INTRODUCTION
This work presents a pseudo-random number generator for low-cost RFID tags. The scheme is simple and sequential, yet its performance equals similar previous works. With equal performance, our proposal uses less die area and clock cycles, proving more suitable for low-cost tags. The scheme is inspired from the well founded pseudo random number generator, the Mersenne Twister. The proposed generator takes low-entropy seeds extracted from a physical characteristic of the tag and produces output that passes popular randomness tests. On the other hand, previous works’ tests are based on random number inputs used from a popular online source, which are not available to tags. The results of previous work repeated with low-entropy inputs are not satisfactory. The performance and randomness claims of our scheme are supported by extensive test results, accompanied by comparisons with previous works.
Algorithm:
x := TRN input
x:= ROTl(x,x)
y := x ⊕ ROTr (x,u)
y := y ⊕ (ROTl (y,s) & b)
y := y ⊕ ( ROTl (y,t) & c)
y := y ⊕ ROTr (y,l)
z := y ⊕ROTl (y & b, p)
The coefficients are := u = 7, (s, b) = (3, 9D2C568016), (t, c) = (5, EFC6000016), l = 18, p=7
EPC GEN2 Standards PRNG Results
UHF C1G2 Standard
- 1. Probability of a single RN16: The probability that any RN16 drawn from the RNG has value RN16=j for any j, shall be bounded by: 0.8/216<P(RN16=j)<1.25/216
- 2. Probability of simultaneously identical sequences: For a tag population of up to 10,000 tags, the probability that any of two or more tags simultaneously generate the same sequence of RN16s shall be less than 0.1%, regardless of when the tags are energized.
- 3. Probability of predicting an RN16: An RN16 drawn from a tag's RNG 10ms after the end of Tr, shall not be predictable with a probability greater than 0.025% if the outcomes of prior draws from RNG, performed under identical conditions, are known.
Our Results
1st test (Probability of a single RN16) for 3051*65536 numbers
|
Lower 16 bits |
Higher 16 bits |
XOR |
|
|
Lower limit |
0.926 |
0.919 |
0.923 |
|
Upper limit |
1.073 |
1.075 |
1.071 |
2nd test (Probability of simultaneously identical sequences)
|
Lower 16 bits |
Higher 16 bits |
XOR |
|
|
Our test result |
0.04 |
0.04 |
0.04 |
|
EPC Gen2 Standard |
0.1 |
0.1 |
0.1 |
3rd test (Probability of predicting an RN16)
|
Serial Correlation (16 bit values) |
|
|
Xor |
0.000008 |
|
Lower 16 bits |
0.000070 |
|
Higher 16 bits |
0.000021 |
ENT TEST RESULTS
|
ENT Test Results |
Lamed |
Akari-1/Akari-2 |
Ours |
|
Entropy (bits/byte) |
7.999999 |
8.000000 / 8.000000 |
7.999999 |
|
Compression Rate |
0% |
0% / 0% |
0% |
|
X2 Statistics |
