We study the equivalence between non-perfect secret sharing (NSS) and symmetric private information retrieval (SPIR) with colluding and unresponsive servers. We prove the equivalence between NSS and SPIR in the following two senses. 1) Given any SPIR protocol, we can construct an NSS protocol. 2) Given any linear NSS protocol, we can construct a SPIR protocol. From this equivalence relation, we prove that the capacity of $\mathsf{n}$-server SPIR with $\mathsf{r}$ responsive servers and $\mathsf{r}$ colluding servers is $(\mathsf{r}-\mathsf{t})/\mathsf{n}$.

翻译：我们研究非完美秘密共享和对称私人信息检索(SPIR)与串通服务器和不反应服务器的对称私人信息检索(SPIR)之间的等同性。我们在以下两个意义上证明了NSS和SPIR之间的等同性。 (1)根据任何SPIR协议,我们可以建立一个NSS协议。(2)根据任何线性NSS协议,我们可以建立一个SPIR协议。从这种等同关系中,我们证明$\mathsf{n}$-服务器与$\mathsf{r}反应服务器和$\mathsf{r}美元串通服务器的容量是$(mathsf{r}-\mathsf{t}/\mathsfsf{t}/\mathsfsf{n}。