=Paper=
{{Paper
|id=Vol-2588/paper7
|storemode=property
|title=Statistical Testing of Blockchain Hash Algorithms
|pdfUrl=https://ceur-ws.org/Vol-2588/paper7.pdf
|volume=Vol-2588
|authors=Alexandr Kuznetsov,Maria Lutsenko,Kateryna Kuznetsova,Olena Martyniuk,Vitalina Babenko,Iryna Perevozova
|dblpUrl=https://dblp.org/rec/conf/cmigin/KuznetsovLKMBP19
}}
==Statistical Testing of Blockchain Hash Algorithms==
https://ceur-ws.org/Vol-2588/paper7.pdf
Statistical Testing of Blockchain Hash Algorithms
Alexandr Kuznetsov 1 [0000-0003-2331-6326], Maria Lutsenko 1 [0000-0003-2075-5796],
Kateryna Kuznetsova 1 [0000-0002-5605-9293], Olena Martyniuk 2 [0000-0002-0377-7881],
Vitalina Babenko 1 [0000-0002-4816-4579] and Iryna Perevozova 3[0000-0002-3878-802X]
1
V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
kuznetsov@karazin.ua, lutsenko.maria.kh@gmail.com,
kate.kuznetsova.2000@gmail.com, vitalinababenko@karazin.ua
2
International Humanitarian University, Odessa, Ukraine, emartynuk2017@gmail.com
3
Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine,
perevozova@ukr.net
Abstract. Various methods are used for statistical testing of cryptographic algo-
rithms, for example, NIST STS (A Statistical Test Suite for the Validation of
Random Number Generators and Pseudo Random Number Generators for
Cryptographic Applications) and DIEHARD (Diehard Battery of Tests of Ran-
domness). Tests consists of verification the hypothesis of randomness for se-
quences generated at the output of a cryptographic algorithm (for example, a
keys generator, encryption algorithms, a hash function, etc.). In this paper, we
use the NIST STS technique and study the statistical properties of the most
common hashing functions that are used or can be used in modern blockchain
networks. In particular, hashing algorithms are considered which specified in
national and international standards, as well as little-known hash functions that
were developed for limited use in specific applications. Thus, in this paper, we
consider the most common hash functions used in more than 90% of blockchain
networks. The research results are given as average by testing data of 100 se-
quences of 108 bytes long, which means that is, the size of the statistical sample
for each algorithm was 1010 bytes. Moreover, each test (for each of the 100 se-
quences) was considered as an independent observation. In addition, the article
presents statistical portraits for each algorithm under study (diagrams of the
numbers of passing each test).
Keywords: statistical testing, hashing algorithms, blockchain technology.
1 Introduction
In this work, statistical studies of the output sequences of cryptographic hash func-
tions are performed, when this functions processing excessive input data. In this case,
input data are formed using a regular counter.
The NIST STS (A Statistical Test Suite for Random and Pseudorandom Number
Generators for Cryptographic Applications) methodology, which is recommended by
The National Institute of Standards and Technology, USA for the study of random
and pseudorandom number generators for cryptographic applications [1, 2]. Both
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attrib-
ution 4.0 International (CC BY 4.0) CMiGIN-2019: International Workshop on Conflict Management in
Global Information Networks.
world-famous hashing functions (standardized at the international and/or national
levels) [3-7] and little-known algorithms [8, 9], which are designed for use only in
certain applications (e.g., in decentralized blockchain systems [10-14]). Specifically,
the statistical security results of the following algorithms are given: GOST 34.311,
STRIBOG256, STRIBOG512, BALLOON 32, BALLOON 64, BLAKE256,
BLAKE512, BMW, CUBEHASH, DJB-2, DJB-2 XOR, ECHO, FUGUE 224,
FUGUE 256, FUGUE 384, FUGUE 512, GROESTL 256, GROESTL 512, HAMSI
224, HAMSI 256, HAMSI 384, HAMSI 512, J-H, KECCАK 256, KECCАK 512,
LOSELOSE, LUFFA, PROGPOW, RANDOMX, RIPEMD160, SCRYPT 1024,
SCRYPT 16384, SHA2 256, SHA2 512, SHABAL 224, SHABAL 256, SHABAL
384, SHABAL 512, SHAVITE, SIMD, SKEIN, WHIRLPOOL, X11.
2 Research methodology and results
The NIST STS statistical test suite recommended by The National Institute of Stand-
ards and Technology, USA [1, 2] was used to conduct studies of various hashing al-
gorithms by statistical security criteria’s. Methods of statistical testing and processing
algorithm of the obtained results are given in [15, 16].
