The new homomorphic encryption scheme reduces polynomial multiplications in ciphertext, implying faster evaluations compared to existing methods like CKKS and BGV.
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
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Dai et al. (2025) studied this question.
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