256.90 (50%) |
259.09 (41.70%) / 250.99 (55.93%) |
212.60 (97.52%) |
|
Arithmetic Mean |
127.5024 |
127.4976 / 127.5031 |
127.5002 |
|
Monte Carlo Estimation |
3.141474228 |
3.141447036 / 3.141512474 |
3.141529759 |
|
Serial Correlation Coefficient |
-0.000023 |
-0.000026 / 0.000013 |
0.000009 |
DIEHARD1 RESULTS
| Test | Extra Rotation Added Values |
Input |
birthday spacings, |
1.00 |
0.00 |
overlapping permutations, |
0.25 |
0.00 |
ranks of 31x31 and 32x32 matrices |
0.00 |
0.00 |
ranks of 6x8 matrices |
1.00 |
0.00 |
monkey tests on 20-bit Words (bitstream) |
0.60 |
0.00 |
monkey tests OPSO, OQSO, DNA |
0.62 |
0.00 |
count the 1's in a stream of bytes |
0.50 |
0.00 |
count the 1's in specific bytes |
0.72 |
0.00 |
parking lot |
1.00 |
0.00 |
minimum distance |
1.00 |
0.00 |
random spheres |
1.00 |
0.00 |
squeeze |
1.00 |
0.00 |
overlapping sums |
0.50 |
0.00 |
runs |
0.75 |
0.00 |
craps. |
1.00 |
0.00 |
SUM |
10.94 |
0.00 |
DIEHARD2 RESULTS
NEW DIEHARD2 TEST DETAILS |
p-value |
Birthday spacings |
0.721339 |
Tough Birthday spacings |
0.547000 |
GCD |
0.732103 |
Gorilla |
0.119000 |
Overlapping Permutations |
0.4208, 0.6911, 0.6770, 0.6521, 0.6798 |
Ranks of 31×31 and 32×32 Matrices |
1 |
Ranks of 6×8 Matrices |
0.909593 |
Monkey tests on 20-bit words |
0.51857165 (Average) |
Monkey Test OPSO |
0.549708522 (Average) |
Monkey Test OQSO |
0.454735393 (Average) |
Monkey Test DNA |
0.603586871 (Average) |
Count the 1's in a stream of bytes |
0.249728 |
Count the 1's in specific bytes |
0.44275264 (Average) |
Parking lot test |
0.682237 |
Minimum distance test |
0.682303 |
Random spheres test |
0.870077 |
The squeeze test |
0.217116 |
Overlapping sums test |
0.773786 |
Runs up and down test |
0.673000 |
The craps test |
0.785901 |
Craps Test With Different Dice |
0.945402 |
Overall KS p-value |
0.223461 |
DIEHARD2 COMPARISON AMONG AKARI-X, LAMED AND OURS
|
Test Name |
Akari-1A/Akari-1B |
Akari-2A/Akari-2B/Akari-2C |
Lamed |
Ours |
|
Birthday spacings |
0.494 |
0.053 |
0.261 |
0.721 |
|
GCD and Gorilla |
0.524 |
0.114 |
0.778* |
0.426 |
|
Overlapping Permutations |
0.597 |
0.465 |
0.311* |
0.624 |
|
Ranks of 31×31 and 32×32 Matrices |
0.735 |
0.739 |
0.699* |
1.000 |
|
Ranks of 6×8 Matrices |
0.798 |
0.139 |
0.521 |
0.910 |
|
Monkey tests on 20-bit words |
0.462 |
0.471 |
0.312* |
0.519 |
|
Monkey Test OPSO |
0.462 |
0.387 |
0.436* |
0.550 |
|
Monkey Test OQSO |
0.448 |
0.520 |
0.742* |
0.455 |
|
Monkey Test DNA |
0.510 |
0.527 |
0.688* |
0.604 |
|
Count the 1's in a stream of bytes |
0.237 |
0.107 |
0.664 |
0.250 |
|
Count the 1's in specific bytes |
0.420 |
0.607 |
0.586* |
0.443 |
|
Parking lot |
