A Public Key Compression Scheme for Fully Homomorphic Encryption Based on Quadratic Parameters With Correction

Abstract

For efficiency improvement and public key size reduction, a new public key compression scheme is proposed for fully homomorphic encryption based on quadratic parameters with correction (QPC-PKC scheme). Compared with existing public key compression schemes, the size of the public key in the proposed scheme is reduced from $\tilde {\mathrm {O}}({\lambda }^{5})$ to $\tilde {\mathrm {O}}({\lambda }^{3.5})$ by reducing the number of subgroup public key elements and the element bit-lengths. Based on the construction mechanisms of the somewhat fully homomorphic encryption (SWHE), a QPC-PKC SWHE scheme is constructed and the parameter constraints are presented. The correctness and semantical security of the proposed QPC-PKC SWHE scheme are then proved based on the error-free approximate greatest common divisor assumption. Finally, the public key size performance of the QPC-PKC scheme is theoretically analyzed, while the public key sizes and running times of the QPC-PKC SWHE scheme are experimentally evaluated. The results show that the public key size of the proposed scheme is significantly reduced compared with the existing schemes, and the encryption efficiency of the QPC-PKC SWHE scheme is also improved as expected.