Cryptology ePrint Archive: Report 2015/474

Fully Homomorphic Encryption without bootstrapping

Masahiro Yagisawa

Abstract: Gentry’s bootstrapping technique is the most famous method of obtaining fully homomorphic encryption. In this paper 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 differential attack, rank attack and so on. The key size of this system and complexity for enciphering/deciphering become to be small enough to handle.

Category / Keywords: secret-key cryptography / fully homomorphic encryption, multivariate algebraic equation, Gröbner basis, octonion

Original Publication (with minor differences): Masahiro, Y. (2015). Fully Homomorphic Encryption without bootstrapping which was published by LAP LAMBERT Academic Publishing, Saarbrücken/Germany .

Date: received 19 May 2015, last revised 20 Jun 2015

Contact author: tfkt8398yagi at hb tp1 jp

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Version: 20150621:055416 (All versions of this report)

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