Towards Fully Homomorphic Encryption From Gentry-Peikert-Vaikuntanathan Scheme

Du, Gang; Ma, Chunguang; Wang, Ding

doi:10.1007/978-3-319-68542-7_21

Cited by 1 publication

(1 citation statement)

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“…[4]- [10]. Subsequently, nowadays FHE has been widely adopted for cloud security [11] [12], e-health care privacy [13], blockchain, [14] i.e., artificial intelligence Cortex blockchain adopted somewhat FHE (SWFHE) to train and infer the model. The first generation methods, however, were somewhat similar, but they had different theoretical assumptions with complex methodologies.…”

Section: Introductionmentioning

confidence: 99%

Noise Free Fully Homomorphic Encryption Scheme Over Non-Associative Algebra

Mustafa

Azar

et al. 2020

IEEE Access

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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 Z n rings. The innovation of the scheme is the compression of a 16-dimensional vector for the application of Frobenius automorphism. For sedenion, we have p 16 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 Z n 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 32dimensional trigintadunion.

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