Fully Homomorphic Encryption on Octonion Ring

Gentry's bootstrapping technique is still the only known method for obtaining fully homomorphic encryption. I propose a new fully homomorphic encryption scheme on non-associative octonion ring over finite field without bootstrapping technique. The security of the proposed fully homomorphic encryption scheme is based on computational difficulty to solve the multivariate algebraic equations of high degree while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients. Because proposed fully homomorphic encryption scheme is based on multivariate algebraic equations with high degree or too many variables, it is against the Gröbner basis attack. The key size of this system and complexity for enciphering/ deciphering become to be small enough to handle.

Autorentext

Masahiro Yagisawa received the B.E. and M.E. degrees from the University of Tokyo in 1974 and 1976. He is a member of IEICE (The Institute of Electronics, Information and Communication Engineers), IPSJ (Information Processing Society of Japan) and JSIAM (The Japan Society for Industrial and Applied Mathematics).