The aim of this research paper is to design a new pseudorandom number generator based on FCSR registers, with not affecting the speed of generation.In the main part, a deep description of the cascades used in the design and describe the working principle of GPRN. The analyzed statistical characteristics are obtained from various generated sequences using test package NIST 800-22 and then confirmed by experiment, that a modeled GPRN has a higher period of repetition and works faster.

1. Generator of Pseudorandom Sequences
Based on a Cascade of FCSR Registers
Roman Valentyn Tkachuk, Sindhu Vasireddy, Routhu
Venkata Sai Kalyan
School of computing,
Blekinge Institute of Technology
Karlskrona, Sweden
{rotk16, siva16, vero16}@student.bth.se
Wlodek J. Kulesza
School of Engineering
Blekinge Institute of Technology
Karlskrona, Sweden
wka@bth.se
Abstract — The main aim of this research paper is to design a
new pseudorandom number generator based on FCSR registers,
with not affecting the speed of generation. This paper explains
about the generators of pseudorandom sequences, in general and
their use in cryptographic systems. There are methods to design
and analyze the stream ciphers using pseudorandom number
generators. In the main part, a deep description of the cascades
used in the design and describe the work principle of GPRN. The
analyzed statistical characteristics are obtained from various
generated sequences using test package NIST 800-22 and then
confirmed by experiment, that a modeled GPRN has a higher
period of repetition and works faster.
Keywords — feedback with carry shift register(FCSR);
generators of pseudorandom sequences(GPRS); period of repeating
of sequence; “truly” random sequence
I. INTRODUCTION
seudorandom numbers are a critical component used
today for various modelling processes, starting from
the study of behavior of the human brain to solve
various calculations in communications. In this field of
informational security, pseudorandom numbers play a critical
role because the stability of an algorithm depends on the
‘randomness’. Pseudorandom numbers are used to generate
stable keys necessary for secure transmission of secret
information over unprotected communication channel. They
are also used for various applications like creating different
kinds of ‘noise’ in cryptosystems.
Security system of any organization depends on all its parts.
Starting from a simple user password generation to a
fingerprint or a handprint scanner to a retina scanner, each
component creates a single system. If one component is not
stable, then the entire system may be rendered ineffective.
And referring to one of the most important components,
namely generators of pseudorandom numbers (GPRN), it is a
systematic approach of the issue without affecting the speed of
generation.
The reason for selecting the feedback with carry shift
register (FCSR) is because of its modern structure. It has been
under development stages since 2011 and even now there are
improvements being made on this register.
II. SURVEY OF RELATED WORKS
A lot of papers have been written in field of GPRS but
none on cascading of FCSRs. General descriptions of
pseudorandom sequences and generators of pseudorandom
sequences are in [1].
The new approach of building register cascades is
described in [3].
Also the problems of modern GPRS and ways of solving
them are described in IEEE paper [4].
III. PROBLEM STATEMENT AND MAIN CONTRIBUTION
Nowadays, it is a big problem for a cypher designer to find
a generator of truly random sequences, without affecting the
speed of generation. GPRN is used to generate a strong key
that provides decryption for the encrypted data without a key.
The objective of this research is to find out what is the
sufficient number of registers in a cascade of FCSRs, to make
a generator more random without affecting the speed of
generation.
The idea is that a cascade of 5 FCSRs will not affect the
speed of generation because there are only 5 additional XOR
operations happening.
This sequence is then tested by a package of statistical
tests, NIST 800-22. A file is obtained which contains
information of tests that have passed and those that have not.
Then based on that file, a diagram is obtained on Microsoft
Excel which is more comprehensive to analyze and see which
sequence is considered as ‘truly’ random.
IV. PROBLEM SOLUTION
The program is run on the Windows 10 environment which
allows these results to be used for a big variety of cyphers
where modeled GPRS can be implemented. To give a
conclusion whether the sequence is ‘truly’ random or not we
need to generate at least 1 billion bits. Moreover, generating
these number of bits give us an opportunity to more precisely
measure the speed of generation, which is the main goal.
P

