Wireless Personal Communications (2021) 119:1577–1587
https://doi.org/10.1007/s11277-021-08295-5
A Novel Encryption Approach Based on Vigenère Cipher
for Secure Data Communication
N. Uniyal1 · G. Dobhal1 · A. Rawat2 · A. Sikander3
Accepted: 11 February 2021 / Published online: 15 March 2021
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
Abstract
Nowadays, with the advancement of technologies in modern life communication and networks, the secrecy of a cryptographic technique has become a strong necessity. The Vernam’s cipher which is a specific form of Vigenère cipher is gaining attention of researchers in the cryptography. But the modern encryption methods based on matrices available
in the literature have their limitations to utilize them. Therefore, motivated by numerous
cryptographic techniques available in the literature, this study presents a novel encryption
approach for secure data communication. The proposed encryption approach is based on
Vigenère cipher in finite dimensional vector space. Furthermore, the proposed approach
relies on an eternal decomposition which is indiscriminate in the key selection inside key
space. To add complexity by text scrambling, a weird substitution cipher key is added to
provide maximum derangement in the encrypted text structure. Additionally, in the lights
of Shannon’s secrecy, a comparison with usual matrix methods relying on LU —decomposition and eigenvalue decomposition is also discussed to justify the perfect secrecy thus
achieved. It is revealed that the proposed encryption approach is a more versatile and perfectly secret encryption scheme that roots on the widening of key space to a mathematical
structure, which not only fulfills the completeness with respect to the proposed decomposition but identical to message space as well.
Keywords Perfect secrecy · Vigenère cipher · Isomorphism · Derangements
* A. Sikander
afzals@nitj.ac.in
N. Uniyal
nuniyal@ddn.upes.ac.in
G. Dobhal
gdobhal@ddn.upes.ac.in
A. Rawat
arawat@ddn.upes.ac.in; rawat.ajay@hotmail.com
1
Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, Uttarakhand,
India
2
School of Computer Science, University of Petroleum and Energy Studies, Dehradun, Uttarakhand,
India
3
Department of Instrumentation and Control Engineering, Dr. B. R. Ambedkar National Institute
of Technology Jalandhar, Punjab, India
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1 Introduction
In this era due to advancement in networking technologies and Internet, the communication has become faster and easier. So the security of data is gaining importance as it is
major concern of the time. Cryptography ensures security of contents while communicating through various channels [1]. In cryptography, mathematical functions are used
for encryption and decryption processes. The function employs a key which is used for
encryption as well as decryption. The strength of a cryptographic algorithm depends
upon retrieving the key value from the domain space. Thus the strength of algorithm
depends on the retrieving time of the key. Cryptanalysis utilizes methods for analyzing
and breaking cryptographic methods. An encryption algorithm transforms plaintext into
ciphertext and using decryption algorithms with the help of keys plaintext is recovered
from ciphertext. The algorithms can be divided into two major groups namely; private
key (or symmetric) algorithms and public key (or asymmetric) algorithms. Symmetric
key uses a single key for both encryption and decryption while asymmetric setting uses
different keys at both ends. The need of cryptography is due to some possible eavesdropping adversary who may be keen to know the conversation between the communicating parties. It is assumed that an eavesdropping adversary is well-versed and capable
to decrypt the ciphertext if the key is known to him. In an attempt to search for the key
used for encryption an adversary may try an exhaustive search inside the key space.
Thus a large key space that cannot be searched exhaustively in a reasonable amount of
time is a necessity in cryptography. However, a large key space is not a guarantee for
security as mono-alphabetic substitution cipher which is easy to break despite the large
key space. Thus, a large key space is a necessary requirement, but not a sufficient one.
In the lights of modern cryptography, an encryption scheme is said to be secure if no
adversary can compute any function of the plaintext from the ciphertext. Hence a secure
encryption apart from a large key space also requires a strong mathematical encrypting
function which an adversary cannot invert in real polynomial time.
An interesting polyalphabetic cipher called Vigenère cipher was given by Blaise de
Vigenère, a French mathematician in sixteenth-century. It was simple and resistive to
the test based on frequency analysis of letters that could easily break simple ciphers like
Caesar cipher [2]. In English language, the 26 alphabets are given numeric value from
0 to 25 in the order as they appear. The basic setting of private-key encryption along
with ciphertext is shown in Fig. 1. Additionally, to encrypt a message of length l (say),
a random sequence of letters (of same length) is chosen and added to obtain ciphertext.
