<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we propose an efficient multivariate encryption scheme based on permutation polynomials over finite fields. We single out a commutative group ℒ(<italic>q, m</italic>) of permutation polynomials over the finite field <italic>F</italic><italic>q</italic><italic>m</italic>. We construct a trapdoor function for the cryptosystem using polynomials in ℒ(2, <italic>m</italic>), where <italic>m</italic> =2<italic>k</italic> for some <italic>k</italic> ≥ 0. The complexity of encryption in our public key cryptosystem is <italic>O</italic>(<italic>m</italic>3) 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 5<italic>m</italic>2+3<italic>m</italic> – 4 left cyclic shifts, 5<italic>m</italic>2 +3<italic>m</italic> + 4 xor operations and 7 permutations on bits for decryption.</abstract>

In this paper we propose an efficient multivariate encryption scheme based on permutation polynomials over finite fields. We single out a commutative group ℒ(q, m) of permutation polynomials over the finite field Fqm. We construct a trapdoor function for the cryptosystem using polynomials in 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.

A Public Key Cryptosystem Using a Group of Permutation Polynomials

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A Public Key Cryptosystem Using a Group of Permutation Polynomials"}

In this paper we propose an efficient multivariate encryption scheme based on permutation polynomials over finite fields. We single out a commutative group...

A Public Key Cryptosystem Using a Group of Permutation Polynomials

Published Online: Dec 31, 2020

Page range: 139 - 162

Received: Jul 15, 2019

DOI: https://doi.org/10.2478/tmmp-2020-0013

Keywords
multivariate cryptography, permutation polynomials, linearized polynomials

© 2020 Rajesh P. Singh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A Public Key Cryptosystem Using a Group of Permutation Polynomials

Published Online: Dec 31, 2020

Page range: 139 - 162

Received: Jul 15, 2019

DOI: https://doi.org/10.2478/tmmp-2020-0013

Keywordsmultivariate cryptography, permutation polynomials, linearized polynomials

© 2020 Rajesh P. Singh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
multivariate cryptography, permutation polynomials, linearized polynomials