dm00073853

AN4230
Application note
STM32 microcontrollers random number generation validation
using NIST statistical test suite
Introduction
Many standards have created requirements and references for the construction, the
validation and the use of random number generators (RNG), in order to verify that the output
they produce is indeed random.
The purpose of this application note is to provide guidelines to verify the randomness of the
numbers generated by the random number generator peripheral embedded in a selection of
STM32 microcontrollers. This verification is based on the National Institute of Standards and
Technology (NIST) Statistical Test Suite (STS) SP 800-22rev1a (April 2010).
This document is structured as follows:
• A general introduction to STM32 microcontrollers random number generator (see
Section 1)
• The NIST SP800-22b test suite (see Section 2)
• The steps needed to run NIST SP800-22b test and analysis (see Section 3)
Table 1. Applicable products
Type
Microcontrollers
June 2016
Product series
STM32F2 series, STM32F4 series, STM32F7 series, STM32L0 series,
STM32L4 series.
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1
Contents
AN4230
Contents
1
STM32 microcontrollers random number generator . . . . . . . . . . . . . . . 4
1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2
STM32 microcontrollers implementation description . . . . . . . . . . . . . . . . . 4
1.2.1
2
3
NIST SP800-22b test suite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2
NIST SP800-22b test suite description . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
NIST SP800-22b test suite running and analyzing . . . . . . . . . . . . . . . . . 8
3.1
3.2
4
True random number generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Firmware description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1.1
On the STM32 microcontroller side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1.2
On the NIST SP800-22b test suite side . . . . . . . . . . . . . . . . . . . . . . . . . . 8
NIST SP800-22b test suite steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.1
First step: random number generator . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2.2
Second step: NIST statistical test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2.3
Third step: tests report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Appendix A Additional information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
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List of figures
List of figures
Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.
Figure 9.
Figure 10.
Block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Block diagram of deviation testing of a binary sequence from randomness
based on NIST test suite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Main sts-2.1.1 screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
File input screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Statistical test screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Parameter adjustment screen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Bitstreams input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Input file format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Statistical testing in progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Statistical testing complete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
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STM32 microcontrollers random number generator
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1
STM32 microcontrollers random number generator
1.1
Introduction
Random number generators (RNG) used for cryptographic applications typically produce
sequences made of random 0 and 1 bits.
There are two basic classes of random number generators:
1.
Deterministic random number generator or pseudo random number generator (PRNG):
A deterministic RNG consisting of an algorithm that produces a sequence of bits from
an initial value called a seed. To ensure forward unpredictability, care must be taken in
obtaining seeds. The values produced by a PRNG are completely predictable if the
seed and generation algorithm are known. Since in many cases the generation
algorithm is publicly available, the seed must be kept secret and generated from a
TRNG.
2.
Non deterministic random number generator or True random number generator
(TRNG):
A nondeterministic RNG producing randomness which depends on some unpredictable
physical source (i.e. the entropy source) outside of any human control.
The RNG hardware peripheral implemented on the STM32 microcontrollers and described
in Section 1.2.1 is a true random number generator.
1.2
STM32 microcontrollers implementation description
1.2.1
True random number generator
The following table lists the STM32 microcontrollers lines that embed the RNG hardware
peripheral:
Table 2. STM32 lines embedding the RNG hardware peripheral
STM32 series
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STM32 lines
STM32F2
STM32F2x5
STM32F2x7
STM32F4
STM32F405/415
STM32F407/417
STM32F410
STM32F427/437
STM32F429/439
STM32F469/479
STM32F7
STM32F7x5
STM32F7x6
STM32L0
STM32L05x
STM32L06x
STM32L072/073
STM32L4
STM32L4x6
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STM32 microcontrollers random number generator
The True random number generator peripheral implemented on STM32 microcontrollers is
based on an analog circuit. This circuit generates a continuous analog noise that will be
used on the RNG processing in order to produce a 32-bit random number.
The analog circuit is made of several ring oscillators whose outputs are XORed.
The RNG processing is clocked by a dedicated clock at a constant frequency and for a
subset of microcontrollers it can also be clocked with a different value of frequency.
For more details about the RNG peripherals please refer to the STM32 microcontroller
reference manual.
Figure 1 shows the TRNG block diagram on STM32 microcontrollers.
Figure 1. Block diagram
ELW$+%EXV
'DWDUHJLVWHU
&RQWUROUHJLVWHU
51*B&5
51*B'5
51*SURFHVVLQJ
51*B&/.
