International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 19 January 2016

Masahiro Yagisawa
ePrint Report ePrint Report
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 plaintext. I also proposed a fully homomorphic encryption with composite number modulus which avoids the weak point by adopting the plaintext including the random numbers in it. In this paper I propose another fully homomorphic encryption with composite number modulus where the complexity required for enciphering and deciphering is smaller than the same modulus RSA scheme. In the proposed scheme it is proved that if there exists the PPT algorithm that decrypts the plaintext from the any ciphertexts of the proposed scheme, there exists the PPT algorithm that factors the given composite number modulus. In addition it is said that the proposed fully homomorphic encryption scheme is immune from the “p and -p attack”. Since 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 Grö;bner basis attack, the differential attack, rank attack and so on.
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