RLWE like problem

Assume we have the polynomial space $$R_q$$ defined as $$R_q = Z_q/(X^n + 1)$$. Additionally, we define the error distribution $$\chi$$ as a discrete centred Gaussian bounded by $$B$$.

Let $$s \gets R_q$$ be a randomly selected secret. For $$i=0,\dots,T-1$$ we construct $$p_i = sc_i + e_i$$, where $$c_i \gets R_q$$ and $$e_i \gets \chi$$ are randomly selected.

Let $$A_i = (c_i, p_i)$$. Can we claim that the joint distribution of $$A_0, ..., A_{T-1}$$ is computationally indistinguishable from uniform? Can they jointly leak $$s$$?

• This is exactly the (decisional) RLWE problem. And, the goal of recovering $s$ from the samples $A_i$ is exactly the search RLWE problem. Jun 5 at 21:31