Abstract
The appearance of fully homomorphic encryption (FHE) scheme induces new ways to construct the single-server private information retrieval protocol. At PKC 2015, Hiromasa et al. proposed the first FHE scheme that encrypts matrices and supports homomorphic matrix addition and multiplication. (hereafter, referred to as HAO15 scheme). Motivated by their work, we construct a LWE-based single-server block private information retrieval protocol. To get almost optimal communication cost, we adopt the homomorphic-ciphertext compression technique proposed by Naehrig et al. And as an intermediate product, we give a homomorphic algorithm, with no need for the secret key, to check the equality between diagonal matrices that are encrypted under HAO15 scheme.
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References
Chor, B., Goldreich, O., Kushilevitz, E., et al.: Private information retrieval. In: Symposium on Foundations of Computer Science. IEEE Computer Society, p. 41 (1995)
Ambainis, A.: Upper bound on communication complexity of private information retrieval. In: International Colloquium on Automata, Languages and Programming, pp. 401–407. Springer-Verlag (1997)
Beimel, A., Ishai, Y.: Information-theoretic private information retrieval: a unified construction. In: International Colloquium on Automata, Languages and Programming, pp. 912–926. Springer-Verlag (2001)
Itoh, T.: Efficient private information retrieval. Tech. Report IEICE ISEC 98(1), 11–20 (1998)
Ishai, Y., Kushilevitz, E.: Improved upper bounds on information-theoretic private information retrieval (Extended Abstract). In: ACM Symposium on Theory of Computing, pp. 79–88. ACM (1999)
Kushilevitz, E., Ostrovsky, R.: Replication is not needed: single database, computationally-private information retrieval. In: Symposium on Foundations of Computer Science, pp. 364–373. IEEE (2002)
Cachin, C., Micali, S., Stadler, M.: Computationally private information retrieval with polylogarithmic communication. In: Advances in Cryptology — EUROCRYPT 1999, pp. 402–414. Springer, Heidelberg (1999)
Wang, S., Agrawal, D., Abbadi, A.E.: Generalizing PIR for practical private retrieval of public data. In: Lecture Notes in Computer Science, vol. 6166, pp. 1–16 (2010)
Kushilevitz, E., Ostrovsky, R.: One-way trapdoor permutations are sufficient for non-trivial single-server private information retrieval. Proc. Eurocrypt. 1807, 104–121 (2000)
Gentry, C.: A Fully Homomorphic Encryption Scheme. Stanford University, Stanford (2009)
Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (Standard) LWE. In: Foundations of Computer Science, pp. 97–106. IEEE (2011)
Yi, X., Kaosar, M.G., Paulet, R., et al.: Single-database private information retrieval from fully homomorphic encryption. IEEE Trans. Knowl. Data Eng. 25(5), 1125–1134 (2013)
Dijk, M.V., Gentry, C., Halevi, S., et al.: Fully homomorphic encryption over the integers. In: International Conference on Theory and Applications of Cryptographic Techniques, pp. 24–43. Springer-Verlag (2010)
Hiromasa, R., Abe, M., Okamoto, T.: Packing messages and optimizing bootstrapping in GSW-FHE. In: Public-Key Cryptography – PKC 2015, pp. 73–82. Springer, Heidelberg (2015)
Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Cryptology Conference, pp. 75–92. Springer, Heidelberg (2013)
Naehrig, M., Lauter, K., Vaikuntanathan, V.: Can homomorphic encryption be practical? In: ACM Cloud Computing Security Workshop, CCSW 2011, Chicago, Il, Usa, October. DBLP, pp. 113–124 (2011)
Beaulieu, R., Treatman-Clark, S., Shors, D., et al.: The SIMON and SPECK lightweight block ciphers, pp. 1–6. IEEE (2015)
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Liu, S., Hu, B. (2020). LWE-Based Single-Server Block Private Information Retrieval Protocol. In: Yang, CN., Peng, SL., Jain, L. (eds) Security with Intelligent Computing and Big-data Services. SICBS 2018. Advances in Intelligent Systems and Computing, vol 895. Springer, Cham. https://doi.org/10.1007/978-3-030-16946-6_37
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DOI: https://doi.org/10.1007/978-3-030-16946-6_37
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