6WDWXVUHJLVWHU
51*B65
&ORFNFKHFNHUDQG
IDXOWGHWHFWRU
$QDORJVHHG
06Y9
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NIST SP800-22b test suite
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2
NIST SP800-22b test suite
2.1
Introduction
The NIST SP800-22b statistical test suite has been carried out using a statistical test suite
(sts) developed by the National institute of standards and technology (NIST) to probe the
quality of random generators for cryptographic applications. A comprehensive description of
the suite was presented in the paper entitled: “A Statistical Test Suite for the Validation of
Random Number Generators and Pseudo Random Number Generators for Cryptographic
Applications”.
2.2
NIST SP800-22b test suite description
The NIST SP800-22b statistical test suite “sts-2.1.1” is a software package which was
developed by the National Institute of Standards and Technology; it can be downloaded
from the NIST web site: search for “NIST Statistical Test Suite download” at
http://csrc.nist.gov.
The source code has been written in ANSI C. The NIST statistical test suite consists of 15
tests that were developed to test the randomness of a binary sequence. These tests focus
on a variety of types of non-randomness that could exist in a sequence. From this point of
view, the test suite can be classified as follows:
Frequency tests
• Frequency (Monobit) test:
To measure the distribution of 0’s and 1’s in a sequence and to check if the result is similar
to the one expected for a truly random sequence.
• Frequency test within a block:
To check whether the frequency of 1’s in an M-bit block is approximately M/2, as would
be expected from the theory of randomness.
• Run tests:
To assess if the expected total number of runs of 1’s and 0’s of various lengths is as
expected for a random sequence.
• Test of the longest run of 1’s in a block:
To examine the long runs of 1’s in a sequence.
Test of linearity
• Binary matrix rank test:
To assess the distribution of the rank for 32x32 binary matrices.
• Linear complexity test:
To determine the linear complexity of a finite sequence.
Test of correlation (by means of Fourier transform)
• Discrete Fourier transform (spectral) test:
To assess the spectral frequency of a bit string via the spectral test based on the discrete
Fourier transform. It is sensitive to the periodicity in the sequence.
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NIST SP800-22b test suite
Test of finding some special strings
• Non-overlapping template matching test:
To assess the frequency of m-bit non-periodic patterns.
• Overlapping template matching test:
To assess the frequency of m-bit periodic templates
Entropy tests
• Maurer’s “Universal Statistical” test:
To assess the compressibility of a binary sequence of L-bit blocks.
• Serial test:
To assess the distribution of all 2m m-bit blocks.
Note:
For m = 1, the serial test is equivalent to the Frequency test of Section 2.2.
• Approximate entropy test:
To assess the entropy of a bit string, comparing the frequency of all m-bit patterns against
all (m+1)-bit patterns.
Random walk tests
• Cumulative sums (Cusums) test:
To assess that the sum of partial sequences is not too large or too small; it is indicative of
too many 0’s or 1’s.
• Random excursion test:
To assess the distribution of states within a cycle of random walk.
• Random excursion variant test:
To detect deviations from the expected number of visits to different states of the random
walk.
Each of the above tests is based on a calculated test statistic value, which is a function of
the testing sequence. The test statistic value is used to calculate a Pvalue where:
Pvalue is the probability that the perfect random number generator would have produced a
sequence less random than the sequence that was tested.
For more details about the NIST statistical test suite, refer to the following NIST document
available on the NIST web site:
“A Statistical Test Suite for Random and Pseudorandom Number Generators for
Cryptographic Applications” Special Publication 800-22 Revision 1a.
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3
NIST SP800-22b test suite running and analyzing
3.1
Firmware description
To run the NIST statistical test suite as described in the previous section, two firmware are
needed, one on the STM32 microcontroller side and one on the NIST SP800-22b test suite
side.
3.1.1
On the STM32 microcontroller side
The firmware package is provided upon request, for more details please contact your local
ST sales representative.
The program allows to generate random numbers using the STM32 microcontroller random
number generator (RNG) peripheral and to retrieve them on a workstation for testing with
the NIST statistical test suite.
Each firmware program is used to generate 10 blocks of 64,000 bytes of random number, so
the output file will contain 5,120,000 random bits to be tested with the NIST statistical test.
