Cryptology ePrint Archive: Report 2016/462

Fully Homomorphic Encryption with Isotropic Elements

Masahiro Yagisawa

Abstract: 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 fully homomorphic encryption scheme with non-zero isotropic octonions. I improve the previous scheme by adopting the non-zero isotropic octonions so that the “m and -m attack” is not useful because in proposed scheme many ciphertexts exist where the plaintext m is not zero and the norm is zero. The improved scheme is based on multivariate algebraic equations with high degree or too many variables while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients. The improved scheme is against the Gröbner basis attack.

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

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 12 May 2016

Contact author: tfkt8398yagi at hb tp1 jp

Available format(s): PDF | BibTeX Citation

Note: In previous report 2015/474,2015/733 in Cryptology ePrint Archive, I proposed fully homomorphic encryption which has the weak point in the enciphering function and is not immune from “m and -m attack”. In this report I propose the improved scheme which overcomes the weak point.

Version: 20160513:121212 (All versions of this report)

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