With the current advances in VLSI technology, traditional algorithms for Residue Number System (RNS) based architectures should be reevaluated to explore the new technology dimensions. In this brief, we introduce A θ(log n) algorithm for large moduli multiplication for RNS based architectures. A systolic array has been designed to perform the modulo multiplication Algorithm. The proposed modulo multiplier is much faster than previously proposed multipliers and more area efficient. The implementation of this multiplier is modular and is based on using simple cells which leads to efficient VLSI realization. A VLSI implementation using 3 micron CMOS technology shows that a pipelined n-bit modulo multiplication scheme can operate with a throughput of 30 M operation per second.