As recommended by the NIST statistical test suite, the output file format can be:
1.
a sequence of ASCII 0's and 1's if the FILE_ASCII_FORMAT Private define is
uncommented in the main.c file
2.
A binary file of random bytes if the FILE_BINARY_FORMAT Private define is
uncommented in the main.c file.
Form more details about the program description and settings, refer to the readme file inside
the firmware package.
Note:
The USART configuration can be changed by the user via the SendToWorkstation() function
in the main.c file.
The output values can be changed by the user by modifying the Private define in the main.c
file:
#define NUMBER_OF_RANDOM_BITS_TO_GENERATE 512000
#define BLOCK_NUMBER 10
3.1.2
On the NIST SP800-22b test suite side
Downloaded on a workstation, the NIST statistical test suite package sts-2.1.1 verifies the
randomness of the output file of the random number generator from STM32
microcontrollers.
The generator file to be analyzed should be stored under the data folder (sts-2.1.1\data).
For more details about how the NIST statistical tests work, refer to section How to Get
Started in “A Statistical Test Suite for Random and Pseudorandom Number Generators for
Cryptographic Applications” Special Publication 800-22 Revision 1a.
3.2
NIST SP800-22b test suite steps
Figure 2 describes the different steps needed to verify the randomness of an output number
generated by STM32 microcontrollers using the NIST statistical test suite package sts-2.1.1.
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NIST SP800-22b test suite running and analyzing
Figure 2. Block diagram of deviation testing of a binary sequence from randomness
based on NIST test suite
3.2.1
First step: random number generator
Connect the STMicroelectonics board to the workstation. Depending on the type of board,
the connection is made via:
•
a null-modem female/female RS232 cable
•
a USB “type A to Mini-B" cable
Run STM32 microcontroller RNG generation via the UART firmware in order to generate a
random number as described in the previous section. You can store data on the workstation
using a terminal emulation application such as HyperTerminal (a program that comes with
Windows operating system, from Windows 98).
3.2.2
Second step: NIST statistical test
Compile sts-2.1.1 package as described in the NIST statistical test suite documentation in
order to create an executable program using visual C++ compiler.
After running the NIST statistical test suite program, a series of menu prompts will be
displayed in order to select the data to be analyzed and the statistical tests to be applied.
In this application note, the NIST statistical test suite is compiled under the name
assess.exe and saved under NIST_Test_Suite_OutputExample folder. As described in the
previous section, the random number is defined as 512,000 bits per block.
The first screen appears as in Figure 3.
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Figure 3. Main sts-2.1.1 screen
When value 0 is entered, the program requires to enter the file name and path of the
random number to be tested.
The second screen appears as in Figure 4.
Figure 4. File input screen
This application note provides you with an example of two files per series, generated with
STM32 microcontroller random number generator with different file formats as
recommended by NIST:
1.
ascii.bin: sequence of ASCII 0's and 1's.
2.
binary.bin: each byte in the data file contains 8 bits of data.
Then, the NIST statistical test suite displays 15 tests that can be run via the screen in
Figure 5.
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Figure 5. Statistical test screen
In this case, ‘1’ has been selected to apply all of the statistical tests. Figure 6 is displayed to
change the parameter adjustments.
Figure 6. Parameter adjustment screen
In this example, the default settings are kept and value ‘0’ is selected to go to the next step.
Figure 7. Bitstreams input
The NIST statistical test suite requires to put the number of bitstreams; here, ‘10’ is entered.
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You have selected 10 blocks of 512,000 bits which equal to 5,120,000 bits.
You must then specify whether the file consists of bits stored in ASCII format or hexadecimal
strings stored in a binary format using the following screen.
Figure 8. Input file format
Value ‘0’ is selected because the file is in ASCII format.
After entering all necessary inputs, the NIST statistical test suite starts analyzing the input
file.
Figure 9. Statistical testing in progress
When the testing process is complete, as shown in Figure 10, the statistical test results can
be found in sts-2.1.1\experiments\AlgorithmTesting.
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Figure 10. Statistical testing complete
3.2.3
Third step: tests report
The NIST statistical tests provide an analytical routine to facilitate the interpretation of the
results. A file named finalAnalysisReport is generated when the statistical testing is
complete and saved under sts2.1.1\experiments\AlgorithmTesting. The report contains a
summary of experimental results of 15 tests, as described in Appendix A.
The NST statistical tests also provide a detailed report for each test, which is saved under
sts-2.1.1\experiments\AlgorithmTesting\<Test suite name>.
