We reinvestigate the general distributed secure source coding based on the common key cryptosystem proposed by Oohama and Santoso (ITW 2021). They proposed a framework of distributed source encryption and derived the necessary and sufficient conditions to have reliable and secure transmission. However, the bounds of the rate region, which specifies both necessary and sufficient conditions to have reliable and secure transmission under the proposed cryptosystem, were derived based on a self-tailored non-standard} security criterion. In this paper we adopt the standard security criterion, i.e., standard mutual information. We successfully establish the bounds of the rate region based on this security criterion. Information spectrum method and a variant of Birkhoff-von Neumann theorem play an important role in deriving the result.

翻译：我们重新研究了Oohama与Santoso（ITW 2021）基于公共密钥密码系统提出的通用分布式安全信源编码方案。他们提出了分布式信源加密框架，并推导出实现可靠安全传输的充要条件。然而，其速率域边界——即在该密码系统下实现可靠安全传输的充要条件范围——是基于一种自定义的非标准安全准则推导得出的。本文采用标准安全准则，即标准互信息测度。基于此安全准则，我们成功建立了速率域的边界。信息谱方法及Birkhoff-von Neumann定理的变体在推导结果过程中发挥了关键作用。