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Title: Noise free fully homomorphic encryption scheme over non-associative algebra
Authors: Mustafa, Iqra 
Mustafa, Hasnain 
Azar, Ahmad Taher 
Aslam, Sheraz 
Mohsin, Syed Muhammad 
Qureshi, Muhammad Bilal 
Ashraf, Nouman 
Major Field of Science: Natural Sciences
Field Category: Computer and Information Sciences
Keywords: Automorphism Aut(V);Frobenius automorphism φ;Fully homomorphic encryption;Multivariate polynomial equations;Sedenion;Totally isotropic subspaces
Issue Date: 2020
Source: IEEE Access, 2020, vol. 8. pp. 136524-136536
Volume: 8
Start page: 136524
End page: 136536
Journal: IEEE Access 
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.
ISSN: 2169-3536
DOI: 10.1109/ACCESS.2020.3007717
Rights: This work is licensed under a Creative Commons Attribution 4.0 License
Attribution-NonCommercial-NoDerivatives 4.0 International
Type: Article
Affiliation : Cork Institute of Technology 
COMSATS University Islamabad 
Prince Sultan University 
Benha University 
Cyprus University of Technology 
Shaheed Zulfikar Ali Bhutto Institute of Science and Technology 
Waterford Institute of Technology 
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