BLISS is a lattice signature scheme published in CRYPTO 2013. The key idea of the paper is use a bimodal distribution to optimize rejection sampling. Here, we investigate using a multi-modal distribution for the same goal.

Essentially we want to keep the following quantity of BLISS small: $\frac{e^x+e^{-x}}{\min_x e^x+e^{-x}}$. By changing it to a four-modal distribution, it becomes $\frac{e^x+e^{-x}+e^{3x}+e^{-3x}}{\min_x e^x+e^{-x}+e^{3x}+e^{-3x}}$, which is however bigger. Thus it does not work.