Abstract
Approximating the shortest vector of a given lattice is one of the most important computational problems in public-key cryptanalysis and lattice-based cryptography. However, existing LLL reduction algorithm and its variants for this problem are too time-consuming for resource-constrained clients. To handle this dilemma, in this paper, we propose an efficient and secure outsourcing algorithm under the cloud environment. Compared with the prior Liu et al.’s algorithm, besides realizing the privacy preservation of client’s input/output information, satisfying verifiability and greatly reducing the local-client’s computational overhead, our algorithm is superior in the following aspects. First, our algorithm is technically concise. The main technique ingredient involved in our algorithm is a skillful combination of the unimodular matrix transformation and the Gram matrix, which is concise and effective. Second, our algorithm does not reduce the quality of the reduced basis, that is, the vector finally obtained by the client is as short as that of the vector generated by the client directly performing the existing reduction algorithm. Last but not least, our algorithm not only works for the LLL reduction algorithm, but also for any other algorithms that solve (approximate-)SVP with Euclidean norm.
This work is supported by National Key Research and Development Program of China (No. 2018YFA0704705, 2020YFA0712300), National Natural Science Foundation of China (No. 61702294, 62032009), National Development Foundation of Cryptography (MMJJ20170126).
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We thank the anonymous referees for their valuable suggestions on how to improve this paper.
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Li, X., Pan, Y., Tian, C. (2021). Cloud-Assisted LLL: A Secure and Efficient Outsourcing Algorithm for Approximate Shortest Vector Problem. In: Deng, R., et al. Information Security Practice and Experience. ISPEC 2021. Lecture Notes in Computer Science(), vol 13107. Springer, Cham. https://doi.org/10.1007/978-3-030-93206-0_14
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