A new class of moduli called the low-weight polynomial form integers (LWPFIs) is introduced. LWPFIs are expressed in a low-weight, monic polynomial form, p = f(t). While the generalized Mersenne numbers (GMNs) proposed by Solinas allow only powers of two for t, LWPFIs allow any positive integers. In our first proposal of LWPFIs, we limit the coefficients of f(t) to be 0 and ±1, but later we ext...