RNG generators based on nuclear decay are a good source of random number. The working principle is relatively simple: they convert the detection of particles in random numbers, using different algorithms. My appliance uses an Arduino board (Diecimila) with a Geiger shield. Both hardware and software components are explained in detail in the following paragraphs.
The days after Fukushima disaster (2011), I and someone I knew bought Geiger counters. I didn't think was even possible that some kind of radioactive cloud was able to reach us here, in Europe, but I had a lot of curiosity about the instrument itself and I found that was a good occasion to learn something interesting.
My first requirement for the instrument I was about to buy was that it had to be a fully documented or, better, an open source project , the second requirement was that it had to be a programmable tool. I found an Arduino shield ( now discontinued ), produced from company called Cooking-Hacks, able to satisfy both those requirements.
The RNG algorithm is made very simple relying on interrupts: in the main loop a register is cyclically increased from 0 to n, when it reaches n is reset to 0. When a particle is detected an interrupt is raised, the main loop is paused and the routine associated to the interrupt is executed, returning the last value of the register as random number then the register is reset to zero and the main loop resumed. The chosen range is 0-15 represented using hexadecimal digits (0-9A-F), that is convenient because two hex digits represent a full random byte.
The random numbers are presented on the LCD display at slow rate and through the serial port at faster rate. The display is intended as "virtual dice" usable, for example, with board games, the special device, instead, to interface the appliance to computer programs.
- compile and deploy the sketch;
- You can read the random numbers on the display or on the serial console;
- This example show how to read produced random numbers from the serial console by command line on OsX systems:
cat /dev/cu.usbserial-A700700G > rndnums.txt- Note: the appliance also write the Geiger radiation values on the serial console, they could be filtered using grep, for example.
Generated a first sample of 100k random bytes (aka 200k couples of hex digits), I started with basic tests, average value, single values distributions, scatter diagrams. This is the scatter diagram composed using 4 bytes for each point (2 bytes X, 2 bytes Y):
Then, after the basic testing just explained, I tested my sequence with ENT (see here: https://www.fourmilab.ch/random/). ENT is a command line tool providing a way to perform common test on a random sequence to verify the quality of its random numbers.
I installed ENT on my Ubuntu machine:
apt-get install entIn the "test" directory present in this repository, some tools able to convert the ascii streams from my appliance console to binary file and able to perform test with ENT, also a file created reading from /dev/urandom of similar length is provided and testes to compare the two related reports from ENT.
A makefile do all the job:
make clean allI tested the randomness both testing the bytes and the single bits in the binary file created from the ASCII file from the appliance console ( see Appendix here or test directory for full result text).
Accordingly with ENT man page: "If the percentage is greater than 99% or less than 1%, the sequence is almost certainly not random. If the percentage is between 99% and 95% or between 1% and 5%, the sequence is suspect. Percentages between 90% and 95% and 5% and 10% indicate the sequence is “almost suspect”", so having 85.17 percent in the bytes test and 60.52 percent in the bits test should be fine.
Averages values should be also ok.
About Monte Carlo Pi Value, as explained in the man page: "he value will approach the correct value of Pi if the sequence is close to random.", then the result, 3.152465586 (error 0.35 percent), should be fine.
In using the conditional here because, to perform more complete tests (i.e. using the dieharder suite - https://webhome.phy.duke.edu/~rgb/General/dieharder.php) a longer random number sequence, 1 to 100 GB of data, should be available but this is beyond my current availability. I hope to perform further tests in the future.
If you found errors or have suggestions about the improvement of this appliance, let me know. Any advice of bug report is welcome.
