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 Suits 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 Vitamin algebra loses its properties.
This scheme would therefore apply as a whole to the following algebras, such as 32-dimensional trigintadunion.