Cryptology ePrint Archive: Report 2018/088

Fully homomorphic public-key encryption with small ciphertext size

Masahiro Yagisawa

Abstract: In previous work I proposed a fully homomorphic encryption without bootstrapping which has the large size of ciphertext. This tme I propose the fully homomorphic public-key encryption scheme on non-associative octonion ring over finite field with the small size of ciphertext. In this scheme the size of ciphertext is one-third of the size in the scheme proposed before. Because proposed scheme adopts the medium text with zero norm, it is immune from the “p and -p attack”. As the proposed scheme is based on computational difficulty to solve the multivariate algebraic equations of high degree, it is immune from 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 21 Jan 2018, last revised 24 Jan 2018

Contact author: tfkt8398yagi at outlook jp

Available format(s): PDF | BibTeX Citation

Note: In previous report 2017/763 in Cryptology ePrint Archive, I proposed “Improved Fully Homomorphic Public-key Encryption without Bootstrapping” which has three ciphertexts corresponding to one plaintext. This time I propose the scheme which has only one ciphertext corresponding to one plaintext. Then in this scheme the size of ciphertext is one-third of the size in the scheme proposed before(2017/763).

Version: 20180128:212418 (All versions of this report)

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