0.233 |
0.511 |
0.433 |
0.682 |
|
Minimum distance |
0.253 |
0.121 |
0.411 |
0.682 |
|
Random spheres |
0.713 |
0.168 |
0.788 |
0.870 |
|
The squeeze |
0.729 |
0.003 |
0.841 |
0.217 |
|
Overlapping sums |
0.311 |
0.000 |
0.173 |
0.774 |
|
Runs up and down |
0.368 |
0.771 |
0.191 |
0.673 |
|
The craps |
0.608 |
0.046 |
0.443* |
0.786 |
|
Overall KS p-value |
0.353 |
0.082 |
0.778 |
0.224 |
Comparison of Diehard tests
|
Scheme |
Diehard1 Score |
Diehard2 Score |
|
Akari-1A |
12.40 |
0.353 |
|
Akari-1B |
12.40 |
0.353 |
|
Akari-2A |
7.50 |
0.082 |
|
Akari-2B |
7.50 |
0.082 |
|
Akari-2C |
7.50 |
0.082 |
|
Lamed |
13.00 |
0.778 |
|
Ours |
10.94 |
0.224 |
NIST RESULTS
C6 |
C7 |
C8 |
C9 |
C10 |
P-VALUE |
PROPORTION |
STATISTICAL TEST |
9 |
6 |
17 |
9 |
7 |
0.202268 |
1.0000 |
Frequency |
9 |
5 |
14 |
13 |
12 |
0.366918 |
0.9900 |
BlockFrequency |
14 |
9 |
7 |
12 |
9 |
0.224821 |
1.0000 |
CumulativeSums |
13 |
12 |
8 |
11 |
9 |
0.455937 |
1.0000 |
CumulativeSums |
12 |
7 |
7 |
8 |
10 |
0.437274 |
1.0000 |
Runs |
15 |
10 |
15 |
5 |
8 |
0.075719 |
0.9800 |
LongestRun |
0 |
0 |
0 |
0 |
0 |
0.000000 |
0.0000 |
* Rank |
15 |
11 |
11 |
8 |
9 |
0.514124 |
0.9900 |
FFT |
13 |
14 |
8 |
13 |
12 |
0.289667 |
0.9900 |
NonOverlappingTemplate |
12 |
16 |
15 |
10 |
11 |
0.153763 |
1.0000 |
NonOverlappingTemplate |
8 |
9 |
19 |
9 |
7 |
0.319084 |
0.9700 |
NonOverlappingTemplate |
12 |
5 |
16 |
11 |
11 |
0.514124 |
0.9800 |
NonOverlappingTemplate |
8 |
10 |
12 |
6 |
9 |
0.202268 |
0.9700 |
NonOverlappingTemplate |
8 |
7 |
11 |
9 |
7 |
0.262249 |
0.9800 |
NonOverlappingTemplate |
7 |
14 |
7 |
5 |
12 |
0.474986 |
0.9700 |
NonOverlappingTemplate |
10 |
5 |
7 |
11 |
7 |
0.122325 |
1.0000 |
NonOverlappingTemplate |
12 |
5 |
12 |
9 |
11 |
0.699313 |
0.9900 |
NonOverlappingTemplate |
13 |
5 |
4 |
9 |
14 |
0.224821 |
1.0000 |
NonOverlappingTemplate |
8 |
8 |
6 |
13 |
8 |
0.455937 |
0.9900 |
NonOverlappingTemplate |
10 |
10 |
7 |
10 |
8 |
0.759756 |
1.0000 |
NonOverlappingTemplate |
10 |
11 |
11 |
10 |
8 |
0.964295 |
0.9900 |
NonOverlappingTemplate |
6 |
14 |
11 |
9 |
5 |
0.657933 |
0.9800 |
NonOverlappingTemplate |
13 |
3 |
9 |
14 |
9 |
0.202268 |
0.9700 |
NonOverlappingTemplate |
8 |
9 |
13 |
7 |
6 |
0.514124 |
0.9900 |
NonOverlappingTemplate |
8 |
11 |
8 |
8 |
9 |
0.236810 |
0.9600 |
* NonOverlappingTemplate |
11 |
10 |
14 |
13 |
6 |
0.419021 |
0.9900 |
NonOverlappingTemplate |
12 |
9 |
12 |
9 |
7 |
0.719747 |
1.0000 |
NonOverlappingTemplate |
9 |
12 |
10 |
13 |
11 |
0.935716 |
0.9800 |
NonOverlappingTemplate |
10 |
10 |
16 |
12 |
9 |
0.699313 |
0.9900 |
NonOverlappingTemplate |
10 |
6 |
16 |
8 |
6 |
0.062821 |
1.0000 |
