Cryptology ePrint Archive: Report 2017/763

Improved Fully Homomorphic Encryption without Bootstrapping

Masahiro Yagisawa

Abstract: Gentry’s bootstrapping technique is the most famous method of obtaining fully homomorphic encryption. In previous work I proposed a fully homomorphic encryption without bootstrapping which has the weak point in the enciphering function. In this paper I propose the improved fully homomorphic public-key encryption scheme on non-associative octonion ring over finite field without bootstrapping technique. The plaintext p consists of two sub-plaintext u and v. The proposed fully homomorphic public-key encryption scheme is immune from the “p and -p attack”. The cipher text consists of three sub-cipher texts. As the 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.

Category / Keywords: public-key cryptography / fully homomorphic public-key encryption, multivariate algebraic equation, Gröbner basis, non-associative ring

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

Date: received 7 Aug 2017

Contact author: tfkt8398yagi at outlook jp

Available format(s): PDF | BibTeX Citation

Version: 20170808:183539 (All versions of this report)

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