=Paper=
{{Paper
|id=Vol-3101/Paper3
|storemode=property
|title=Assessing Risk of Enterprise Bankruptcy by Indicators of Financial and Economic Activity Using Bayesian Networks
|pdfUrl=https://ceur-ws.org/Vol-3101/Paper3.pdf
|volume=Vol-3101
|authors=Sergiy Gnatyuk,Dinara Ospanova,Volodymyr Lytvynenko,Zhazira Amirgaliyeva,Nurali Nabot Shohiyon
|dblpUrl=https://dblp.org/rec/conf/citrisk/GnatyukOLAS21
}}
==Assessing Risk of Enterprise Bankruptcy by Indicators of Financial and Economic Activity Using Bayesian Networks==
https://ceur-ws.org/Vol-3101/Paper3.pdf
Studies on the Computational Model of PRNG for Data
Privacy Risk Mitigation in 5G Networks
Sergiy Gnatyuk1,2,3, Dinara Ospanova4, Volodymyr Lytvynenko5, Zhazira Amirgaliyeva6
and Nurali Nabot Shohiyon7
1Yessenov University, microdistrict 32, Main building, Aktau, 130000, Kazakhstan
2National Aviation University, Liubomyra Huzara ave.1, Kyiv, 03058, Ukraine3Yessenov
3State Scientific and Research Institute of Cybersecurity Technologies and Information Protection, Maksyma
Zalizniaka str.3/6, Kyiv, 03142, Ukraine
4Kazakh Humanitarian Juridical Innovative University, Lenin str, 11, Semey, 070000, Kazakhstan
5Kherson National Technical University, Beryslavske shose 24, Kherson, 73008, Ukraine
6Al-Farabi Kazakh National University, 71 al-Farabi Ave., Almaty, 050040, Kazakhstan
7Dangara State University, Markazi str. 25, Dangara, 735320, Tajikistan
Abstract
Today, pseudo-random number generators (PRNGs) are used in various systems and applications,
including as key generators in stream ciphers, blockchain, game industry and others. The
implementation of the latest information and communication technology (in particular, modern 5G
networks) strengthens the requirements for privacy risk mitigation of critical data and forces the
development of new methods and means for cryptographic security. In the paper, a computational
model of PRNG was developed and studied. It allows to build efficient algorithms for privacy risk
mitigation. Based on this model, software PRNGs have been developed and studied (speed and
security parameters were verified). These will be useful for confidentiality ensuring and data privacy
risk mitigation in modern 5G networks as well as blockchain technologies.
Keywords1
Computational Model, PRNG, Data Privacy, Risk, Algorithm, 5G Networks, Blockchain.
1. Introduction
Today randomness is an important unit in many modern computer applications (especially
games, simulations, cryptography). Computers use a form of randomness known as pseudo
randomness, it means simulation of randomness. A pseudo random event looks random but is
completely predictable or deterministic (result of completely predictable mathematical
algorithm). Pseudo-random number generator (PRNG) can be used as key generator in stream
ciphers [1] to form large key sequence with small input data of PRNG. This generator creates bit
sequence similar to random sequence by statistical parameters. In practice, these sequences are
CITRisk’2021: 2nd International Workshop on Computational & Information Technologies for Risk-Informed Systems, September
16–17, 2021, Kherson, Ukraine
EMAIL: s.gnatyuk@yu.edu.kz (S.Gnatyuk); odm-1778@mail.ru (D.Ospanova); immun56@gmail.com (V.Lytvynenko);
zh.amirgaliyeva@gmail.com (Z.Amirgaliyeva); shoev_n@list.ru (N.N.Shohiyon)
ORCID: 0000-0003-4992-0564 (S.Gnatyuk); 0000-0002-2206-7367 (D.Ospanova); 0000-0002-1536-5542 (V.Lytvynenko); 0000-
0003-0484-8060 (Z.Amirgaliyeva); 0000-0003-2843-0945 (N.N.Shohiyon)
© 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
not random and can be reproduced – key sequence should be as longer as possible and variable.
PRNG output must be the function of encryption key and it’s very important for privacy
ensuring. To generate random numbers by computer the hardware should be used (for example,
noise from semiconductor devices; bits of digitized sound from the microphone; intervals
between interruptions of external or internal devices; intervals between keystrokes; air
temperature on hardware components). New communication standard 5G has improved
requirements for confidentiality (privacy) as well as novel secure encryption algorithms and
PRNG should be developed (Fig. 1) [2].
