Leveled Homomorphic Encryption Based on NTRU Without Re-Linearization

Xiaokang Dai, Haoyong Wang, Wenyuan Wu and Yong Feng
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Xiaokang Dai: Chongqing Institute of Green and Intelligent Technology, Chinese Academy Sciences, Chongqing, China & Chongqing School, University of Chinese Academy of Sciences, Chongqing, China
Haoyong Wang: Chongqing Institute of Green and Intelligent Technology, Chinese Academy Sciences, Chongqing, China & Chongqing School, University of Chinese Academy of Sciences, Chongqing, China
Wenyuan Wu: Chongqing Institute of Green and Intelligent Technology, Chinese Academy Sciences, Chongqing, China & Chongqing School, University of Chinese Academy of Sciences, Chongqing, China
Yong Feng: Chongqing Institute of Green and Intelligent Technology, Chinese Academy Sciences, Chongqing, China & Chongqing School, University of Chinese Academy of Sciences, Chongqing, China

International Journal of Information Security and Privacy (IJISP), 2025, vol. 19, issue 1, 1-20

Abstract: The hardness of the NTRU problem has not been well understood until 2021, when Pellet-Mary and Stehlé (2021) gave a reduction from the Gap-SVP problem on the ideal lattice to the NTRU-Search problem. Assuming the equivalence of the NTRU-Decision and the NTRU-Search problem, with this reduction together, we construct a leveled homomorphic encryption scheme. Compared to homomorphic schemes based on RLWE such as CKKS and BGV, the ciphertext of our scheme is a single polynomial. As a result, ciphertext multiplication involves only one multiplication of two polynomials, rather than the tensor multiplication of polynomial vectors as in BGV, CKKS schemes. In particular, by introducing a label, the ciphertext of our scheme does not need to be linearized after multiplication. This significantly accelerates the speed of homomorphic evaluation by reducing the number of polynomial multiplications from 6 to 1. Complexity analysis and experimental results indicate that the ciphertext multiplication in our scheme is approximately 4~5 times faster than CKKS and BFV schemes

Date: 2025
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