Note:
You can find two examples per series of complete NIST statistical test suite output reports
under “NIST_Test_Suite_OutputExample” .
1.
2.
Example of an Ascii_File_Format. This example has 2 folders:
–
Input_File which contains the random number generator saved with the ascii
format.
–
Final_Analysis_Report which contains the complete NIST statistical test suite
output report based on this input file, the summary of experimental results and the
report of each test.
Example of a Binary_File_Format. This example has 2 folders:
–
Input_File which contains the random number generator saved with the binary
format.
–
Final_Analysis_Report which contains the complete NIST statistical test suite
output report based on this input file, the summary of experimental results and the
report of each test.
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Conclusion
4
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Conclusion
This application note describes the main guidelines and steps to verify the randomness of
numbers generated by the STM32 microcontrollers random number generator peripheral
using NIST statistical test suite SP800-22rev1a, April 2010.
15 tests of NIST statistical test suite are passed in accordance with the minimum pass rate
for each statistical test run on each STM32 series support the RNG peripheral.
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Additional information
Appendix A
Additional information
The results are represented as a table with p rows and q columns.
•
The number of rows, p, corresponds to the number of statistical tests applied.
•
The number of columns, q = 13, is distributed as follows:
–
columns 1-10 correspond to the frequency of P-values10,
–
column 11 is the P-value that arises via the application of a chi-square test11,
–
column 12 is the proportion of binary sequences that passed,
–
column 13 is the corresponding statistical test.
An example is shown in Table 3. For more details, refer to finalAnalysisReport file under sts2.1.1\experiments\AlgorithmTesting).
Table 3. Example
-----------------------------------------------------------------------------RESULTS FOR THE UNIFORMITY OF P-VALUES AND THE PROPORTION OF PASSING
SEQUENCES
-----------------------------------------------------------------------------generator is <data/ascii.bin>
-----------------------------------------------------------------------------C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 P-VALUE PROPORTION STATISTICAL TEST
-----------------------------------------------------------------------------0 1 2 1 2 1 1 1 0 1 0.911413
10/10
Frequency
1 1 0 1 3 0 2 1 1 0 0.534146
10/10
BlockFrequency
0 1 3 3 0 1 0 2 0 0 0.122325
10/10
CumulativeSums
1 1 3 1 0 1 1 1 0 1 0.739918
10/10
CumulativeSums
2 0 2 2 1 1 0 1 0 1 0.739918
10/10
Runs
1 0 1 1 0 3 1 1 0 2 0.534146
9/10
LongestRun
1 2 1 0 2 1 1 0 0 2 0.739918
10/10
Rank
3 0 1 2 1 1 0 1 0 1 0.534146
9/10
FFT
1 1 1 0 0 2 1 2 0 2 0.739918
