are going to depict our algorithm carefully. We firstly choose the one-dimensional map depicted before to be the iteration map of our TRNGs algorithm. We then get the pattern of the mouse movement showed in Figure

The mouse movement pattern.

What is more, we add perturbation in each iteration, which will increase the randomness and break the periodic phenomenon. We replace the parameter

Using the algorithm we proposed above and the pattern we have, we produced 1000000 TRNs. We firstly draw the kernel density map in Figure

Kernel density map.

Histogram of the sequence.

Considering

Moreover, we draw the autocorrelation function of our binary sequences TRNs using the equation in (

The autocorrelation function

The autocorrelation function then is shown in Figure

Autocorrelation function.

We also test our binary sequences with the NIST statistical test suite [

In Table

Average time required to generate a random number using different approaches.

Approach | Our algorithm | Spatiotemporal chaos | NPTM |
---|---|---|---|

Total time (milliseconds) | 217 | 230 | 282 |

800-22 test’s results.

Test | Our algorithm | Spatiotemporal chaos ( | Spatiotemporal chaos ( | NPTM | Conclusion |
---|---|---|---|---|---|

Frequency test | 0.723674 | 0.3295 | 0.0938 | 0.1223 | Random |

Frequency test within a block | 0.777709 | 0.8303 | 0.9175 | 0.2236 | Random |

Runs test | 0.603211 | 0.9881 | 0.8999 | 0.0391 | Random |

Test for the longest run of ones in a block | 0.784089 | 0.3782 | 0.2019 | 0.0616 | Random |

Binary matrix rank test | 0.26483 | 0.8274 | 0.6724 | 0.3221 | Random |

Discrete fourier transform test | 0.807748 | 0.2087 | 0.0346 | 0.2622 | Random |

Maurer’s “universal statistical” test | 0.441263 | 0.2457 | 0.1466 | 0.0640 | Random |

Linear complexity test | 0.626767 | 0.5725 | 0.4654 | 0.3267 | Random |

Nonoverlapping template matching test | 0.904832 | 0.6238 | 0.5383 | 0.0012 | Random |

Overlapping template matching test | 0.625651 | 0.2264 | 0.0141 | 0.4118 | Random |

Approximate entropy test | 0.70213 | 0.5039 | 0.4180 | 0.9737 | Random |

Serial test | 0.617075 | 0.3448 | 0.1057 | 0.6434 | Random |

Cumulative sums test | 0.737518 | 0.2788 | 0.1314 | 0.1875 | Random |

Random excursions test | 0.72264 | 0.3538 | 0.4072 | 0.6352 | Random |

Random excursions variant test | 0.863832 | 0.7459 | 0.6731 | 0.9216 | Random |

By comparing the items in Table

In this paper, we first summarize some drawbacks of two proposed mouse movement TRNGs and propose a novel TRNG which conquers the flaws of the former two. The new algorithm is based on mouse movement and a one-dimensional chaotic map. The approach utilizes the

And then, we do some experiments and we compare the time cost of the three approaches and get the result that ours is a little bit faster than the other two. Last but not least, we test the three sequences with the NIST statistical test suite. Results show that our algorithm is better than the other two and is suitable to produce TRNs on universal PC.

This research is supported by the National Natural Science Foundation of China (nos. 61173183, 60973152, and 60573172), the Superior University Doctor Subject Special Scientific Research Foundation of China (no. 20070141014), and the Natural Science Foundation of Liaoning province (no. 20082165).