The NIST Statistical Test Suite was developed during the AES competition for the
study of random or pseudorandom number generators and is the most common tool
for assessing the statistical security of cryptographic primitives. The use of this pack-
age allows us to estimate how closely the crypto algorithms under study approximate
the generators of "random" sequences, that is, with a high probability to confirm
whether the generated sequence is statistically secure. The order of testing of a single
binary sequence S is as follows:
the null hypothesis H 0 is advanced - the assumption that this binary sequence S is
random;
the test statistic с(S) is calculated according to the sequence S;
the probability function P f c S is calculated using a special function and
test statistics;
the probability value Р is compared with the threshold value [0,96; 0,99] . If so
P , the hypothesis H 0 is accepted. Otherwise, an alternative hypothesis is ac-
cepted.
The test suite contains 15 statistical tests, but in fact, depending on the input pa-
rameters, 188 probability values of Р are calculated, which can be considered as the
result of individual tests.
Frequency (Monobits) Test. Aims to determine the relation between zeros and ones
in a binary sequence of a certain length. For a truly random binary sequence, the
number of zeros and ones is almost the same. The test estimates how close the unit is
to 0.5.
Test for Frequency Within a Block. The essence of the test is to determine the frac-
tion of ones inside the block with a length of m bits, i.e. it is necessary to find out
whether the repetition rate of ones in the block with a length of m bits is approximate-
ly equal m 2 , as might be assumed in the case of a random sequence.
Runs Test. This test searches for rows, that is, continuous sequences of identical
bits. A series (runs) of length k bits consists of k absolutely identical bits, beginning
and ending with a bit containing the opposite value. In this test, you need to find out if
the number of such rows really matches their number in random order. In particular, it
is determined whether the ones and zeros in the initial sequence quickly or slowly
alternate.
Test for The Longest Run of Ones in a Block. This test determines the longest row
of ones inside the block with a length of m bits. It is necessary to find out whether the
length of such a row actually meets the expectation of the length of the longest row of
ones in the case of a completely random sequence.
Random Binary Matrix Rank Test. Here, we calculate the rank of non-continuous
sub-matrices constructed from the initial binary sequence. The purpose of this test is
to test for linear dependence of fixed length substrings that make up the initial se-
quence.
Discrete Fourier Transform (Spectral) Test. The essence of the test is to estimate
the peak height of the discrete Fourier transform of the initial sequence. The purpose
is to identify periodic properties of the input sequence, for example, closely spaced
repetitive sections. The idea is that the number of peaks in excess of the 95% ampli-
tude threshold is much greater than 5%.
Non-Overlapping (Aperiodic) Template Matching Test. This test calculates the
number of predefined templates found in the original sequence. It is necessary to
identify random or pseudorandom number generators that form too often non-periodic
patterns. As in Overlapping Template Matching Test, a window with a length of m
bits is also used to search for specific patterns with a length of m bits. If no pattern is
found, the window shifts one bit. If a pattern is found, then the window moves to the
bit that follows the pattern found, and the search continues.
Overlapping (Periodic) Template Matching Test. The essence of this test is to cal-
culate the number of predefined templates that were found in the original sequence.
As in Non-Overlapping Template Matching Test, a window with a length of m bits is
also used to search for specific patterns with a length of m bits. The search itself is
conducted in a similar way. If no pattern is found, the window shifts one bit. The
difference between this test and previous test is that when the pattern is found, the
window moves only one bit forward, and then the search continues.
Maurer's Universal Statistical Test. In here determines the number of bits between
the same patterns in the initial sequence (a measure that is directly related to the
length of the compressed sequence). It is necessary to find out whether this sequence
can be significantly compressed without loss of information. If this can be done, then
it is not truly random.
Linear Complexity Test. The test is based on the principle of the linear shift register
feedback. You need to find out if the input sequence is complex enough to be consid-
ered completely random. Absolutely random sequences are characterized by long
linear shift registers. If such a register is too short, then it is assumed that the se-
quence is not completely random.
Serial Test. This test is to calculate the frequency of all possible overlaps of the m
bit length patterns at the initial bit sequence. The purpose is to determine whether the
number of occurrences of overlapping 2m patterns by the length of the m bits is
approximately the same as in the case of an absolutely random input bit sequence.
The latter is known to be monotonous, that is, each pattern with a length of m bits
appears in a sequence with equal probability. It is worth noting that when m 1 , so
the periodicity test goes into the frequency bit test.
Approximate Entropy Test. As in the periodicity test, this test focuses on calculat-
ing the frequency of all possible overlaps of the m bit length patterns at the initial bit
sequence. It is necessary to compare the overlap frequencies of two consecutive
blocks of the initial sequence with the lengths m and m 1 with the overlap frequen-
cies of similar blocks in a completely random sequence.