2. TABLE I. RESULTS OF RESEARCH
Type of
cascade
NIST tests
passed
Period of
sequence
Speed of
generation
3 FCSR YES 1012 25.5 Mbps
5 FCSR YES 1018 25.5 Mbps
A. Modeling
Basically an FCSR is a register which has a significant
advantage – a carry register.
Fig. 1 Scheme of FCSR
Instead of performing XOR operations on all bits of
sequence, these bits XOR up with each other and with the
contents of the carry register. The result is mod 2 and becomes
the new bit. The result divided by 2 becomes the new content
of the carry register.
The maximum period of FCSR is b-1, where b is an
integer of communication. This number sets the branch and is
defined as:
b = 2bl + 22
b2 + 23
b3 + . . . + 2n
bn-1 (1)
The Carry register gives an advantage over the custom
LFSR, i.e. the sequence is not bound to the XOR operation
between bits. This is very important because it makes the
register better and makes the sequence more random.
In order to make the cascade of FCSRs work properly we
need to combine them with an XOR operation [1]. This is
connected to the NIST 800-22 test package, because in order
to pass the first test - Linear Complexity, the sequence needs
to be reversible. This implies that the number of ‘1s’ and ‘0s’
in the sequence should be almost equal.
B. Application
To apply the work of designed cascade of FCSRs, the
program is written in Microsoft Visual Studio’s WPF
environment using C# and XAML programming languages.
Program has a comprehensive user interface which allows the
common user to work with it.
After starting the program, a window is seen where a path
to the text file, in which the random sequence to be generated
can be selected. After that a cascade of registers which will be
used for generation will be chosen. Further, there are options
to choose from whether the period and speed of generation
needs to be measured or not. This is necessary because the
operations can significantly decrease the performance of the
program. After all the steps are done, click on the «Generate»
button and wait for the line under the button to fill up with
green color indicates the progress of generation.
C. Verification
Cascades of 3 FCSRs and 5 FCSRs with 32 bits in each
were used to generate sequences. Then using the NIST 800-22
tests package the results about whether the tests have passed
or not is obtained. Test is considered passed only in case when
statistical value lies in interval from 0.98 to 0.999, other way
the test is not passed.
Fig. 2 Diagram of results of 3 FCSRs cascade
The results of 3 FCSRs cascade testing show that all the
tests were passed but the values are spread all over the
interval.
Fig. 3 Diagram of results of 5 FCSRs cascade
The results of 5 FCSRs cascade show much better results,
statistical values lay in interval from 0.985 to 0.995.
V. CONCLUSION
Summarizing, all the obtained results show that a cascade
of 5 FCSRs pass the package of statistical tests NIST 800-22
without affecting the speed of generation. This generator has a
good characteristics and can be implemented in a big variety
of already existing cryptographic algorithms [2].
Future work: Designing of new cypher which has this
GPRS embedded. This cascade of FCSRs can be extended to
be implemented on other operating system platforms as well.
REFERENCES
[1] B. Stoyanov and K. Kordov, “Pseudorandom Bit Generator with Parallel
Implementation,” in Large-Scale Scientific Computing, I. Lirkov, S.
Margenov, and J. Waśniewski, Eds. Springer Berlin Heidelberg, 2013, pp.
557–564.
[2] Karthikeyan, S., Sairam, N., Manikandan, G., Sivaguru, J.: A parallel
approach for improving data security. J. Theor. Appl. Inf. Technol. 39(2),
119–125 (2012)
[3] M. Francois, T. Grosges, D. Barchiesi, and R. Erra, “A New Pseudo-
Random Number Generator Based on Two Chaotic Maps,” Informatica,
vol. 24, no. 2, pp. 181–197, Jan. 2013.
[4] M. Jessa and M. Jaworski, “Producing secure pseudorandom sequences
with combined multiplicative congruential generators,” in 2012 19th
International Conference on Systems, Signals and Image Processing
(IWSSIP), 2012, pp. 160–163.

3. Biographies
Routhu Venkata Sai Kalyan was born in
Hyderabad City, India, in
1995. He received his B.Tech Degree in
Electronics and Communication Engineering
from Jawaharlal Nehru Technological
University, Hyderabad, in 2015. He is
currently pursuing his M.Sc. Degree in
Electrical Engineering with emphasis on
Telecommunication Systems at Blekinge
Institute of Technology(BTH), Karlskrona,
Sweden.
From 2013 to 2015, he worked as a
coordinator of Swetcha Organization, Hyderabad, India. He has attended
for Internship programme at Corporate Research & Development, Bharat
Heavy Electrical Limited, India, in 2015. He worked as a member of
NULL, India’s active open security community, Hyderabad chapter.
Mr. Kalyan was the winner of poster presentation, National Level
Techno Cultural Fest, Quest, in 2015 and the Hyderabad Quizzotic
Winner, 2014.
Vasireddy Sindhu was born in Hyderabad,
India, in 1994. She had finished her
schooling from the Narayana Olympiad
school, Ashok Nagar, Hyderabad in 2009.
She then completed her intermediate
schooling from Vijaya Ratna junior college,
Nallakunta, Hyderabad in 2011. She joined
into the Integrated Double Degree Master’s
Program(IDDMP) in Jawaharlal Nehru
Technological University
Hyderabad(JNTUH). She completed her
Bachelor of Technology(B.TECH) there
and is currently pursuing Master’s in
Telecommunications specialisation in Blekinge Tekniska
Hogskola(BTH).
She has done her Industrial Internship at Ananth Technologies Ltd
(ATL), Hyderabad, a supplier of missile and rocket parts to Indian Space
Research Organisation(ISRO) in Sriharikota for two months. She
involved in various stages of products manufactured under their guidance.
Ms. Vasireddy has been awarded the proficiency in academics
award for three consecutive years from 2003-2006 in high school. She
has participated in several workshops and conducted two workshops, one
is the Internet of things(IOT) and one other is the Embedded systems and
has also actively participated in many science Olympiads.
Tkachuk Roman-Valentyn was born in
Pidbirtsy Village, Pustomuty district, L’viv
region, Ukraine in 1995. He received the
B.Sc. degree in informational security from
the L’viv Polytechnic Nationa University,
Lviv, Ukraine, in 2016.
From 2014 to 2016 he was in team of
researchers who were developing new
algorithm of generation of pseudorandom
numbers. He is an author of 2 research
papers and co-author of 3 articles. His
research interests include pseudorandom number generators, stream
cyphers, symmetric and asymmetric cryptography, cryptology, malware
analysis, digital forensics, web security, software security and ethical
hacking.
Mr. Tkachuk was a recipient of President scholarship for excellent
studies and big contribution to university research project in 2015, Higher
scholarship for excellent studies from 2013-2016.
Wlodek J. Kulesza received the M.Sc. and
the Ph.D. degrees from Lodz University of
Technology, Poland, and a docent degree
from Linköping University, Sweden. In
2001 he became Professor in Measurement
Science at the University of Kalmar,
Sweden. Since 2005 he has held a
Professor position at the Blekinge Institute
of Technology, Sweden.
His current research interests are
multi-sensor systems and wireless sensor
networks.
Prof. Kulesza has been IEEE member
since 1995.