We pose and investigate the distributed secure source coding based on the
common key cryptosystem. This cryptosystem includes the secrecy amplification
problem for distributed encrypted sources with correlated keys using
post-encryption-compression, which was posed investigated by Santoso and
Oohama. In this paper we propose another new security criterion which is
generally more strict compared to the commonly used security criterion which is
based on the upper-bound of mutual information between the plaintext and the
ciphertext. Under this criterion, we establish the necessary and sufficient
condition for the secure transmission of correlated sources.Comment: 7 pages, 3 figure. The short version was submitted to ISIT 2021. We
have some typos in the short version. Those are fixed in this version. arXiv
admin note: text overlap with arXiv:1801.0492