Carlos Martin's comment can be verified by an standard book on Japanese armour. 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 armour with either zero, one or two rings. *Do* is the Japanse word for body armour.

Reference:

I. Bottomley and A. P. Hopson<br>
"Arms and Armour of the Samuari"<br>
Published by Defoe Publishing<br>
Copyright 1988 Bison Books Ltd<br>
ISBN 1 870 98105 7