Cumulative Sum (Cusum) Test. The test is the maximum deviation (from zero) at
an arbitrary bypass determined by the cumulative sum of the given digits 1, 1 in
the sequence. It is necessary to determine whether the cumulative sum of the partial
sequences occurring in the input sequence is too large or too small compared to the
expected behavior of such a sum for a completely random input sequence. Thus, the
cumulative amount can be regarded as an arbitrary bypass. For a random sequence,
the deviations from the bypass should be near zero.
Random Excursions Test. The essence of this test is to calculate the number of cy-
cles that have strictly k excursions with an arbitrary bypass of the cumulative sum.
The arbitrary bypass of a cumulative sum begins with partial sums after the sequence
0,1 is translated into the corresponding sequence 1, 1 . An arbitrary bypass
cycle consists of a series of single-length steps performed in random order. In addi-
tion, such a bypass begins and ends on the same element. The purpose of this test is to
determine whether the number of visits to a particular state within a cycle differs from
a similar number in the case of a completely random input sequence. In fact, this test
is a set consisting of eight tests that are conducted for each of the eight cycle states: -
4, -3, -2, -1 and +1, +2, +3, +4.
Random Excursions Variant Test. This test calculates the total number of excur-
sions to a given condition when you randomly bypass the cumulative sum. The pur-
pose is to determine deviations from the expected number of visits to different states
at random bypass. In fact, this test consists of 18 tests for each state: -9, -8, ..., -1 and
+1, +2, ..., +9.
Thus, as a result of binary sequence testing, a vector P P1 , P2 ...P188 of probabil-
ity values Pj is formed. The analysis of the components Pj of this vector allow us to
point to specific defects in the randomness of the tested sequence.
Passing each of the 15 statistical tests is an important criterion for evaluating a
pseudorandom generator. Therefore, not even matching one or more criteria means
that the stream cannot withstand cryptanalysis at a high level. If, on the other hand,
the generator passes all the tests, this does not indicate the security of the generator,
since such tests do not take into account the features of the actual design of the gener-
ator.
The accumulated experience of statistical testing shows that the number of tests
passed by the generator being tested depends directly on the selected cryptographic
algorithm output sequence. To ensure the reliability of the results of statistical testing
in the work [15-18], it is proposed to evaluate the mathematical expectation of the
number of tests passed X i by the investigated generator (crypto algorithm), consider-
ing each i test as a single observation (experience), i.e. as a specific implementation
of some random variable X .
When conducting statistical surveys, 100 sequences with a length of 108 bytes were
generated for each algorithm, i.e. the size of the statistical sample for each algorithm
reached 1010 bytes. Each testing (for each of the 100 sequences) was considered as an
independent observation. Table 1 summarizes the statistical test results for each algo-
rithm studied.
Table 1. The statistical testing results of hashing algorithms
Algorithm Name M099 D099 S099 P099 M096 D096 S096 P096 MIN
GOST 34.311 132.90 43.93 6.62 1 186.83 1.46 1.20 1 182
STRIBOG256 131.92 55.93 7.47 1 186.70 1.81 1.34 1 181