For example, an encryption of the message let him go using the key calf gives ciphertext
kffnlnsu as follows (Table 1):
Mathematically, the process can be described as follows:
Let M = C = K = (ℤ26 )n , n being a positive integer. For a key k = (k1 , k2 , … kn ) we
have
(
)
Ek x1 , x2 … , xn = (x1 + k1 , x2 + k2 , … , xn + kn )
Dk (y1 , y2 … , yn ) = (y1 − k1 , y2 − k2 , … , yn − kn )
The Vigenère cipher becomes vulnerable for Kasiski attack if the text message is
long enough and key is repeating. The reason is that bigrams or trigrams appearing
more often in English language may get mapped to same ciphertext in case of a long
message [3, 4].
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A Novel Encryption Approach Based on Vigenère Cipher for Secure…
Fig. 1 Basic setting of private-key encryption
Table 1 Example of Vigenère
cipher
Type of text
Corresponding code
Plaintext
lethimgo
Key
Ciphertext
calfcalf
kffnlnsu
A specific case of Vigenère cipher is Vernam cipher where the key length is taken
equal to message length. This cipher has been proved to be unbreakable and provides
perfect secrecy but for the large size of message the large size of key is a problem.
Over the last few years, several modifications in Vigenère cipher have been given
by the researchers to meet the enhanced modern standards of security. To increase the
security of the cipher, a modified version of Vigenère cipher was given by adding bits of
random padding [2]. A Vigenère cipher with varying key technique was given by Kester
[5] which used successive keys that are dependent on an initial key. Later on, the character set was expanded to include special characters too instead of merely conventional
26 alphabets [6]. Another attempt based on hybrid of Vigenère cipher with transposition
cipher and Caesar cipher respectively were given in [7, 8]. Ali and Sarhan strengthened the Vigenère cipher by combining it with stream cipher [9]. Subandi et al., in their
three-pass protocol used Vigenère cipher with keystream generator modification [10].
A modified Vigenère encryption algorithm and its hybrid implementation with Base64
and AES was given in [11]. Recently a novel key substitution encryption architecture
was proposed to encrypt various types of images [12]. A new concept for encryption
in higher dimensional vector spaces involving vector decomposition was proposed in
[13]. An insight into steganography for the hidden messages was explored in [14] and
its modified version using Caesar cipher was proposed in [15]. A particular branch of
matrix methods cryptography was further explored in [16] where the size of key domain
is emphasized for security.
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N. Uniyal et al.
Under the modern matrix encryption-decryption methods using conventional decomposition methods for key matrix, perfect secrecy is not achieved due to the inherent restriction imposed on key-space by the nature of decomposition itself. In this paper, we propose
a novel encryption-decryption matrix method based on key space maximization, which
achieves perfect secrecy without too many encryption rounds.
Our main contributions are as under:
(1) A generalized encryption-decryption matrix method eternally applicable in any arbitrary human language.
(2) The necessary requirement for perfect secrecy i.e. making key space cardinally equivalent to message space is achieved. Further, its integration with Vernam cipher suffices
to achieve perfect secrecy.
(3) The difficulty of sharing and storage of a long key is resolved due to symmetric nature
of keys.
2 Preliminaries
2.1 Perfectly Secret Encryption
Briefly presenting some of the syntax required in an encryption scheme:
The symbols M, K and C denote the message space, key space and ciphertext space
respectively. Π = (Gen, Enc, Dec) denotes the scheme consisting of algorithms of key generation, encryption and decryption. The encryption algorithm being probabilistic in nature,
we write c ← Enck (m) to denote that a ciphertext c is the encrypted output for message
m ∈ M processed with key k ∈ K. Analogously, the decryption algorithm being deterministic in nature so we write m =∶ Deck (c) to denote that message m is the decrypted output
for some ciphertext c ∈ C processed with key k ∈ K. We let PrivKA,Π denote an execution
of private key experiment for some given Π and any adversary A . Further, it is assumed
that the schemes are perfectly correct i.e. ∀m ∈ M, ∀k ∈ K and the output c ← Enck (m),
the probability for m =∶ Deck (c) is always 1. We now present here the idea of perfect
secrecy of an encryption scheme using the undermentioned definition [3] .
Definition 2.1 An encryption scheme Π (= (Gen, Enc, Dec)
) over a message space M is
perfectly secret if for every adversary A, Pr PrivKA,Π = 1 = 12 holds.