Figure 1: Privacy ensuring procedures in different network communication standards
2. Related papers analysis
Analysis of related papers in this direction [3-6] shows different approaches in PRNG creation
that influences on their characteristics and properties. There are two following categories of
PRNGs:
1) Cryptographically secure PRNG based on
stream ciphers (Dragon-128, SEAL, RC4, RC5, RC6, Grain, Yamb, Phelix);
block ciphers (AES, ANSI X9.17, DES),
one way functions (BBS, RSA, Dual_EC_DRBG, GPSSD).
2) Cryptographically insecure PRNG based on
elementary recurents (linear congruental generator, polinomyal congruental
generator, additive Fibonacci generator, lagged Fibonacci generator and others);
operations in finite fields (Galois generator, De Bruijn generator, Golman generator
and others).
Most up-to-date cryptographic applications require random numbers, for example key
generation, cryptographic nonces, salts in certain signature schemes, including ECDSA,
RSASSA-PSS. The security and privacy of 5G is better than in 4G (Fig. 2) [7] by using many
secure algorithms.
Figure 2: 4G/5G encryption comparison
But there are many relevant tasks related with data privacy ensuring in 4G/5G that can be solved
by PRNG development and implementation. From this viewpoint, the main target of this paper is
development and study of the computational model of PRNG for data privacy risk mitigation in
5G networks.
3. The main part of the research study
3.1. Theoretical principles of the model construction
On the basis of analysis, as a prototype of computational model well-known PRNG Trivium [8]
was chosen. Trivium is a synchronous stream cipher designed by cryptographers C. De Cannière
and B. Preneel to provide a flexible trade-off between speed and gate count in hardware, and
reasonably efficient software implementation. Trivium was one of the eSTREAM competition
winners and its recommended for using in modern communication networks as hardware unit.
To improve PRNG Trivium following modifications were proposed:
1. Parameters n , t , e , k were specified and after their fixing new PRNG structure is
forming (capacity of operations is changing). All operations are performing not on the bits but on
the vectors of some size (bytes).
2. To improve non-linearity parameters substitution operation S ( x) was specified. For any
new formed PRNG new unique S ( x) can be specified.
3. To generate pseudo-random sequences PRNG internal status vector Ei , key vector for
sequence generation K and index of the current iteration of forming (generation) i are used.
4. For generation function Fgen stage of variables initialization was modified, the dynamic
carry shift and substitution operations were specified.
5. For generation function Fgen usage of independent functions FA , FB , FC and FD was
proposed, these functions depend on internal status vector of previous generation stage, key
vector K and index of current iteration of generation i . Output of the functions FA , FB , FC
and FD will be the data of necessary length (input and output data length will be different). For
any new formed PRNG new unique functions FA , FB , FC and FD can be specified. In fact,
these functions are independent byte-oriented PRNGs (without requirements for
cryptographically security), they can work in parallel. For synchronization and optimization of
sequence generation procedure the speed of sequence generation should be something like
similar.
6. Final stage of sequence m forming and operation ordering were modified as well as the
substitution operation was specified.
Various PRNGs can be constructed by modification / fixing parameters n , t , e , k as well
all specifying functions FA , FB , FC , FD and operation S ( x ) .
Computational model description
Let n, t ∈ Z + , then for generation pseudo-random sequence M , M ∈ V , V ∈ {0,1} N
N N
with length N= n ⋅ t bits it is necessary to form t sequences with length n bit:
M = ( m1 , m2 , ..., mt −1 , mt ) , mi ∈ Vn , i = 1, t .
Process of generation every mi , mi ∈ Vn , i = 1, t performs in the following manner:
mi , Ei = Fgen ( Ei −1 , K , i ) , i = 1, t ,
where Ei is internal status vector of PRNG after generation i -th mi , Ei ∈ Ve , e ∈ Z + ,
E0 = IV , IV is initialization vector, IV ∈ Ve , K is key vector for sequence generation,
K ∈ Vk , k ∈ Z + , Fgen is function of generation the sequence mi .
Function Fgen ( E , K , i ) is performing by 2 following stages:
1) variables initialization;
2) sequence forming.
Stage 1 of function Fgen ( E , K , i ) performing. At the beginning the processing of internal
status vector is performing E , E ∈ Ve :
=E S ( E ) <<< i ,
where x <<< y is operation of right dynamic carry shift of argument x on y bits, S ( x ) is
some substitution operation.
