Noise free fully homomorphic encryption scheme over non-associative algebra

Mustafa, Iqra and Mustafa, Hasnain and Azar, Ahmad Taher and Aslam, Sheraz and Mohsin, Syed Muhammad and Qureshi, Muhammad Bilal and Ashraf, Nouman (2020) Noise free fully homomorphic encryption scheme over non-associative algebra. IEEE Access, 8. pp. 136524-136536. ISSN 2169-3536

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Abstract

Among several approaches to privacy-preserving cryptographic schemes, we have concentrated on noise-free homomorphic encryption. It is a symmetric key encryption that supports homomorphic operations on encrypted data. We present a fully homomorphic encryption (FHE) scheme based on sedenion algebra over finite Zn rings. The innovation of the scheme is the compression of a 16-dimensional vector for the application of Frobenius automorphism. For sedenion, we have p16 different possibilities that create a significant bijective mapping over the chosen 16-dimensional vector that adds permutation to our scheme. The security of this scheme is based on the assumption of the hardness of solving a multivariate quadratic equation system over finite Zn rings. The scheme results in 256n multivariate polynomial equations with 256+16n unknown variables for n messages. For this reason, the proposed scheme serves as a security basis for potentially post-quantum cryptosystems. Moreover, after sedenion, no newly constructed algebra loses its properties. This scheme would therefore apply as a whole to the following algebras, such as 32-dimensional trigintadunion.

Item Type:	Article
Additional Information:	Funding Information: This work was supported by the Prince Sultan University, Riyadh, Saudi Arabia. Publisher Copyright: © 2013 IEEE.
Uncontrolled Keywords:	/dk/atira/pure/subjectarea/asjc/1700
Departments or Groups:
Depositing User:	Admin SSL
Date Deposited:	19 Oct 2022 23:02
Last Modified:	15 Aug 2023 02:30
URI:	http://repository-testing.wit.ie/id/eprint/3718

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