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Leveled Homomorphic Encryption Based on NTRU Without Re-Linearization

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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)

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

Suggested Citation

  • Xiaokang Dai & Haoyong Wang & Wenyuan Wu & Yong Feng, 2025. "Leveled Homomorphic Encryption Based on NTRU Without Re-Linearization," International Journal of Information Security and Privacy (IJISP), IGI Global Scientific Publishing, vol. 19(1), pages 1-20, January.
    • Handle: RePEc:igg:jisp00:v:19:y:2025:i:1:p:1-20
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