# Conjugate-Invariant ring for 2x slots of real numbers The work[^1] suggest to use all message slots and not just half as in standard CKKS - by using a new scheme based on RLWE over a sub ring of the cyclic ring called the *conjugate-invariant* ring. they show this is as a secure as standard RLWE. They use NTT which is not nega-cyclic but like to standard FFT i.e., modulo $X^n-1$. HEAAN also add more noise as the noise of the imaginary part affect the computation. also, the complex imaginary part of each slots is not utilized for most ML computations. this is not efficient as well. Note that this method does not support bootstrapping - not sure why. I see that [[@Bootstrapping Bits with CKKS]] paper switch between standard scheme over the complex numbers and the one proposed here. Tag: #idea Reference: [Approximate Homomorphic Encryption over the Conjugate-invariant Ring](https://eprint.iacr.org/2018/952.pdf) ## Created 2026-02-09 10:32 [^1]: [Approximate Homomorphic Encryption over the Conjugate-invariant Ring](https://eprint.iacr.org/2018/952.pdf)