NonOverlappingTemplate |
8 |
7 |
12 |
13 |
6 |
0.437274 |
0.9600 |
* NonOverlappingTemplate |
10 |
10 |
9 |
6 |
14 |
0.494392 |
1.0000 |
NonOverlappingTemplate |
8 |
12 |
15 |
9 |
11 |
0.455937 |
1.0000 |
NonOverlappingTemplate |
10 |
12 |
15 |
7 |
13 |
0.249284 |
1.0000 |
NonOverlappingTemplate |
10 |
6 |
9 |
12 |
10 |
0.867692 |
0.9900 |
NonOverlappingTemplate |
6 |
10 |
8 |
14 |
12 |
0.474986 |
1.0000 |
NonOverlappingTemplate |
12 |
9 |
12 |
7 |
8 |
0.883171 |
0.9800 |
NonOverlappingTemplate |
12 |
8 |
7 |
13 |
7 |
0.816537 |
1.0000 |
NonOverlappingTemplate |
10 |
7 |
10 |
10 |
10 |
0.798139 |
0.9900 |
NonOverlappingTemplate |
13 |
9 |
12 |
11 |
5 |
0.350485 |
0.9900 |
NonOverlappingTemplate |
8 |
13 |
11 |
9 |
11 |
0.401199 |
0.9900 |
NonOverlappingTemplate |
10 |
7 |
8 |
8 |
14 |
0.534146 |
0.9900 |
NonOverlappingTemplate |
12 |
13 |
5 |
7 |
12 |
0.319084 |
1.0000 |
NonOverlappingTemplate |
13 |
8 |
6 |
11 |
9 |
0.678686 |
0.9900 |
NonOverlappingTemplate |
9 |
14 |
11 |
6 |
9 |
0.834308 |
0.9800 |
NonOverlappingTemplate |
7 |
12 |
16 |
16 |
6 |
0.162606 |
0.9900 |
NonOverlappingTemplate |
12 |
10 |
14 |
11 |
6 |
0.779188 |
0.9900 |
NonOverlappingTemplate |
9 |
9 |
14 |
10 |
9 |
0.514124 |
0.9900 |
NonOverlappingTemplate |
10 |
8 |
11 |
8 |
6 |
0.090936 |
0.9900 |
NonOverlappingTemplate |
7 |
11 |
13 |
7 |
6 |
0.595549 |
0.9900 |
NonOverlappingTemplate |
9 |
11 |
9 |
19 |
7 |
0.191687 |
1.0000 |
NonOverlappingTemplate |
5 |
8 |
7 |
12 |
11 |
0.514124 |
0.9900 |
NonOverlappingTemplate |
10 |
9 |
8 |
12 |
17 |
0.319084 |
0.9800 |
NonOverlappingTemplate |
9 |
11 |
12 |
9 |
11 |
0.759756 |
0.9800 |
NonOverlappingTemplate |
9 |
11 |
9 |
8 |
16 |
0.834308 |
1.0000 |
NonOverlappingTemplate |
11 |
14 |
9 |
9 |
12 |
0.657933 |
0.9800 |
NonOverlappingTemplate |
9 |
11 |
12 |
6 |
10 |
0.739918 |
0.9900 |
NonOverlappingTemplate |
9 |
7 |
12 |
15 |
6 |
0.334538 |
0.9800 |
NonOverlappingTemplate |
6 |
11 |
16 |
13 |
5 |
0.066882 |
0.9700 |
NonOverlappingTemplate |
2 |
11 |
12 |
9 |
13 |
0.090936 |
0.9900 |
NonOverlappingTemplate |
12 |
7 |
13 |
11 |
12 |
0.554420 |
0.9700 |
NonOverlappingTemplate |
20 |
5 |
13 |
5 |
11 |
0.019188 |
1.0000 |
NonOverlappingTemplate |
15 |
8 |
13 |
10 |
5 |
0.455937 |
0.9900 |
NonOverlappingTemplate |
12 |
7 |
15 |
6 |
8 |
0.455937 |
0.9800 |
NonOverlappingTemplate |
13 |
11 |
12 |
11 |
9 |
0.514124 |
1.0000 |
NonOverlappingTemplate |
6 |
13 |
10 |
11 |
16 |
0.401199 |
0.9800 |
NonOverlappingTemplate |
6 |
7 |
8 |
13 |
10 |
0.595549 |
1.0000 |
NonOverlappingTemplate |
6 |
16 |
9 |
8 |
8 |
0.102526 |
0.9900 |
NonOverlappingTemplate |
11 |
13 |
12 |
11 |
6 |
0.739918 |