Here PrivKA,Π = 1 means the output is 1 which is possible if A succeeds in breaking the
encryption scheme. Hence an encryption scheme is perfectly secret if no adversary A can
succeed with probability more that 12 . Besides the aforementioned definition for the notion
of perfect secrecy, a few decades later Shannon characterized |M| ≤ |K| i.e. the key space
is at least as large as the message space and gave the following theorem.
Theorem 2.2 (Shannon’s theorem) [3]. Let Π = (Gen, Enc, Dec) be an encryption scheme
over a message space M for which |M| = |K| = |C|. The scheme is perfectly secret if and
only if:
1. Every key k ∈ K is chosen with equal probability 1∕|K| by algorithm Gen.
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2. For every m ∈ M and every c ∈ C, there exists a unique key k ∈ K such that Enck (m)
outputs c.
To meet the stated hypothesis |M| = |K| = |C| one needs to seek the spaces which
are equal in their sizes. However, this task can be simplified to a large extent if we
choose M = K i.e. the key space being the message space itself. The reason of choice
is probabilistic rather than set theoretic as K is eventually the sample space for each
key k, equally probable with probability 1∕|K|. This amounts to say that the encryptiondecryption rules must not misbehave to any key k ∈ M and to an adversary the key
becomes as random as the message.
3 Proposed Methodology
We proposed a method which is hybrid of Vigenère cipher and Substitution cipher, the
later works on the output of the former. The method also aims to encrypt a message in
any language evolved on some universal set of arbitrary finite symbols.
Let us take a random primary key K from Mn (ℤp𝛼 ), the vector space of n × n matrices over the field ℤp𝛼 ;p being prime and 𝛼 ∈ ℕ. We propose a unique decomposition of
K as follows:
( 𝛼
)
[( 𝛼
)
]
)
)
p +1 (
p −1 (
�
�
K=
K+K +
K+K +K
2
2
⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟
skew−symmetric
symmetric
where the symbol ′ is used to indicate the transpose operation.
Using
little�
algebra
of
matrices
one
can
verify
that
]
( 𝛼 )(
[( 𝛼 )(
�)
�)
p +1
p +1
K
+
K
=
K
+
K
and
]� 2 [( 𝛼 )(
]
[( 𝛼2 )(
)
)
�
�
p −1
K + K + K + p 2−1 K + K + K = 0.
2
( 𝛼 )(
( 𝛼 )(
)
�
�)
Matrices p 2+1 K + K and p 2−1 K + K are additive inverse of each other and
hence can be used as encryption and decryption keys at opposite ends. Arranging row
wise the characters of a message in an n × n structure T , the plaintext matrix each entry
of which belongs to some universal set consisting of arbitrary alphabets and special
characters, p𝛼 in number. On encryption let TC be the cipher text matrix. For encryption,
the equations are
TC = f (T ∗∗ )
(1)
[
( 𝛼
)
]
p +1
�
T ∗∗ = 𝜎max T +
(K + K ) 𝜎max .
2
(2)
and
For decryption, the equations are
( )
T ∗∗ = f −1 TC
(3)
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N. Uniyal et al.
1582
and
−1 ∗∗ −1
T = 𝜎max
T 𝜎max +
(
)
p𝛼 − 1 (
�)
K+K .
2
(4)
Here f ∶ ℤp𝛼 → F is a bijective map from ℤp𝛼 onto F, an arbitrary field of p𝛼 characters, all unique. 𝜎max is the secondary key shared between the two parties. We prefer to
pick out𝜎max ∈ Mn (ℤp𝛼 ), which among the subdomain symmetric group Sn of all permutation matrices resides at the farthest end in sense of complexity. Since Sn must contain
some 𝜎max which is unique (up to isomorphism in cycle structure), we must have disjoint
cycles 𝜌i ∈ Sn , 1 ≤ i ≤ k for which 𝜎max = 𝜌1 .𝜌2 … 𝜌k s.t. |𝜌1 | + |𝜌2 | + ⋯ + |𝜌k | = n and
lcm{||𝜌1 ||, |𝜌2 |, … , |𝜌k |} is maximum.
3.1 Flow of Encryption–Decryption Process
The steps of the algorithm are as under:
Flow of Encryption Process:
1. Insert T, keys K(and 𝜎)max ; and a bijection f ∶ ℤp𝛼 → F for a specific F.
(
𝛼
�)
2. Determine T + p 2+1 K + K = T ∗ .
3. Determine 𝜎max T ∗ 𝜎max = T ∗∗ .
4. Determine TC = f (T ∗∗ ) as cipher text matrix.
Flow of Decryption Process:
1.