Value Char Occurrences Fraction
0 393 0.003804
1 416 0.004027
2 403 0.003901
3 407 0.003940
4 391 0.003785
5 433 0.004192
6 370 0.003582
7 412 0.003988
8 421 0.004075
9 408 0.003950
10 388 0.003756
11 388 0.003756
12 425 0.004114
13 425 0.004114
14 420 0.004066
15 400 0.003872
16 413 0.003998
17 387 0.003746
18 385 0.003727
19 388 0.003756
20 428 0.004143
21 403 0.003901
22 393 0.003804
23 426 0.004124
24 399 0.003862
25 443 0.004288
26 396 0.003833
27 374 0.003620
28 427 0.004133
29 393 0.003804
30 404 0.003911
31 404 0.003911
32 437 0.004230
33 ! 417 0.004037
34 " 405 0.003920
35 # 427 0.004133
36 $ 406 0.003930
37 % 392 0.003795
38 & 424 0.004104
39 ' 393 0.003804
40 ( 425 0.004114
41 ) 404 0.003911
42 * 437 0.004230
43 + 409 0.003959
44 , 397 0.003843
45 - 386 0.003737
46 . 398 0.003853
47 / 412 0.003988
48 0 420 0.004066
49 1 395 0.003824
50 2 432 0.004182
51 3 427 0.004133
52 4 399 0.003862
53 5 420 0.004066
54 6 430 0.004162
55 7 413 0.003998
56 8 388 0.003756
57 9 423 0.004095
58 : 388 0.003756
59 ; 406 0.003930
60 < 378 0.003659
61 = 389 0.003766
62 > 393 0.003804
63 ? 414 0.004008
64 @ 428 0.004143
65 A 383 0.003708
66 B 409 0.003959
67 C 393 0.003804
68 D 410 0.003969
69 E 392 0.003795
70 F 388 0.003756
71 G 399 0.003862
72 H 391 0.003785
73 I 412 0.003988
74 J 437 0.004230
75 K 437 0.004230
76 L 394 0.003814
77 M 363 0.003514
78 N 382 0.003698
79 O 429 0.004153
80 P 414 0.004008
81 Q 376 0.003640
82 R 408 0.003950
83 S 394 0.003814
84 T 396 0.003833
85 U 401 0.003882
86 V 407 0.003940
87 W 411 0.003979
88 X 450 0.004356
89 Y 413 0.003998
90 Z 430 0.004162
91 [ 411 0.003979
92 \ 423 0.004095
93 ] 391 0.003785
94 ^ 408 0.003950
95 _ 403 0.003901
96 ` 367 0.003553
97 a 419 0.004056
98 b 369 0.003572
99 c 396 0.003833
100 d 410 0.003969
101 e 393 0.003804
102 f 409 0.003959
103 g 417 0.004037
104 h 374 0.003620
105 i 406 0.003930
106 j 402 0.003891
107 k 413 0.003998
108 l 391 0.003785
109 m 401 0.003882
110 n 396 0.003833
111 o 388 0.003756
112 p 426 0.004124
113 q 394 0.003814
114 r 386 0.003737
115 s 427 0.004133
116 t 399 0.003862
117 u 400 0.003872
118 v 416 0.004027
119 w 417 0.004037
120 x 381 0.003688
121 y 392 0.003795
122 z 392 0.003795
123 { 421 0.004075
124 | 384 0.003717
125 } 403 0.003901
126 ~ 428 0.004143
127 384 0.003717
128 391 0.003785
129 397 0.003843
130 385 0.003727
131 418 0.004046
132 366 0.003543
133 402 0.003891
134 374 0.003620
135 422 0.004085
136 390 0.003775
137 381 0.003688
138 398 0.003853
139 411 0.003979
140 413 0.003998
141 392 0.003795
142 390 0.003775
143 421 0.004075
144 402 0.003891
145 419 0.004056
146 378 0.003659
147 412 0.003988
148 423 0.004095
149 423 0.004095
150 434 0.004201
151 375 0.003630
152 456 0.004414
153 357 0.003456
154 389 0.003766
155 386 0.003737
156 440 0.004259
157 409 0.003959
158 367 0.003553