STRIBOG512 131.64 48.99 6.99 1 186.76 1.88 1.37 1 182
BALLOON 32 134.20 60.56 7.78 1 187.10 1.09 1.04 1 185
BALLOON 64 126.50 0.25 0.50 1 183.00 1.00 1.00 1 182
BLAKE256 133.31 55.13 7.42 1 186.75 1.90 1.38 1 183
BLAKE512 132.65 55.74 7.46 1 186.73 1.59 1.26 1 183
BMW 132.39 48.99 6.99 1 186.92 1.55 1.24 1 182
CUBEHASH 131.22 55.65 7.46 1 186.80 1.44 1.2 1 183
DJB-2 8.92 1.21 1.10 1 11.64 0.29 0.53 1 10
DJB-2 XOR 2.99 2.16 1.47 1 4.94 1.69 1.30 1 0
ECHO 131.96 53.85 7.33 1 186.51 2.16 1.47 1 182
FUGUE 224 133.07 45.78 6.76 1 186.61 2.11 1.45 1 180
FUGUE 256 132.42 43.74 6.61 1 186.78 2.25 1.50 1 180
FUGUE 384 131.03 57.22 7.56 1 186.66 1.78 1.33 1 182
FUGUE 512 133.02 62.31 7.89 1 186.76 2.14 1.46 1 180
GROESTL 256 133.23 56.01 7.48 1 186.72 2.14 1.46 1 181
GROESTL 512 133.01 58.58 7.65 1 187.14 0.90 0.94 1 184
HAMSI 224 132.84 53.65 7.32 1 186.66 2.36 1.53 1 112
HAMSI 256 131.71 51.42 7.17 1 186.87 1.87 1.36 1 181
HAMSI 384 132.86 51.26 7.15 1 187.19 1.21 1.10 1 182
HAMSI 512 132.17 51.16 7.15 1 186.45 2.68 1.63 1 179
J-H 131.70 71.63 8.46 1 186.69 2.43 1.56 1 180
KECCАK 256 131.27 58.79 7.66 1 186.52 2.70 1.64 1 181
KECCАK 512 132.40 48.12 6.93 1 186.78 1.41 1.18 1 182
LOSELOSE 16.00 0.00 0.00 1 16.00 0.00 0.00 1 16
LUFFA 133.11 47.07 6.86 1 186.71 1.50 1.22 1 183
PROGPOW 130.00 0.00 0.00 1 188.00 0.00 0.00 1 188
RANDOMX 0.00 0.00 0.00 1 0.00 0.00 0.00 1 0
RIPEMD160 84.79 84.04 9.16 1 132.11 80.95 8.99 1 105
SCRYPT 1024 133.80 68.36 8.26 1 187.10 1.49 1.22 1 184
SCRYPT 16384 140.00 0.00 0.00 1 185.00 0.00 0.00 1 185
Algorithm Name M099 D099 S099 P099 M096 D096 S096 P096 MIN
SHA2 256 132.70 57.39 7.57 1 186.74 1.67 1.29 1 182
SHA2 512 133.01 51.78 7.19 1 186.87 1.99 1.41 1 182
SHABAL 224 132.76 50.12 7.08 1 186.67 2.52 1.58 1 180
SHABAL 256 133.18 61.72 7.85 1 186.61 2.39 1.54 1 115
SHABAL 384 131.63 45.61 6.75 1 186.54 2.00 1.41 1 180
SHABAL 512 132.81 45.41 6.73 1 186.87 1.57 1.25 1 182
SHAVITE 132.01 53.72 7.33 1 186.9 1.53 1.23 1 182
SIMD 133.09 39.54 6.28 1 186.85 1.58 1.25 1 182
SKEIN 131.90 46.97 6.85 1 186.71 1.26 1.12 1 184
WHIRLPOOL 132.29 47.90 6.92 1 186.78 1.59 1.26 1 182
X11 132.46 46.48 6.81 1 186.80 1.28 1.13 1 184
X12 133.10 21.29 4.61 1 186.20 2.36 1.53 1 183
X13 137.00 74.56 8.63 1 186.90 0.69 0.83 1 185
X14 131.40 24.44 4.94 1 186.90 0.69 0.83 1 123
X15 130.10 31.49 5.61 1 186.20 4.56 2.13 1 182
X16 0.90 0.09 0.30 1 1.00 0.00 0.00 1 1
X17 3.20 0.36 0.60 1 5.80 0.16 0.40 1 5
Table 1 provides the following data:
"M096" and "M099" – estimates of expected value (the sample mean) of the num-
ber of passed tests by criterion Pj 0,96 and criterion Pj 0,99 , respectively;
"D096" and "D099" ("S096" and "S099") – estimates of the statistical dispersion
(standard deviation) of the results of testing the number of statistical tests complet-
ed by the criterion Pj 0,96 and criterion Pj 0,99 , accordingly;
"P099" – the confidence value for the number of statistical tests completed by cri-
terion Pj 0,99 and accuracy 2 ;
"P096" – the value of the confidence probability for the number of statistical tests
passed by criterion Pj 0,96 and accuracy 1 ;
"Min096" – the minimum values of the number of statistical tests passed by the
criterion Pj 0,96 .
The results of statistical studies (statistical portraits) of hashing algorithms are
shown in Fig. 1-40. On the abscissa scale the statistical test number (from 1 to 188) is
given, on the ordinate scale the fraction of passing of the corresponding test is given.