0.9900 |
NonOverlappingTemplate |
5 |
13 |
8 |
13 |
5 |
0.514124 |
1.0000 |
NonOverlappingTemplate |
9 |
9 |
9 |
10 |
16 |
0.867692 |
0.9800 |
NonOverlappingTemplate |
11 |
9 |
13 |
8 |
16 |
0.474986 |
0.9900 |
NonOverlappingTemplate |
15 |
10 |
6 |
10 |
10 |
0.437274 |
0.9900 |
NonOverlappingTemplate |
6 |
6 |
13 |
13 |
11 |
0.637119 |
1.0000 |
NonOverlappingTemplate |
11 |
8 |
5 |
15 |
14 |
0.171867 |
0.9800 |
NonOverlappingTemplate |
13 |
6 |
9 |
10 |
10 |
0.494392 |
0.9700 |
NonOverlappingTemplate |
10 |
14 |
8 |
5 |
11 |
0.514124 |
1.0000 |
NonOverlappingTemplate |
9 |
10 |
10 |
7 |
6 |
0.249284 |
0.9800 |
NonOverlappingTemplate |
13 |
10 |
3 |
11 |
11 |
0.262249 |
0.9900 |
NonOverlappingTemplate |
6 |
8 |
7 |
14 |
11 |
0.191687 |
0.9700 |
NonOverlappingTemplate |
8 |
8 |
10 |
13 |
8 |
0.759756 |
1.0000 |
NonOverlappingTemplate |
9 |
4 |
11 |
12 |
13 |
0.350485 |
0.9900 |
NonOverlappingTemplate |
13 |
14 |
8 |
13 |
12 |
0.304126 |
0.9900 |
NonOverlappingTemplate |
15 |
6 |
8 |
3 |
15 |
0.066882 |
1.0000 |
NonOverlappingTemplate |
13 |
8 |
6 |
17 |
12 |
0.153763 |
1.0000 |
NonOverlappingTemplate |
6 |
10 |
12 |
8 |
11 |
0.834308 |
1.0000 |
NonOverlappingTemplate |
9 |
11 |
15 |
13 |
6 |
0.437274 |
0.9900 |
NonOverlappingTemplate |
5 |
5 |
12 |
14 |
11 |
0.090936 |
0.9800 |
NonOverlappingTemplate |
9 |
8 |
12 |
9 |
10 |
0.455937 |
0.9900 |
NonOverlappingTemplate |
13 |
12 |
6 |
5 |
12 |
0.595549 |
1.0000 |
NonOverlappingTemplate |
6 |
9 |
16 |
15 |
6 |
0.102526 |
0.9900 |
NonOverlappingTemplate |
10 |
7 |
11 |
14 |
13 |
0.595549 |
0.9900 |
NonOverlappingTemplate |
6 |
10 |
8 |
9 |
12 |
0.739918 |
0.9900 |
NonOverlappingTemplate |
7 |
7 |
8 |
8 |
13 |
0.867692 |
0.9900 |
NonOverlappingTemplate |
11 |
15 |
5 |
17 |
6 |
0.000474 |
0.9900 |
NonOverlappingTemplate |
8 |
18 |
10 |
7 |
7 |
0.236810 |
0.9900 |
NonOverlappingTemplate |
9 |
11 |
10 |
12 |
10 |
0.834308 |
1.0000 |
NonOverlappingTemplate |
6 |
11 |
17 |
7 |
8 |
0.437274 |
1.0000 |
NonOverlappingTemplate |
9 |
9 |
7 |
8 |
14 |
0.595549 |
0.9800 |
NonOverlappingTemplate |
11 |
10 |
12 |
7 |
8 |
0.383827 |
1.0000 |
NonOverlappingTemplate |
9 |
6 |
11 |
5 |
8 |
0.455937 |
0.9700 |
NonOverlappingTemplate |
11 |
7 |
8 |
9 |
7 |
0.366918 |
0.9800 |
NonOverlappingTemplate |
7 |
16 |
11 |
11 |
14 |
0.145326 |
1.0000 |
NonOverlappingTemplate |
10 |
9 |
13 |
9 |
7 |
0.798139 |
1.0000 |
NonOverlappingTemplate |
11 |
9 |
9 |
12 |
11 |
0.455937 |
0.9900 |
NonOverlappingTemplate |
10 |
9 |
9 |
6 |
6 |
0.058984 |
1.0000 |
NonOverlappingTemplate |
9 |
9 |
11 |
10 |
14 |
0.678686 |
0.9700 |
NonOverlappingTemplate |
8 |
15 |
8 |
12 |
6 |
0.289667 |