Next the internal status vector E of PRNG and key vector K are disintegrated on 4
components:
E = ( Ea , Eb , Ec , Ed ) , E ∈ Ve , e = a + b + c + d ,
Ea ∈ Va , Eb ∈ Vb , Ec ∈ Vc , Ed ∈ Vd , a, b, c, d ∈ Z + ,
K = ( K a , K b , K c , K d ) , K ∈ Vk , k = a′ + b′ + c′ + d ′ ,
K a ∈ Va′ , K b ∈ Vb′ , K c ∈ Vc′ , K d ∈ Vd ′ , a′, b′, c′, d ′ ∈ Z + .
Vectors Ea , Eb , Ec , Ed and K a , K b , K c , K d will be used in the next stage of the
function Fgen ( E , K , i ) .
Stage 2 of function Fgen ( E , K , i ) . On this stage the forming of sequence m , m ∈ Vn is
performing. For this objective 4 additional functions FA ( Ea , K a , i ) , FB ( Eb , K b , i ) ,
FC ( Ec , K c , i ) і FD ( Ed , K d , i ) are using, where FA , FB , FC and FD are functions, that have
internal status vector and key vector as input data, and sequence with length n bits as output
data. These functions can be constructed on the base of non-linear shift registers, block and
stream symmetric ciphers, hash functions and others.
In this case, process of sequence m , m ∈ Vn and new value of internal status vector E ,
E ∈ Ve generation in function Fgen ( E , K , i ) will be follow:
Stage 1. Formation of additional vectors A , B , C і D and calculation of new values of
vectors Ea , Eb , Ec , Ed :
A, Ea = FA ( Ea , K a , i ) , A ∈ Vn , Ea ∈ Va ,
B, Eb = FB ( Eb , K b , i ) , B ∈ Vn , Eb ∈ Vb ,
C , Ec = FC ( Ec , K c , i ) , C ∈ Vn , Ec ∈ Vc ,
D, Ed = FD ( Ed , K d , i ) , D ∈ Vn , Ed ∈ Vd .
Stage 2. Calculation of the new value internal status vector E , E ∈ Ve :
E = ( Eb , Ed , Ea , Ec ) .
Stage 3. Formation of the sequence m , m ∈ Vn :
AB= A <<< B , AB ∈ Vn ,
CD= C <<< D , CD ∈ Vn ,
BC= B + CD , BC ∈ Vn ,
AD
= AB ⊕ D , AD ∈ Vn ,
m AD ⊕ S ( BC ) , m ∈ Vn ,
=
where ⊕ і + are operations modulo addition 2 and 2n respectively, S ( x ) is substitution
operation.
Output of the function Fgen ( E , K , i ) will be vectors m , m ∈ Vn and E , E ∈ Ve :
( m, E ) = Fgen ( E , K , i ) .
In this Section computational model of PRNG was described. Based on PRNG Trivium, this
model includes internal status vector and key vector processing, dynamic carry shift and 4 non-
linear functions. It allows to construct effective PRNGs for privacy ensuring in modern
communication networks (5G networks and others).
3.2. Software PRNG development
On the basis of developed computational model 3 PRNGs 5Gen-1, 5Gen-2 and 5Gen-3 was
constructed:
5Gen-1 was constructed with following set of parameters n = 128 , a = 128 , b = 100 ,
c = 111 , d = 173 , e = a + b + c + d = 512 , a′ = 128 , b′ = 128 , c′ = 128 , d ′ = 128 ,
k = a′ + b′ + c′ + d ′ = 512 . FA , FB , FC and FD are functions based on the non-linear shift
(
register. As substitution S ( x ) the operation S ( x ) = s0 ( x31 ) , ..., s0 ( x0 ) ) was used, where
x j ∈ V16 , j = 0,31 , S 0 is the substitution on the set V16 .
Substitution S is constructed with parameters, presented in Table 1.
0
Table 1
Parameters for substitution table S construction for 5Gen-1 algorithm
0
M C V
{ 903, 3206, 640C, C818,
9031, 2063, 40C6, 818C,
6D71 19CF
319, 632, C64, 18C8,
3190, 6320, C640, 8C81 }
5Gen-2 was constructed with following set of parameters n = 256 , a = 138 , b = 120 , c = 116 ,
d = 138 , e = a + b + c + d = 512 , a′ = 128 , b′ = 128 , c′ = 128 , d ′ = 128 ,
k = a′ + b′ + c′ + d ′ = 512 . FA , FB , FC and FD are functions based on the non-linear shift
(
register. As substitution S ( x ) the operation S ( x ) = s7 ( x63 ) , ..., s0 ( x0 ) ) was used, where
x j ∈ V8 , j = 0,63 , S is substitution on the set V , b = 0,7 (by the order 8 different
b 8
substitution tables are using).