10/10
NonOverlappingTemplate
1 1 0 0 1 1 1 3 0 2 0.534146
10/10
NonOverlappingTemplate
0 2 1 0 4 0 2 0 0 1 0.066882
10/10
NonOverlappingTemplate
0 0 0 1 1 3 0 2 1 2 0.350485
10/10
NonOverlappingTemplate
0 1 2 2 1 1 1 2 0 0 0.739918
10/10
NonOverlappingTemplate
2 2 1 0 2 0 1 1 1 0 0.739918
10/10
NonOverlappingTemplate
1 0 2 2 1 1 1 0 1 1 0.911413
10/10
NonOverlappingTemplate
0 0 1 1 0 0 2 3 1 2 0.350485
10/10
NonOverlappingTemplate
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1 1 1 0 4 0 0 0 2 1 0.122325
10/10
NonOverlappingTemplate
1 0 1 0 2 3 0 0 2 1 0.350485
10/10
NonOverlappingTemplate
0 1 0 2 2 2 2 0 1 0 0.534146
10/10
NonOverlappingTemplate
1 0 1 1 2 0 2 1 0 2 0.739918
10/10
NonOverlappingTemplate
0 1 2 0 0 0 3 2 1 1 0.350485
10/10
NonOverlappingTemplate
2 1 1 1 2 2 0 0 1 0 0.739918
10/10
NonOverlappingTemplate
1 1 2 3 1 0 1 0 1 0 0.534146
10/10
NonOverlappingTemplate
1 3 1 3 1 1 0 0 0 0 0.213309
10/10
NonOverlappingTemplate
1 1 2 0 2 2 0 0 1 1 0.739918
10/10
NonOverlappingTemplate
2 1 1 1 1 0 1 1 1 1 0.991468
10/10
NonOverlappingTemplate
2 0 0 0 1 4 0 1 0 2 0.066882
10/10
NonOverlappingTemplate
2 0 0 1 2 2 1 0 0 2 0.534146
10/10
NonOverlappingTemplate
0 2 1 1 0 3 1 1 0 1 0.534146
10/10
NonOverlappingTemplate
0 2 1 1 2 1 1 0 1 1 0.911413
10/10
NonOverlappingTemplate
0 0 1 0 4 0 2 1 0 2 0.066882
10/10
NonOverlappingTemplate
1 2 1 2 0 2 2 0 0 0 0.534146
10/10
NonOverlappingTemplate
3 0 1 1 0 1 3 1 0 0 0.213309
10/10
NonOverlappingTemplate
2 0 1 0 1 0 1 4 0 1 0.122325
10/10
NonOverlappingTemplate
0 1 1 0 1 1 0 1 4 1 0.213309
10/10
NonOverlappingTemplate
3 2 0 0 1 0 3 1 0 0 0.122325
10/10
NonOverlappingTemplate
0 3 0 2 1 1 1 1 0 1 0.534146
10/10
NonOverlappingTemplate
0 1 1 4 0 0 1 0 1 2 0.122325
10/10
NonOverlappingTemplate
0 0 2 0 1 2 1 4 0 0 0.066882
10/10
NonOverlappingTemplate
2 1 2 0 0 1 2 1 1 0 0.739918
10/10
NonOverlappingTemplate
1 1 2 2 0 0 0 1 2 1 0.739918
10/10
NonOverlappingTemplate
1 0 1 3 1 0 1 2 1 0 0.534146
10/10
NonOverlappingTemplate
1 3 2 1 1 0 0 1 0 1 0.534146
10/10
NonOverlappingTemplate
2 0 0 0 0 0 2 1 1 4 0.066882
10/10
NonOverlappingTemplate
0 1 1 0 1 0 1 2 1 3 0.534146
10/10
NonOverlappingTemplate
1 2 0 0 2 2 0 1 1 1 0.739918
10/10
NonOverlappingTemplate
1 3 0 2 0 0 0 2 2 0 0.213309
9/10
NonOverlappingTemplate
3 1 0 0 0 2 1 0 3 0 0.122325
10/10
NonOverlappingTemplate
1 0 2 0 3 0 1 1 1 1 0.534146
10/10
NonOverlappingTemplate
0 1 1 1 0 2 2 2 0 1 0.739918
10/10
NonOverlappingTemplate
2 1 0 0 3 1 1 0 2 0 0.350485
10/10
NonOverlappingTemplate
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Additional information
0 0 1 2 1 4 1 1 0 0 0.122325
10/10
NonOverlappingTemplate
1 1 0 1 1 3 2 0 1 0 0.534146
10/10
NonOverlappingTemplate
2 1 0 2 1 0 1 0 1 2 0.739918
10/10
NonOverlappingTemplate
0 0 2 3 1 1 0 1 1 1 0.534146
10/10
NonOverlappingTemplate
1 1 1 0 1 3 1 0 1 1 0.739918
9/10
NonOverlappingTemplate
0 1 4 0 0 1 2 1 1 0 0.122325
10/10
NonOverlappingTemplate
1 3 0 0 0 0 1 1 2 2 0.350485