2.
3.
4.
−1
Insert cipher text
( T)C , keys∗∗K and 𝜎max ; and bijection f ∶ F → ℤp𝛼.
−1
Determine f TC = T .
−1 ∗∗ −1
Determine T ∗ = 𝜎max
( T𝛼 𝜎)max .
�
∗
Retrieve T = T + p 2−1 (K + K ) as text matrix.
4 Discussion and Probabilistic Comparison
The distinction of the novel decomposition is featured in the privilege of autocratic selecany
tion of primary key K
( ≠𝛼 O)(Zero matrix).(For
) choice of K , the suggested decomposi𝛼
�
�
tion fetches factors p 2+1 (K + K ) and p 2−1 (K + K ) which always exist in Mn (ℤp𝛼 ).
The incorporated operations like transposing, vector addition and scalar multiplication
guarantee that each factor is well within the vector space Mn (ℤp𝛼 ). Since this space also
includes a multiplicative subgroup Sn of all permutation matrices; the elements of which
are essentially well suited for shuffling purpose, we hence have chosen the most impregnable member of Sn which shuffles the elements of T ∗ to its maximum. Though any element
of maximum order guarantees this impregnability but choosing one of them suffices due to
the structural isomorphism in cycle structure. The idea is motivated by the perfect shuffling
of the deck of playing cards where an adversary’s algorithm needs to apply maximum iterations for sorting.
For an adversary, the probability that he predicts the primary key is substantially diminished due to the maximization of possibility space to Mn (ℤp𝛼 ). WLOG, we assume that the
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A Novel Encryption Approach Based on Vigenère Cipher for Secure…
distribution is uniform inside the message space M and denote X = x as the random variable inside sample key spaceK. Assume that the universal set of p𝛼 plaintext symbols and
the order n of cipher matrix is known to the adversary, the probability of guessing primary
key is Pr(X = K) = 𝛼n1 2 .
p
Further, if Sdn is the set of all 𝜎max where the suffix dn is used to indicate the deranging
nature of the elements of set then the conditional probability of prediction of secondary
substitution key 𝜎max is
�
�
Pr X = 𝜎max =
� �
�Sdn �
� �
�
�
�Mn (ℤp𝛼 )�
�
�
=
∑n
(−1)k n!
k!
p𝛼n2
k=0
An analysis on the number of 𝜎max can be done by having a microscopic look on a finer
subdomain of Sn ⊂ Mn (ℤ37 ) which essentially is the set Sdn(say) of derangements. The elements of Sdn are permutations which do not fix any of the n symbols thereby imparting the
maximum cycle length to each of its element. A good choice of 𝜎max as a key will eventually come out from a specific subclass of Sdn , containing all highest order permutations
which lies at the farthest from the one having zero perturbation at all. Thus, the order of
each element in this subclass must be highest. Precisely speaking, 𝜎max is the weirdest of all
possible derangements in Sdn for which the computational time complexity of any sorting
algorithm is quite high. Fixing n = 10 to verify this (Table 2):
Since there will be 10 C5 .4! × 5 C3 .2! = 120960 𝜎max in number which are unique up to
isomorphism in cycle structure hence ending by all odds picking the correct 𝜎max is a challenging task for an adversary. Further, the proposed method is not limited for encryption in
a specific language as the number p𝛼 is unbounded and secrecy remains to be intact even
on increasing the length of message.
In contrast to the methods based on LU —decomposition [17] of K = [kij ] where it is
required to have full rank and k11 ≠ 0; the key space is eventually some
( proper
) subset of
General Linear group of non-singular matrices i.e. K ⊂ GLn (ℤp𝛼 ) ⊂ Mn ℤp𝛼 = M which
implies |K| < |M|. Hence perfect security cannot be claimed.
Table 2 Cycle structure of
derangements of Sd10
Cycle type
Order of
permutation
(1 2 3 4 5 6 7 8 9 10)
10
(1 2 3 4 5 6 7 8)(9 10)
(1 2 3 4 5 67)(8 9 10)
(1 2 3 4 5 6)(7 8 9 10)
(1 2 3 4 5)(6 7 8 9 10)
(1 2 3 4 5 6)(7 8)(9 10)
𝜎max → (1 2 3 45)(6 7 8)(9 10)
(1 2 3 4)(5678)(910)
(1 2 3 4)(5 6 7)(8 9 10)
(1234)(56)(78)(910)
(123)(456)(78)(910)
(12)(34)(56)(78)(910)
8
21
12
5
6
30
4
12
4
6
2
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N. Uniyal et al.
