Secure Outsourcing of Lattice Basis Reduction

Abstract

In the recent twenty years, lattice basis reduction algorithm, such as the celebrated LLL (A.K. Lenstra-H.W. Lenstra Jr.-L. Lovasz) algorithm plays an important role in the public-key schemes design and cryptanalysis. To assess the security of the public-key cryptosystems by lattice reduction algorithms, the most time-consuming part is running the lattice reduction algorithm on the corresponding lattice with high dimension or big coefficients. In this paper, we investigate secure outsourcing for lattice basis reduction for the first time. We propose a lattice basis reduction scheme such that the clients can outsource their main computation workloads to the untrusted cloud servers. We employ rounding technique and unimodular transformation matrix for privacy protection before sending the target lattice basis to the cloud. The results returned from the cloud need to be decrypted and verified to satisfy reduction conditions. The experimental results indicate that our scheme is correct, efficient and feasible.