10/10
NonOverlappingTemplate
2 1 1 1 1 0 1 0 2 1 0.911413
10/10
NonOverlappingTemplate
2 1 2 0 1 1 0 1 1 1 0.911413
9/10
NonOverlappingTemplate
1 0 1 0 2 2 1 2 0 1 0.739918
10/10
NonOverlappingTemplate
0 1 3 1 1 1 1 2 0 0 0.534146
10/10
NonOverlappingTemplate
4 0 0 0 2 1 2 0 0 1 0.066882
10/10
NonOverlappingTemplate
0 0 0 0 2 0 1 2 2 3 0.213309
10/10
NonOverlappingTemplate
2 2 0 0 3 1 0 1 0 1 0.350485
10/10
NonOverlappingTemplate
2 0 2 0 1 0 2 2 0 1 0.534146
9/10
NonOverlappingTemplate
1 0 1 0 0 1 3 0 3 1 0.213309
9/10
NonOverlappingTemplate
1 2 1 1 0 1 3 0 0 1 0.534146
10/10
NonOverlappingTemplate
0 1 2 0 1 0 1 2 0 3 0.350485
10/10
NonOverlappingTemplate
2 0 2 0 0 0 2 0 3 1 0.213309
10/10
NonOverlappingTemplate
2 1 2 1 0 1 0 2 0 1 0.739918
10/10
NonOverlappingTemplate
1 0 1 0 4 0 0 1 2 1 0.122325
10/10
NonOverlappingTemplate
0 0 0 2 1 1 3 2 1 0 0.350485
10/10
NonOverlappingTemplate
1 3 1 0 2 0 1 0 0 2 0.350485
9/10
NonOverlappingTemplate
0 0 1 0 0 3 1 2 3 0 0.122325
10/10
NonOverlappingTemplate
0 1 0 2 1 0 1 2 3 0 0.350485
10/10
NonOverlappingTemplate
0 0 0 2 4 2 1 1 0 0 0.066882
10/10
NonOverlappingTemplate
1 0 0 2 0 1 2 1 2 1 0.739918
9/10
NonOverlappingTemplate
0 0 2 0 1 2 0 0 1 4 0.066882
10/10
NonOverlappingTemplate
1 1 0 1 1 1 2 0 2 1 0.911413
10/10
NonOverlappingTemplate
0 0 0 5 2 0 1 2 0 0 0.004301
10/10
NonOverlappingTemplate
2 1 0 0 1 1 0 1 3 1 0.534146
10/10
NonOverlappingTemplate
1 1 1 0 0 2 1 2 0 2 0.739918
10/10
NonOverlappingTemplate
2 0 2 1 0 1 2 0 1 1 0.739918
10/10
NonOverlappingTemplate
0 1 3 0 1 0 1 2 1 1 0.534146
10/10
NonOverlappingTemplate
1 1 1 1 1 1 1 2 1 0 0.991468
10/10
NonOverlappingTemplate
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Additional information
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AN4230
0 0 3 2 2 2 0 1 0 0 0.213309
10/10
NonOverlappingTemplate
2 1 2 1 1 1 0 0 1 1 0.911413
10/10
NonOverlappingTemplate
0 1 1 1 0 1 2 1 2 1 0.911413
10/10
NonOverlappingTemplate
1 0 0 2 3 2 0 0 1 1 0.350485
10/10
NonOverlappingTemplate
2 2 1 0 0 1 1 3 0 0 0.350485
10/10
NonOverlappingTemplate
2 0 2 2 0 0 0 1 0 3 0.213309
10/10
NonOverlappingTemplate
1 1 1 2 0 0 2 2 0 1 0.739918
10/10
NonOverlappingTemplate
3 2 1 0 1 0 0 0 1 2 0.350485
9/10
NonOverlappingTemplate
2 0 1 1 2 1 1 0 1 1 0.911413
10/10
NonOverlappingTemplate
0 2 0 0 1 0 1 3 2 1 0.350485
10/10
NonOverlappingTemplate
1 0 3 1 0 0 1 2 1 1 0.534146
9/10
NonOverlappingTemplate
1 2 0 2 0 4 0 0 0 1 0.066882
10/10
NonOverlappingTemplate
1 0 1 0 2 0 1 1 4 0 0.122325
9/10
NonOverlappingTemplate
1 1 1 1 0 0 3 2 1 0 0.534146
10/10
NonOverlappingTemplate
2 0 1 0 0 1 1 1 1 3 0.534146
9/10
NonOverlappingTemplate
3 0 1 1 1 1 1 1 1 0 0.739918
10/10
NonOverlappingTemplate
1 0 0 1 1 1 1 3 0 2 0.534146
10/10
NonOverlappingTemplate
3 3 1 1 0 0 0 1 1 0 0.213309
10/10
NonOverlappingTemplate
1 0 0 1 1 0 1 1 4 1 0.213309
10/10
NonOverlappingTemplate
0 2 2 3 1 1 0 1 0 0 0.350485
10/10
NonOverlappingTemplate