Substitution S , i = 0,7 is constructed with parameters, presented in Tables 2-9.
i
Table 2
Parameters for substitution table S construction for 5Gen-2 algorithm
0
M C V
{ 29, 52, A4, 49, 92, 25, 4a, 94 } 07 D8
Table 3
Parameters for substitution table S construction for 5Gen-2 algorithm
1
M C V
{ 70, E0, C1, 83, 7, E, 1C, 38 } A2 44
Table 4
Parameters for substitution table S construction for 5Gen-2 algorithm
2
M C V
{ 3E, 7C, F8, F1, E3, C7, 8F, 1F } 72 63
Table 5
Parameters for substitution table S construction for 5Gen-2 algorithm
3
M C V
{ E3, C7, 8F, 1F, 3E, 7C, F8, F1 } 43 9B
Table 6
Parameters for substitution table S construction for 5Gen-2 algorithm
4
M C V
{ E5, CB, 97, 2F, 5E, BC, 79, F2 } A0 8C
Table 7
Parameters for substitution table S construction for 5Gen-2 algorithm
5
M C V
{ AB, 57, AE, 5D, BA, 75, EA, D5 } 7B C6
Table 8
Parameters for substitution table S construction for 5Gen-2 algorithm
6
M C V
{ 91, 23, 46, 8C, 19, 32, 64, C8 } ED B0
Table 9
Parameters for substitution table S construction for 5Gen-2 algorithm
7
M C V
{ F8, F1, E3, C7, 8F, 1F, 3E, 7C} 18 75
5Gen-3 was constructed with following set of parameters n = 128 , a = 128 , b = 128 , c = 128 ,
d = 128 , e = a + b + c + d = 512 , a′ = 128 , b′ = 128 , c′ = 128 , d ′ = 128 ,
k = a′ + b′ + c′ + d ′ = 512 . FA , FB , FC and FD are functions based on AES-128 algorithm. As
substitution S ( x ) the operation S ( x ) = ( s ( x ) , ..., s ( x )) was used, where
0 63 0 0 x j ∈ V8 ,
j = 0,63 , S − підстановка на множині V .
0 8
Substitution S is constructed with parameters, presented in Tables 10.
0
Table 10
Parameters for substitution table S construction for 5Gen-3 algorithm
0
M C V
{ 20, 40, 80, 1, 2, 4, 8, 10} 59 6B
3.3. Experimental study and discussion
Statistical parameters investigation
Statistical parameters of developed PRNGs were investigated using traditional techniques
NIST STS [9] and DIEHARD [13]. Given results were compared with testing results of
generator BBS as well as stream ciphers SNOW [10] and Trivium (used in 5G networks). NIST
STS are used to determine the qualitative and quantitative features of the sequences randomness.
Three basic criteria are used to draw conclusions about passing random sequences of statistical
tests are following:
Criterion for decision-making based on the establishment of some threshold level.
Criterion based on establishing a fixed confidence interval.
Criterion for some appropriate statistical test probability value P-value.
The statistical test is based on the verification of null hypothesis H0 – that the sequence under
study is random. Alternative hypothesis H1 is also provided – the sequence under study is not
random. Therefore, the generated sequence is examined by a set of tests, each of which
concludes whether the hypothesis H0 is rejected or accepted. For each test, adequate randomness
statistics are selected based on which the hypothesis H0 is further rejected or accepted.
Theoretically, the distribution of statistics for the null hypothesis is calculated using
mathematical methods. The critical value is then determined from such an exemplary
distribution. When performing the test, the value of the test statistic is calculated, which is
compared to the critical value. In case of exceeding the test critical value over the reference,
hypothesis H1 is accepted, otherwise – hypothesis H0.
