arXiv subjects

Indivar Gupta

Publications and source records attributed to Indivar Gupta.

3 recordsLinked to original sources

arXiv2026

Cryptographic Applications of Twisted Goppa Codes

This article defines multi-twisted Goppa (MTG) codes as subfield subcodes of duals of multi-twisted Reed-Solomon (MTRS) codes and examines their properties. We show that if $t$ is the degree of the MTG polynomial defining an MTG code, its minimum distance is at least $t + 1$ under certain conditions. Extending earlier methods limited to single twist at last position, we use the extended Euclidean algorithm to efficiently decode MTG codes with a single twist at any position, correcting up to $\left\lfloor \tfrac{t}{2} \right\rfloor$ errors. This decoding method highlights the practical potential of these codes within the Niederreiter public key cryptosystem (PKC). Furthermore, we establish that the Niederreiter PKC based on MTG codes is secure against partial key recovery attacks. Additionally, we also reduce the public key size by constructing quasi-cyclic MTG codes using a non-trivial automorphism group.

cs.IT↗

arXiv2024

Symmetric Encryption Scheme Based on Quasigroup Using Chained Mode of Operation

In this paper, we propose a novel construction for a symmetric encryption scheme, referred as SEBQ which is based on the structure of quasigroup. We utilize concepts of chaining like mode of operation and present a block cipher with in-built properties. We prove that SEBQ shows resistance against chosen plaintext attack (CPA) and by applying unbalanced Feistel transformation [19], it achieves security against chosen ciphertext attacks (CCA). Subsequently, we conduct an assessment of the randomness of the proposed scheme by running the NIST test suite and we analyze the impact of the initial vector, secret key and plaintext on ciphertext through an avalanche effect analysis. We also compare the results with existing schemes based on quasigroups [11,46]. Moreover, we analyze the computational complexity in terms of number of operations needed for encryption and decryption process.

cs.CR↗

arXiv2022

Characteristic properties of $\sigma$-A-nuclei of a quasigroup

In this paper, we investigate the properties of $\sigma$-A-nuclei of a quasigroup including relations between them and relations between their respective component sets, where $\sigma \in S_3$. We also find connections between components of $\sigma$-A-nuclei of a quasigroup and components of $\sigma$-A-nuclei of the isostrophic images. Further, we investigate the properties of various inverse quasigroups using the derived connections. These properties will not only make the study of $\sigma$-A-nuclei of a quasigroup simple but also reduce the time required in the computation of $\sigma$-A-nuclei of a quasigroup for different values of $\sigma$.

math.GR↗