2 1 0 3 0 0 2 0 1 1 0.350485
10/10
NonOverlappingTemplate
1 0 0 3 0 1 1 2 0 2 0.350485
9/10
NonOverlappingTemplate
1 2 0 1 0 0 3 2 0 1 0.350485
10/10
NonOverlappingTemplate
2 1 1 1 2 0 1 1 1 0 0.911413
10/10
NonOverlappingTemplate
0 0 1 2 1 1 1 3 0 1 0.534146
10/10
NonOverlappingTemplate
0 0 2 1 3 0 3 0 0 1 0.122325
10/10
NonOverlappingTemplate
0 2 2 1 0 0 2 1 1 1 0.739918
10/10
NonOverlappingTemplate
1 2 0 2 2 1 0 0 1 1 0.739918
10/10
NonOverlappingTemplate
1 1 2 0 2 1 3 0 0 0 0.350485
10/10
NonOverlappingTemplate
2 1 0 1 1 1 3 1 0 0 0.534146
9/10
NonOverlappingTemplate
2 4 0 1 1 1 0 0 0 1 0.122325
10/10
NonOverlappingTemplate
0 0 1 0 2 2 2 2 0 1 0.534146
10/10
NonOverlappingTemplate
2 1 2 0 1 1 1 1 0 1 0.911413
10/10
NonOverlappingTemplate
1 1 1 4 1 1 1 0 0 0 0.213309
10/10
NonOverlappingTemplate
1 0 0 2 0 1 2 1 3 0 0.350485
10/10
NonOverlappingTemplate
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Additional information
4 0 2 0 2 0 1 0 0 1 0.066882
10/10
NonOverlappingTemplate
0 1 2 2 0 0 0 2 2 1 0.534146
10/10
NonOverlappingTemplate
1 0 2 0 1 1 0 3 1 1 0.534146
10/10
NonOverlappingTemplate
4 1 1 0 0 0 0 1 1 2 0.122325
10/10
NonOverlappingTemplate
2 1 0 0 1 1 2 1 1 1 0.911413
10/10
NonOverlappingTemplate
0 1 1 1 0 0 1 4 1 1 0.213309
10/10
NonOverlappingTemplate
1 2 2 0 0 5 0 0 0 0 0.004301
10/10
NonOverlappingTemplate
0 2 2 2 0 2 0 1 1 0 0.534146
10/10
NonOverlappingTemplate
3 1 1 0 0 2 0 1 1 1 0.534146
10/10
NonOverlappingTemplate
2 1 0 1 1 1 0 2 1 1 0.911413
10/10
NonOverlappingTemplate
1 1 2 1 0 1 1 0 1 2 0.911413
10/10
NonOverlappingTemplate
0 1 2 3 0 2 0 2 0 0 0.213309
10/10
NonOverlappingTemplate
0 1 0 1 3 1 2 0 0 2 0.350485
10/10
NonOverlappingTemplate
3 0 0 3 1 0 1 0 1 1 0.213309
9/10
NonOverlappingTemplate
0 1 0 2 0 2 1 0 3 1 0.350485
10/10
NonOverlappingTemplate
1 1 3 2 0 1 0 1 0 1 0.534146
10/10
NonOverlappingTemplate
0 1 0 3 0 0 0 1 0 5 0.002043
10/10
NonOverlappingTemplate
2 1 0 1 0 0 3 1 1 1 0.534146
10/10
NonOverlappingTemplate
2 0 0 0 2 1 1 0 3 1 0.350485
10/10
NonOverlappingTemplate
0 2 1 1 2 2 0 0 0 2 0.534146
10/10
NonOverlappingTemplate
0 0 1 0 3 0 1 1 1 3 0.213309
10/10
NonOverlappingTemplate
1 0 2 2 0 0 0 2 3 0 0.213309
10/10
NonOverlappingTemplate
1 2 2 1 1 1 0 1 0 1 0.911413
10/10
NonOverlappingTemplate
1 1 1 1 4 0 0 1 0 1 0.213309
9/10
NonOverlappingTemplate
0 1 1 2 2 1 0 0 2 1 0.739918
10/10
NonOverlappingTemplate
2 1 0 0 2 0 1 2 1 1 0.739918
10/10
NonOverlappingTemplate
1 0 1 1 0 0 2 3 1 1 0.534146
10/10
NonOverlappingTemplate
2 1 0 0 1 2 2 0 0 2 0.534146
10/10
NonOverlappingTemplate
0 0 2 0 1 0 3 3 0 1 0.122325
10/10
NonOverlappingTemplate
1 1 1 2 0 3 1 0 0 1 0.534146
10/10
NonOverlappingTemplate
1 0 1 1 1 2 2 1 0 1 0.911413
10/10
NonOverlappingTemplate
0 1 2 0 1 1 2 0 1 2 0.739918
10/10
NonOverlappingTemplate
1 2 0 0 1 3 1 1 0 1 0.534146
10/10
NonOverlappingTemplate
2 1 1 0 1 0 0 2 0 3 0.350485
10/10
NonOverlappingTemplate
2 1 0 0 1 1 0 1 3 1 0.534146
10/10
NonOverlappingTemplate
