Elementary symmetric polynomials $S_n^k$ are used as a benchmark for the bounded-depth arithmetic circuit model of computation. In this work we prove that $S_n^k$ modulo composite numbers $m=p_1p_2$ can be computed with much fewer multiplications than over any field, if the coefficients of monomials $x_{i_1}x_{i_2}\cdots x_{i_k}$ are allowed to be ... more >>>