Lfhss:(a more efficient) leveled fully homomorphic signature scheme with shortened signature size

Abstract Homomorphic signatures have important potential in cloud computing and data privacy protection, but there are still problems such as low signature efficiency, high overhead, and difficulty in instantiation. To solve these problems, an efficient leveled fully homomorphic signature scheme LFHSS with shortened signature values is constructed. The scheme is based on the GPV framework and the RSIS problem on the NTRU lattice. By using the Fast Fourier Sampling algorithm, it achieves efficient signatures with smaller size. It introduces a homomorphic trapdoor function and designs three basic evaluations: homomorphic addition, multiplication, and scalar multiplication. These operations enable the LFHSS scheme to support homomorphic evaluations of functions consisting of addition, multiplication, and scalar multiplication within a certain circuit depth. Additionally, it is proven to be strongly unforgeable, and the scheme is implemented in software with correctness testing and performance analysis conducted. The experimental results show that the security level of LFHSS is 1.14 times higher than that of BCFL23, and the signature generation speed is 300+ times faster, the homomorphic evaluation speed is 7.8 times faster, and the verification speed is 48K times faster than that of BCFL23. The signature length of LFHSS is only 4.86% of BCFL23. The work in this paper is of great significance to the design and application of homomorphic signatures.