1584
Comparing on probabilistic grounds the probability of Vigenère
key�prediction by an
∏n−1 �
adversary is Pr(X = K) ≈ ∏n−1 1𝛼n 𝛼i ; the denominator i=0 p𝛼n − p𝛼i being the numi=0 (p −p )
ber of non-singular linear maps in GLn (ℤp𝛼 ). Observe that
1
∏n−1 �
i=0
p𝛼n
−
p𝛼i
� =
1
1
1
=
.
�
� >> 𝛼n 𝛼n
p .p … p𝛼n
p𝛼n2
(p𝛼n − 1)(p𝛼n − p𝛼 ) … p𝛼n − p(n−1)𝛼
�������������
n factors
The proposed method is also superior to one with encryption based on eigen-decomposition as not every matrix possesses eigenvalues in the field ℤp𝛼 . Hence, the key space
cannot include the matrices having irreducible characteristic polynomials in the field ℤp𝛼 .
This eventually results |K| < |M| and perfect secrecy cannot be achieved. Though singular value decomposition doesn’t limit the size of key space but due to its non-uniqueness
[18], the proposed method clearly has an edge in the uniqueness of decomposition. The
effectiveness of the proposed method is analyze in terms of different parameters as shown
in Table 3 and it is observed that the proposed method exhibits superior performance as
compared to other methods available in the literature.
5 Method Secrecy
A cryptographic algorithm needs to be perfectly secure from attacks and the formal way to
say this is to achieve Shannon’s security. Informally, a scheme is said to be Shannon secure
if the key space and the plaintext space are identical in size. Since the key K can be any
member of Mn (Zp𝛼 ), the space of plaintext itself hence the proposed method agrees Theorem 2.2. Further, the probability of breaking both keys simultaneously is
� ∑n (−1)k n
�
Pr PrivKA,Π = 1 = k=02𝛼n2k which is in accordance to the Definition 2.1. For p𝛼 = 37 in
p(
)
3 × 3 matrix setting, Pr PrivKA,Π = 1 = 1.18 × 10−28 ≈ 0. It proves that the scheme is
secure for encryption even with the usual set of alpha-numeric characters without symbols
k
∑n
2
and punctuation marks. The denominator p2𝛼n dominates abruptly the sum k=0 (−1)k! n! as
with)smaller set of symbols where a
the size of n is increased. This too holds for languages
(
carefully chosen sufficiently large n keeps Pr PrivKA,Π = 1 ≤ 12.
In layman’s words, the primary key comes from a vast key space and secondary key
which in its family hierarchy lies at the top in complexity sense. Thus, an adversary has
to hover vastly in the primary key domain and penetrate deeply in the (secondary key)
domain. The entropy of the cipher text is maximized and the probability Pr PrivKA,Π = 1
Table 3 Comparative analysis of key generation methods
Parameters
Key generation methods
Proposed method
Randomness
Truly random
Relative sizes of mes- |K| = |M|
sage and key spaces
Uniqueness of keys
Unique
Perfect secrecy
Achieved
13
SVD method
Eigen decomposition
LU decomposition
Truly random
Not truly random
Not truly random
|K| = |M|
|K| < |M|
|K| < |M|
Not-unique
Achieved
Unique
Not achieved
Unique
Not achieved
A Novel Encryption Approach Based on Vigenère Cipher for Secure…
1585
is minimized. In addition, an implication of Shannon’s theorem is that if there exists a perfectly secret encryption scheme Π = (Gen, Enc, Dec) for a particular probability distribution over M then it is perfectly secret in general.
( )
K = [kij ] ∈ Mn ℤp𝛼
the
encryption
Mathematically,
for
some
( 𝛼 )(
)
p +1
∗
∗
tij +
kij + kji → tij may give same tij for two or more distinct tij and two or more tij∗
2
for same tij . The map tij ↦ tij∗ is not one–one and hence impossible to invert mathematically. Due to the non-uniqueness of tij for some known tij∗ it also serves as a one-way function; thus hard to invert computationally as well. Thus an adversary cannot retrieve the
corresponding plaintext character by spotting the same characters at different positions in
the ciphertext. It easily deludes an adversary in the case where a tail of zeros is amalgamated to a short text message for its accommodation in matrix structure. This property of
Vigenère cipher ensures that the ciphertext doesn’t disclose anything about the plaintext,
despite the unlimited computational power of an adversary [3].
