Efficient Private Information Retrieval Protocol with Homomorphically Computing Univariate Polynomials

Table 2

Comparisons of several noiseless FHE schemes.

Schemes	Algebraic structure	Ciphertext space	Length	Security
Nuida [24]	Noncommutative group	Vector of dimension 2		Judgement of the kernel element
Yagisawa [25]	Octonion ring	Octonion ring		Immune from the Grobner basis attacks
Ours	Truncated polynomial ring	Vector of dimension 3		One-way security

Length : the length ratio between the plaintext and ciphertext. : the number of elements in group .