Noise Free Fully Homomorphic Encryption Scheme Over Non-Associative Algebra

Noise Free Fully Homomorphic Encryption Scheme Over Non-Associative Algebra

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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 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 ALL IN ONE LIGHTLY SWEET 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 Course a pied - Enfant - Chaussures - Ligth trainer constructed algebra loses its properties.This scheme would therefore apply as a whole to the following algebras, such as 32-dimensional trigintadunion.