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Additional information
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2 0 1 0 1 2 1 0 2 1 0.739918
10/10
OverlappingTemplate
1 0 2 1 0 2 2 1 1 0 0.739918
10/10
Universal
1 1 0 0 2 0 2 3 1 0 0.350485
10/10
ApproximateEntropy
0 1 1 1 1 0 0 0 1 0
----
5/5
RandomExcursions
1 1 0 0 2 0 0 0 0 1
----
5/5
RandomExcursions
0 1 1 1 0 0 0 0 1 1
----
5/5
RandomExcursions
0 0 0 0 0 1 1 0 2 1
----
5/5
RandomExcursions
1 0 0 0 3 0 0 0 1 0
----
5/5
RandomExcursions
0 0 0 1 1 0 0 1 1 1
----
5/5
RandomExcursions
1 0 1 1 0 2 0 0 0 0
----
5/5
RandomExcursions
1 0 0 0 1 1 1 0 1 0
----
5/5
RandomExcursions
2 1 0 1 1 0 0 0 0 0
----
5/5
RandomExcursionsVariant
2 1 0 0 1 1 0 0 0 0
----
5/5
RandomExcursionsVariant
1 1 0 2 1 0 0 0 0 0
----
5/5
RandomExcursionsVariant
1 2 0 1 1 0 0 0 0 0
----
5/5
RandomExcursionsVariant
1 1 1 1 0 0 0 1 0 0
----
5/5
RandomExcursionsVariant
1 1 0 1 1 0 0 0 0 1
----
5/5
RandomExcursionsVariant
0 1 0 2 1 0 0 0 0 1
----
5/5
RandomExcursionsVariant
0 0 0 1 0 1 0 3 0 0
----
5/5
RandomExcursionsVariant
0 0 0 0 0 0 2 1 1 1
----
5/5
RandomExcursionsVariant
0 0 1 0 0 0 1 1 1 1
----
5/5
RandomExcursionsVariant
0 0 0 1 0 0 2 0 2 0
----
5/5
RandomExcursionsVariant
0 1 0 0 1 1 1 1 0 0
----
5/5
RandomExcursionsVariant
1 0 0 2 0 1 1 0 0 0
----
5/5
RandomExcursionsVariant
1 0 0 0 2 1 0 0 0 1
----
5/5
RandomExcursionsVariant
0 0 0 1 1 0 1 1 1 0
----
5/5
RandomExcursionsVariant
0 0 0 0 2 0 2 0 0 1
----
5/5
RandomExcursionsVariant
0 0 1 0 1 2 1 0 0 0
----
5/5
RandomExcursionsVariant
0 0 1 0 0 2 2 0 0 0
----
5/5
RandomExcursionsVariant
1 1 0 0 0 2 3 0 2 1 0.350485
10/10
Serial
0 2 1 0 3 1 0 1 1 1 0.534146
10/10
Serial
2 1 1 1 0 1 1 3 0 0 0.534146
10/10
LinearComplexity
----------------------------------------The minimum pass rate for each statistical test, with the exception of the random excursion
(variant) test, is approximately 8 for a sample size of 10 binary sequences.
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Additional information
The minimum pass rate for the random excursion (variant) test is approximately 4 for a
sample size of 5 binary sequences.
For further guidelines, construct a probability table using the MAPLE program provided in
the addendum section of the documentation.
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Revision history
AN4230
Revision history
Table 4. Document revision history
Date
Revision
13-May-2013
1
Initial release.
2
Updated Section : Introduction.
Updated Section 1: STM32 microcontrollers random number
generator.
Added Figure 2: STM32 lines embedding the RNG hardware
peripheral.
Updated Figure 1: Block diagram.
Updated Section 3.1: Firmware description.
Updated Section 3.2.1: First step: random number generator.
Updated Section 3.2.2: Second step: NIST statistical test.
Updated Section 4: Conclusion.
22-Jun-2016
22/23
Changes
DocID024118 Rev 2
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