Fig. 1. BALLOON32 Fig. 2. BALLOON64
Fig. 3. BLAKE 256 Fig. 8. DJB-2XOR
Fig. 4. BLAKE 512 Fig. 9. ECHO
Fig. 5. BMW Fig. 10. KECCАK 256
Fig. 6. CUBEHASH Fig. 11. KECCАK 512
Fig. 7. DJB-2 Fig. 12. LOSELOSE
Fig. 13. LUFFA Fig. 18. GOST_256
Fig. 14. FUGUE224 Fig. 19. Stribog_512
Fig. 15. FUGUE256 Fig. 20. WHIRLPOOL512
Fig. 16. FUGUE384 Fig. 21. GROESTL 256
Fig. 17. FUGUE512 Fig. 22. GROESTL 512
Fig. 23. HAMSI 224 Fig. 28. RIPEMD160
Fig. 24. HAMSI 256 Fig. 29. SCRYPT 1024
Fig. 25. HAMSI 384 Fig. 30. SHA2 256
Fig. 26. HAMSI 512
Fig. 31. SHA2 512
Fig. 27. J-H
Fig. 32. SHABAL 224
Fig. 33. SHABAL 256 Fig. 36. SHAVITE
Fig. 34. SHABAL 384 Fig. 37. SIMD
Fig. 35. SHABAL 512 Fig. 38. SKEIN
Fig. 39. STREEBOG 256 Fig. 40. X11
The results of statistical studies indicate that certain high-speed algorithms cannot
be applied in cryptographic applications. This applies, for example, to the algorithms
DJB-2, LOSELOSE, and others, because these algorithms, in fact, do not compute a
cryptographic checksum. However, most of the cryptographic hashing algorithms,
that have been studied, have shown high statistical properties and have high rates of
indistinguishability criterion with truly random sequence.
3 Conclusions
Hashing functions are a complex and very important cryptographic primitive that is
used in almost all mechanisms and protocols of cryptographic security of information
(password generation, encryption, pseudorandom sequence generation, electronic
signature generation, etc.). In recent years, the use of hashing has expanded signifi-
cantly. In particular, with the advent and rapid spread of decentralized distributed
systems based on so-called "linked lists" (blockchain) technology, there was an urgent
need for fast, safe and reliable hashing functions, because of their unpredictable and
irreversible features secure blockchain chains are being built. The task of choosing a
hash function is much more complicated due to the proliferation of specialized com-
putants that are being developed and practically used to look for prototypes of pre-
formed hash values (ASIC-mining). By investing in the acquisition of ASICs, indi-
vidual players can be deliberately advantaged compared to other blockchain users and
can, therefore, cause non-trust and compromise of decentralized technologies (e.g.,
different cryptocurrencies, distributed storage, smart- contracts, etc.). Therefore, the
study of the properties of modern hashing algorithms and the rationale for their rec-
ommendations for the national blockchain technology segment development is cer-
tainly an important and extremely relevant scientific task.
The results obtained shows that most hashing functions satisfy the criteria of statis-
tical security (by the NIST STS method), that is, by different indicators the output
sequences (hash values) do not differ (in the statistical sense) from the truly random
sequences. These are mainly known and standardized algorithms, which are applied in
various cryptographic applications and have already been substantially researched and
studied in previous tests. However, among the algorithms in Table 1 there are those
whose statistical certainty is either unsatisfactory or completely unacceptable. For
example, the well-known hashing algorithm RIPEMD160, which is standardized in
ISO/IEC 10118-3:2018 and accepted for use in the European Union, has shown low
values of statistical security (the average number of statistical tests with Pj 0,96
completed does not exceed 85). That is, if the RIPEMD160 algorithm inputs an ex-
cess sequence (in our studies, the input sequence was formed by a regular counter),
the generated hash sequences differ from the random sequence, i.e. they have some
determinism. Although we have not identified any specific defects in the
RIPEMD160 algorithm, the results indicate that some of the generated hash codes are
flawed in terms of randomness and unpredictability.
The unsatisfactory performance of the DJB-2, DJB-2 XOR, and LOSELOSE hash-
ing algorithms should be noted separately. In terms of statistical security, they are not
acceptable for practical use in cryptographic applications. This conclusion is predicta-
ble because the DJB-2, DJB-2 XOR, and LOSELOSE algorithms are essentially not
cryptographic, and the calculation of the hash sequences in them is similar to a regular
checksum. But, as the results show, even when using statistically dangerous algo-
rithms as part of cascading mining schemes (for example, in the X family hash algo-
rithms), the generated hash sequences also do not satisfy statistical security indicators
(see last two lines of the Table 1).
Thus, choosing a hashing algorithm for building blockchain system elements is ex-
tremely important and painstaking. In view of the results obtained, in addition to per-
formance, it is also necessary to consider the reliability and security of cryptocurren-
cies. Also important is the availability of Specialized Computers (ASICs), which
greatly accelerate mining in certain consensus protocols. Therefore, to justify the
choice of hashing algorithms, it is necessary to consider various factors and perfor-
mance indicators, including the features of building a specific blockchain system,
consensus protocols, processing and messaging algorithms, etc.
This research might be useful for the improvement of various methods of infor-
mation security, as well as other practical use [17-22].
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