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 13 Vol.:(0123456789) N. Uniyal et al. 1578 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]. 13 1579 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. 13 1580 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. 13 A Novel Encryption Approach Based on Vigenère Cipher for Secure… 1581 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) 13 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 13 1583 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 13 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. References 1. Shannon, C. E. (1949). Communication theory of secrecy systems. Bell Systems Technical Journal, 28(4), 656–715. 2. Wilson, P. I., & Garcia, M. (2006). A Modified Version of the Vigenère Algorithm. IJCSNS International Journal of Computer Science and Network Security, 6(3B), 140–143. 3. Shannon, C. E. (1948). A mathematical theory of communication. The Bell System Technical Journal 27, 379–423, 623–656 (Reprinted in C.E. Shannon and W. Weaver The Mathematical Theory of Communication; University Illinois Press: Champaign, IL, USA, 1949). 4. Shannon, C. E., & Warren, W. (2009). The Mathematical Theory of Communication (pp. 12–29). University of Illinois Press. 13 1586 N. Uniyal et al. 5. Kester, Q. A. (2012). A cryptosystem based on Vigenère cipher with varying key. International Journal of Advanced Research in Computer Engineering and Technology, 1(10), 108–113. 6. Khalid, M., Wadhwa, N., & Malhotra, V. (2012). Alpha-qwerty cipher. International Journal of Advanced Computing, 3(3), 107–118. 7. Kester, Q. A. (2013). A hybrid cryptosystem based on Vigenère cipher and columnar transposition cipher. International Journal of Advanced Technology and Engineering Research, 3(1), 141–147. 8. Omolara, O. E., Oludare, A. I., & Abdulahi, S. E. (2014). Developing a modified hybrid caesar cipher and vigenere cipher for secure data communication. International Journal of Computer Engineering and Intelligent Systems, 5(5), 34–46. 9. Ali, F. M. S., & Sarhan, F. H. (2014). Enhancing security of vigenere cipher by stream cipher. International Journal of Computer Applications, 100(1), 1–4. 10. Subandi, A., Mieyanti, R., Sandy, C. L. M., & Sembiring, R. W. (2017). Three-pass protocol implementation in vigenere cipher classic cryptography algorithm with keystream generator modification. Advances in Science, Technology and Engineering Systems Journal, 2(5), 1–5. 11. Singh, G. (2014). Modified vigenere encryption algorithm and its hybrid implementation with base64 and AES. In IEEE Journal. 12. Song, Y., Zhu, Z., Zhang, W., Yu, H., & Zhao, Y. (2019). Efficient and secure image encryption algorithm using a novel key-substitution architecture. In IEEE Journal. 13. Okamoto, T., & Takashima, K. (2008). Homomorphic encryption and signatures from vector decomposition. In S. D. Galbraith & K. G. Paterson (Eds.), Pairing 2008. LNCS (Vol. 5209, pp. 57–74). Springer. 14. Johnson, N. F. (1998). Exploring steganography: Seeing the unseen. IEEE Transaction on Computer, 31(2), 26–34. 15. Benni, P., & Hetty Rohayani, A. H. (2015). A new modified Caesar cipher cryptography method with legible ciphertext from a message to be encrypted. Procedia Computer Science, 59, 195–204. 16. Uniyal, N., Dobhal, G., & Semwal, P. (2020). Enhanced security of encrypted text by KDMT: Keydomain maximization technique. IJRTE, 8(5), 1385–1388. 17. Othman, A. A. (2013). Binary LU encryption. In IEEE Journal. 18. Hu, Q. (1997). On the uniqueness of the Singular value decomposition in meteorological applications. Journal of Climate, 10(7), 1762–1766. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and 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. 13 A Novel Encryption Approach Based on Vigenère Cipher for Secure… 1587 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. 13