For the experiments, the following input parameters were selected for the use of NIST STS:
1. The length of the test sequence n=106 bit.
2. The number of sequences being tested m=100.
3. Significance level α = 0, 01 .
4. Number of tests q=188, among them: Frequency − 1, Block Frequency − 1, Cumulative
Sums − 2, Runs − 1, Longest Run − 1, Rank − 1, FFT − 1, Non Overlapping Template − 148,
Overlapping Template − 1, Universal − 1, Approximate Entropy − 1, Random Excursions − 8,
Random Excursions Variant − 18, Serial − 2, Linear Complexity − 1.
The confidence interval rule was applied, the lower bound being 0.96015. For every
algorithms 10 files with sequences (100 Mbit) and investigated by NIST STS technique.
The results of testing are presented on Fig. 3-5.
Figure 3: Statistical portrait of 5Gen-1 algorithm by NIST STS technique
Figure 4: Statistical portrait of 5Gen-2 algorithm by NIST STS technique
Figure 5: Statistical portrait of 5Gen-3 algorithm by NIST STS technique
Also developed algorithms were investigated by DIEHARD technique (one of the best practice
and traditional approach in cryptography for measuring quality of PRNG and statistical security).
Results of testing for 5Gen-3 algorithms presented on Fig. 6 (other two algorithms 5Gen-1 and
5Gen-2 showed 100% results).
Figure 6: Statistical testing results of 5Gen-3 algorithm by DIEHARD technique
Results presented on Fig. 3-5 as well as detail experimental data (Table 11) show that developed
algorithms 5Gen-1, 5Gen-2 and 5Gen-3 have passed complex control by NIST STS technique
and show better results (in some cases) than existed and well-known algorithms [11-12].
Results presented on Fig. 6 show that developed algorithms have passed complex security
control by DIEHARD technique as well as verified good quality of PRNG and statistical security
of potential systems based on these algorithms [14-16].
Table 11
Results of statistical parameters investigation by NIST STS technique
Test total amount, where passed
PRNG
99% sequences 96% sequences
BBS 133.4 (70.96%) 188 (100%)
SNOW 134.8 (71.70%) 188 (100%)
Trivium 130.1 (69.20%) 187.6 (99.78%)
5Gen-1 134.1 (71,32%) 188 (100%)
5Gen-2 136.4 (72,55%) 187.8 (99.89%)
5Gen-3 137.3 (73,03%) 188 (100%)
Speed parameters investigation
For investigation developed PRNGs 5Gen-1, 5Gen-2, 5Gen-3 were realized as software tools
using programming language С++. Given results were compared with results of well-known
SNOW generator. Experimental study was carried out using work station Intel Core i3-3220
3.3GHz and files with different size. Average results are presented on the Table 12.
Table 12
Results of speed parameters investigation
File 1, 1 МB File 2, 10 МB File, 100 МB
PRNG
t ,s v , МB/s t ,s v , МB/s t ,s v , МB/s
SNOW 0.011 90.91 0.107 93.46 1.01 99.01
5Gen-1 0.009 111.11 0.091 109.89 0.88 113.64
5Gen-2 0.010 100.00 0.098 102.04 0.92 108.70
5Gen-3 0.014 71.43 0.112 89.29 0.99 101.01
As we can see from Table 12 speed of the developed algorithms are higher in comparison with
SNOW till 21% outside two results of 5Gen-3 algorithm.
4. Conclusions
In this paper analysis of different approaches in PRNG creation and implementation was carried
out. Two categories of PRNGs were defined (cryptographically secure and cryptographically
insecure) as well cryptographic applications that require random numbers were defined (key
generation, cryptographic nonces, salts in certain signature schemes). But there are many
relevant tasks related with data privacy risk mitigation and confidentiality ensuring in 4G/5G
that can be solved by advanced PRNG development and implementation.
Computational model of PRNG was developed. Based on PRNG Trivium, this model
includes internal status vector and key vector processing, dynamic carry shift and 4 non-linear
functions. It allows to construct effective PRNGs for data privacy risk mitigation in modern
communication networks (5G networks and others).
On the basis of developed computational model 3 PRNGs 5Gen-1, 5Gen-2 and 5Gen-3 was
constructed and realized as software tools. These PRNGs have passed complex statistical testing
by NIST STS technique as well as speed parameters investigation (developed algorithms are
higher in comparison with SNOW till 21%).
Additionally, developed algorithms were investigated by DIEHARD technique (one of the
best practice and traditional approach in cryptography for measuring quality of PRNG and
statistical security). These algorithms have passed complex security control by DIEHARD
technique as well as verified good quality of PRNG and statistical security of potential systems
based on these algorithms.
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