It is shown that decomposition via Chinise Remainder does not
yield polynomial size depth 3 threshold circuits for iterated
multiplication of n-bit numbers. This result is achieved by
proving that, in contrast to multiplication of two n-bit
numbers, powering, division, and other related problems, the
resulting subproblems, iterated multiplication modulo
polylog(n)-bit numbers, do not have polynomial size approxi-
mation schemes over the set of all threshold functions.
We use a lower bound argument based on probabilistic
communication complexity.