0.9700 |
NonOverlappingTemplate |
12 |
9 |
12 |
6 |
10 |
0.474986 |
0.9900 |
NonOverlappingTemplate |
6 |
7 |
7 |
7 |
16 |
0.085587 |
0.9800 |
NonOverlappingTemplate |
11 |
6 |
8 |
15 |
17 |
0.162606 |
1.0000 |
NonOverlappingTemplate |
9 |
9 |
8 |
11 |
9 |
0.935716 |
0.9900 |
NonOverlappingTemplate |
11 |
8 |
13 |
13 |
16 |
0.350485 |
0.9800 |
NonOverlappingTemplate |
8 |
13 |
12 |
9 |
3 |
0.455937 |
1.0000 |
NonOverlappingTemplate |
13 |
7 |
9 |
5 |
13 |
0.145326 |
0.9900 |
NonOverlappingTemplate |
12 |
13 |
10 |
12 |
9 |
0.699313 |
0.9900 |
NonOverlappingTemplate |
4 |
7 |
12 |
11 |
12 |
0.080519 |
0.9800 |
NonOverlappingTemplate |
8 |
12 |
12 |
13 |
9 |
0.401199 |
1.0000 |
NonOverlappingTemplate |
9 |
11 |
15 |
6 |
6 |
0.657933 |
1.0000 |
NonOverlappingTemplate |
11 |
6 |
12 |
12 |
11 |
0.867692 |
0.9800 |
NonOverlappingTemplate |
5 |
9 |
11 |
9 |
7 |
0.289667 |
0.9900 |
NonOverlappingTemplate |
7 |
5 |
13 |
13 |
10 |
0.657933 |
0.9800 |
NonOverlappingTemplate |
7 |
8 |
5 |
17 |
9 |
0.080519 |
1.0000 |
NonOverlappingTemplate |
11 |
12 |
6 |
6 |
14 |
0.162606 |
0.9900 |
NonOverlappingTemplate |
15 |
16 |
8 |
10 |
6 |
0.350485 |
1.0000 |
NonOverlappingTemplate |
16 |
17 |
8 |
9 |
6 |
0.137282 |
0.9800 |
NonOverlappingTemplate |
11 |
7 |
8 |
10 |
12 |
0.883171 |
0.9900 |
NonOverlappingTemplate |
7 |
7 |
10 |
13 |
6 |
0.401199 |
0.9900 |
NonOverlappingTemplate |
7 |
13 |
8 |
13 |
9 |
0.249284 |
0.9900 |
NonOverlappingTemplate |
8 |
11 |
11 |
9 |
15 |
0.678686 |
1.0000 |
NonOverlappingTemplate |
17 |
12 |
10 |
7 |
9 |
0.514124 |
1.0000 |
NonOverlappingTemplate |
7 |
10 |
13 |
15 |
5 |
0.350485 |
0.9900 |
NonOverlappingTemplate |
13 |
17 |
8 |
8 |
12 |
0.262249 |
1.0000 |
NonOverlappingTemplate |
13 |
11 |
8 |
10 |
10 |
0.883171 |
1.0000 |
NonOverlappingTemplate |
7 |
9 |
15 |
9 |
9 |
0.834308 |
1.0000 |
NonOverlappingTemplate |
9 |
12 |
13 |
11 |
8 |
0.897763 |
1.0000 |
NonOverlappingTemplate |
16 |
7 |
10 |
8 |
15 |
0.249284 |
0.9900 |
NonOverlappingTemplate |
11 |
10 |
12 |
6 |
10 |
0.759756 |
0.9700 |
NonOverlappingTemplate |
9 |
8 |
16 |
8 |
4 |
0.275709 |
0.9800 |
NonOverlappingTemplate |
8 |
17 |
9 |
12 |
11 |
0.474986 |
0.9800 |
NonOverlappingTemplate |
13 |
10 |
12 |
8 |
12 |
0.616305 |
0.9800 |
NonOverlappingTemplate |
8 |
9 |
8 |
9 |
9 |
0.719747 |
0.9900 |
NonOverlappingTemplate |
8 |
11 |
12 |
14 |
6 |
0.275709 |
1.0000 |
NonOverlappingTemplate |
12 |
7 |
14 |
9 |
5 |
0.514124 |
0.9900 |
NonOverlappingTemplate |
13 |
11 |
6 |
16 |
9 |
0.401199 |
0.9700 |
NonOverlappingTemplate |
10 |
8 |
8 |
14 |
13 |
0.883171 |
0.9700 |
NonOverlappingTemplate |
8 |
10 |
11 |
13 |
13 |
0.719747 |
0.9900 |
