Carlos Martin's comment can be verified by an standard book on Japanese armor. The rings are discussed in the book "Arms and Armour of the Samurai" cited below. I shall quote the relevant paragraph ad verbatim from page 108.
"Commanders still carried fans with which to direct the movement of their troops; these were even more necessary since the wearing of masks made speech difficult. A new form of insignia, indicating rank, was introduced; it took the form of a tassel of hair or paper often gilded, which hung from a short batton. These sai hai were either tucked into the sash or hung from a ring (sai hai no kan) provided for that purpose on the right breast of the do. A second ring, supposedly for a towel but more probably simply to balance the appearance of the do, was added the left breast on some armours; this became virtually standard during the Edo period."
The book contains many high quality pictures of full suits of armor with either zero, one or two rings. Do is the Japanese word for body armor.
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