159 409 0.003959
160 396 0.003833
161 ? 403 0.003901
162 ? 397 0.003843
163 ? 414 0.004008
164 ? 398 0.003853
165 ? 425 0.004114
166 ? 446 0.004317
167 ? 399 0.003862
168 ? 404 0.003911
169 ? 385 0.003727
170 ? 428 0.004143
171 ? 411 0.003979
172 ? 419 0.004056
173 ? 399 0.003862
174 ? 371 0.003591
175 ? 403 0.003901
176 ? 441 0.004269
177 ? 368 0.003562
178 ? 382 0.003698
179 ? 370 0.003582
180 ? 396 0.003833
181 ? 412 0.003988
182 ? 364 0.003524
183 ? 391 0.003785
184 ? 403 0.003901
185 ? 406 0.003930
186 ? 420 0.004066
187 ? 382 0.003698
188 ? 367 0.003553
189 ? 401 0.003882
190 ? 402 0.003891
191 ? 407 0.003940
192 ? 419 0.004056
193 ? 417 0.004037
194 ? 382 0.003698
195 ? 445 0.004308
196 ? 365 0.003533
197 ? 381 0.003688
198 ? 404 0.003911
199 ? 425 0.004114
200 ? 385 0.003727
201 ? 427 0.004133
202 ? 378 0.003659
203 ? 406 0.003930
204 ? 385 0.003727
205 ? 409 0.003959
206 ? 398 0.003853
207 ? 404 0.003911
208 ? 385 0.003727
209 ? 401 0.003882
210 ? 412 0.003988
211 ? 439 0.004250
212 ? 445 0.004308
213 ? 418 0.004046
214 ? 393 0.003804
215 ? 392 0.003795
216 ? 391 0.003785
217 ? 407 0.003940
218 ? 405 0.003920
219 ? 444 0.004298
220 ? 417 0.004037
221 ? 375 0.003630
222 ? 409 0.003959
223 ? 378 0.003659
224 ? 387 0.003746
225 ? 373 0.003611
226 ? 393 0.003804
227 ? 407 0.003940
228 ? 396 0.003833
229 ? 390 0.003775
230 ? 401 0.003882
231 ? 389 0.003766
232 ? 409 0.003959
233 ? 375 0.003630
234 ? 384 0.003717
235 ? 409 0.003959
236 ? 389 0.003766
237 ? 411 0.003979
238 ? 396 0.003833
239 ? 387 0.003746
240 ? 455 0.004404
241 ? 417 0.004037
242 ? 402 0.003891
243 ? 416 0.004027
244 ? 423 0.004095
245 ? 382 0.003698
246 ? 423 0.004095
247 ? 410 0.003969
248 ? 420 0.004066
249 ? 389 0.003766
250 ? 393 0.003804
251 ? 429 0.004153
252 ? 426 0.004124
253 ? 417 0.004037
254 ? 398 0.003853
255 ? 396 0.003833
Total: 103304 1.000000
Entropy = 7.998386 bits per byte.
Optimum compression would reduce the size
of this 103304 byte file by 0 percent.
Chi square distribution for 103304 samples is 231.52, and randomly
would exceed this value 85.17 percent of the times.
Arithmetic mean value of data bytes is 127.2572 (127.5 = random).
Monte Carlo value for Pi is 3.152465586 (error 0.35 percent).
Serial correlation coefficient is -0.005576 (totally uncorrelated = 0.0).Value Char Occurrences Fraction
0 413451 0.500284
1 412981 0.499716
Total: 826432 1.000000
Entropy = 1.000000 bits per bit.
Optimum compression would reduce the size
of this 826432 bit file by 0 percent.
Chi square distribution for 826432 samples is 0.27, and randomly
would exceed this value 60.52 percent of the times.
Arithmetic mean value of data bits is 0.4997 (0.5 = random).
Monte Carlo value for Pi is 3.152465586 (error 0.35 percent).
Serial correlation coefficient is 0.000822 (totally uncorrelated = 0.0).