NonOverlappingTemplate |
9 |
14 |
12 |
10 |
9 |
0.699313 |
1.0000 |
NonOverlappingTemplate |
8 |
8 |
8 |
11 |
9 |
0.514124 |
0.9700 |
NonOverlappingTemplate |
12 |
14 |
13 |
6 |
12 |
0.616305 |
0.9800 |
NonOverlappingTemplate |
8 |
9 |
6 |
12 |
9 |
0.897763 |
1.0000 |
NonOverlappingTemplate |
6 |
12 |
11 |
10 |
15 |
0.779188 |
1.0000 |
NonOverlappingTemplate |
11 |
5 |
13 |
9 |
15 |
0.616305 |
0.9900 |
NonOverlappingTemplate |
11 |
8 |
13 |
8 |
10 |
0.816537 |
0.9900 |
NonOverlappingTemplate |
9 |
10 |
8 |
5 |
11 |
0.816537 |
1.0000 |
NonOverlappingTemplate |
9 |
4 |
11 |
12 |
13 |
0.249284 |
0.9900 |
NonOverlappingTemplate |
3 |
16 |
7 |
10 |
6 |
0.085587 |
1.0000 |
OverlappingTemplate |
0 |
0 |
0 |
0 |
0 |
0.000000* |
1.0000 |
Universal |
9 |
15 |
7 |
7 |
12 |
0.616305 |
0.9800 |
ApproximateEntropy |
0 |
1 |
1 |
2 |
1 |
0.739918 |
1.0000 |
RandomExcursions |
0 |
1 |
5 |
1 |
1 |
0.035174 |
1.0000 |
RandomExcursions |
3 |
0 |
0 |
1 |
1 |
0.122325 |
1.0000 |
RandomExcursions |
2 |
1 |
3 |
1 |
0 |
0.534146 |
1.0000 |
RandomExcursions |
0 |
3 |
0 |
1 |
1 |
0.213309 |
1.0000 |
RandomExcursions |
0 |
3 |
1 |
1 |
1 |
0.534146 |
0.9167 |
RandomExcursions |
1 |
1 |
1 |
1 |
2 |
0.991468 |
1.0000 |
RandomExcursions |
0 |
5 |
1 |
1 |
3 |
0.002043 |
1.0000 |
RandomExcursions |
3 |
2 |
1 |
0 |
0 |
0.213309 |
1.0000 |
RandomExcursionsVariant |
2 |
2 |
0 |
2 |
1 |
0.739918 |
1.0000 |
RandomExcursionsVariant |
2 |
1 |
0 |
2 |
3 |
0.350485 |
1.0000 |
RandomExcursionsVariant |
3 |
1 |
1 |
2 |
2 |
0.534146 |
1.0000 |
RandomExcursionsVariant |
0 |
2 |
0 |
3 |
3 |
0.122325 |
1.0000 |
RandomExcursionsVariant |
1 |
0 |
1 |
1 |
3 |
0.534146 |
1.0000 |
RandomExcursionsVariant |
1 |
0 |
2 |
1 |
2 |
0.534146 |
1.0000 |
RandomExcursionsVariant |
2 |
1 |
2 |
1 |
2 |
0.911413 |
1.0000 |
RandomExcursionsVariant |
2 |
2 |
3 |
1 |
1 |
0.534146 |
1.0000 |
RandomExcursionsVariant |
1 |
4 |
1 |
0 |
2 |
0.122325 |
1.0000 |
RandomExcursionsVariant |
1 |
1 |
2 |
3 |
1 |
0.739918 |
1.0000 |
RandomExcursionsVariant |
1 |
2 |
3 |
1 |
0 |
0.534146 |
1.0000 |
RandomExcursionsVariant |
1 |
0 |
2 |
1 |
1 |
0.534146 |
1.0000 |
RandomExcursionsVariant |
3 |
1 |
1 |
0 |
2 |
0.534146 |
1.0000 |
RandomExcursionsVariant |
1 |
0 |
2 |
2 |
0 |
0.213309 |
1.0000 |
RandomExcursionsVariant |
3 |
0 |
1 |
2 |
0 |
0.213309 |
1.0000 |
RandomExcursionsVariant |
1 |
1 |
1 |
0 |
2 |
0.739918 |
1.0000 |
RandomExcursionsVariant |
0 |
1 |
1 |
1 |
1 |
0.739918 |
1.0000 |
RandomExcursionsVariant |
13 |
7 |
8 |
8 |
10 |
0.834308 |
1.0000 |
Serial |
8 |
12 |
7 |
10 |
9 |
0.779188 |
0.9900 |
Serial |
7 |
4 |
6 |
13 |
9 |
0.122325 |
0.9900 |
LinearComplexity |