6 Conclusion and Future Scope
A novel encryption approach for data communication is suggested in this paper. The concept of Vigenère cipher in finite dimensional vector space is being employed to maintain
perfect secrecy of the data. The proposed approach is perfectly secure as each letter
reserves a distinct key and the condition
( |K|
( ) Selection of
) = |M| is also inherent therein.
keys from the broadened key space Mn ℤp𝛼 rather than the usual GLn ℤp𝛼 solely owes to
the proposed decomposition. Instead of the aforesaid freedom in key selection, added is the
security due to the lesser probability of key-prediction by an unauthenticated party. Though
|K| = |M| ensures maximized key space thereby enhancing the secrecy of the key but in
attempt for dragging out the key length equal to that of message the key-storage may be a
challenge. However, this challenge up (
to some
is substantially overcome by
)( extent though;
𝛼
�)
the symmetric nature of primary keys p 2±1 K + K and deranging nature of secondary
key 𝜎max . Nonetheless, the aforementioned decomposition opens a scope for further
improvement in the direction of key secrecy.
Funding No funding.
Compliance with Ethical Standards
Conflict of interest The authors declare that they have no conflict of interest.
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institutional affiliations.
Dr. N. Uniyal is working as an Assistant Professor(SG) with the
Department of Mathematics, University of Petroleum and Energy
Studies, Uttarakhand, India. He had worked with the Department of
Mathematics, Uttaranchal University, Uttarakhand, India. He also
earned a Ph.D. degree from the Central University of Garhwal in Differential Geometry in 2012. Dr. Nitin Uniual has over 13 years of
teaching and research experience. He has published more than 20
research articles in reputed National and International journals. He has
qualified CSIR-NET multiple times with the highest 9th rank in India.
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A Novel Encryption Approach Based on Vigenère Cipher for Secure…
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Dr. G. Dobhal is currently working as Assistant Professor with the
Department of Mathematics, University of Petroleum and Energy
Studies, Dehradun, Uttarakhand, India. He has completed B.Sc. degree
in Physics, Chemistry and Mathematics and M.Sc. degree in Mathematics from D.B.S.(P.G) College, Dehradun, India. He has also earned
Ph.D. degree from Hemwati Nandan Bahuguna Garhwal Central University, Srinagar, India. His area of Specialization includes Differential
Geometry, Approximation Theory.
A. Rawat has over 16 years of experience in academics and industry in
India and abroad. He is an Official Instructor of Google and Confluent.
He received an MS degree from BITS Pilani, India, and presently he is
pursuing a Ph.D. from the Department of Computer Science and Engineering, Uttarakhand Technical University, Dehradun, India. Also,
currently, he is working in the capacity of Assistant Professor(SG)
with the School of Computer Science, UPES, Uttarakhand, India. He
had worked with the Department of Computer Science, Graphic Era
University, Uttarakhand, India, as an Assistant Professor. He is also
having industry experience as Software Engineer in NIIT Technologies, New Delhi, India. His area of interest includes Cloud computing,
fault tolerance, Big Data. He has acquired various international certifications such as Google Professional Data Engineer, Google Professional Architect, Confluent Developer, Confluent Operation, Databricks Apache Spark, RedHat OpenStack. He has published papers in
national and international journals. He has delivered trainings in
Google Singapore and many other countries.
A. Sikander is working as an Assistant Professor with the Department
of Instrumentation and Control Engineering, Dr. B. R. Ambedkar
National Institute of Technology, Jalandhar, Punjab, India. Dr.
Sikander has over 10 years of teaching and research experience in the
diverse field of Control Engineering. He is serving as Editorial board
member and guest Editor of numerous reputed journals. His areas of
interest include control theory and applications, circuit design, model
order reduction, optimization, robotics and renewable energy. He is
actively involved in various research projects funded by CSIR, ISRO,
and MHRD, etc. He has guided 8 M.Tech. students whereas 2 Ph.D.
research scholars, 1 JRF and 1 M.Tech. Student are under process. He
has published 65 research articles in reputed National and International journals and conferences.
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