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A public key cryptosystem using a group of permutation polynomials: Tatra Mt. Math. Publ. Number Theory and Cryptology '20

In: Tatra Mountains Mathematical Publications, vol. 77, no. 3
Rajesh P. Singh - Bhaba K. Sarma - Anupam Saikia

Details:

Year, pages: 2020, 139 - 162
Language: eng
Keywords:
multivariate cryptography; permutation polynomials; linearized polynomials
Article type: Mathematics
Document type: Scientific paper
About article:
In this paper we propose an efficient multivariate encryption sche me based on permutation polynomials over finite fields. We single out a commutative group $\mathfrak{L}(q,m)$ of permutation polynomials over the finite field $Fqm$. We construct a trapdoor function for the cryptosystem using polynomials in $\mathfrak{L}(2,m)$, where $m=2k$ for some $k≥ 0$. The complexity of encryption in our public key cryptosystem is $O(m3)$ multiplications which is equivalent to other multivariate public key cryptosystems. For decryption only left cyclic shifts, permutation of bits and xor operations are used. It uses at most $5m2+3m-4$ left cyclic shifts, $5m2+3m+4$ xor operations and $7$ permutations on bits for decryption.
How to cite:
ISO 690:
Singh, R., Sarma, B., Saikia, A. 2020. A public key cryptosystem using a group of permutation polynomials: Tatra Mt. Math. Publ. Number Theory and Cryptology '20. In Tatra Mountains Mathematical Publications, vol. 77, no.3, pp. 139-162. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0013

APA:
Singh, R., Sarma, B., Saikia, A. (2020). A public key cryptosystem using a group of permutation polynomials: Tatra Mt. Math. Publ. Number Theory and Cryptology '20. Tatra Mountains Mathematical Publications, 77(3), 139-162. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0013
About edition:
Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Published: 20. 12. 2020
Rights:
The Creative Commons Attribution-NC-ND 4.0 International Public License