Shiv Narain

Work place: Department of Mathematics Arya P.G. College Panipat, India



Research Interests: Information-Theoretic Security, Network Security, Information Security, Hardware Security


Shiv Narain received his Ph.D. from Kurukshetra University Kurukshetra, India and currently working as Assistant Professor, Post Graduate Department Of Mathematics Arya P.G. College ,Panipat India. His research interests are Group Theory, Fuzzy Set Theory, Cryptography and Fractional Calculus.

Author Articles
Non-singular Transformation Based Encryption Scheme

By Sunil Kumar Sandeep Kumar Gaurav Mittal Dharminder Dharminder Shiv Narain

DOI:, Pub. Date: 8 Aug. 2021

In this paper, we propose a novel variant of the Hill cipher based on vector spaces. In the classical Hill cipher, a non-singular matrix is used for encryption but it is well known that this cipher is vulnerable to the known-plaintext attack. In our proposed cryptosystem, we eradicate this problem by encrypting each plaintext block with a new invertible key matrix. This makes our scheme immune to all existing attacks in literature on this type of ciphers and so the resulting cipher can be used as other state-of-art block cipher. To generate the invertible matrices which serve as the dynamic keys, we make use of the vector spaces along with randomly generated basis and non-singular linear transformation. In addition to this, we also study the computational complexity of the proposed cryptosystem and compare this with the computational complexities of other schemes based on Hill cipher. 

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