Ring-planarized cylindrical arrays with application to modular multiplication

Cylindrical arrays have been shown useful for VLSI implementation of a variety of problems including matrix-matrix multiplication and algebraic path determination. However, spiral feedback paths limit their scalability due to performance degradation in interconnect-delay dominant environments. A recently proposed feedback-pipelining technique can efficiently address this problem when signal paths are non-diametric in the projection direction. However, this method may incur excessive penalties when the latter condition does not hold. In this paper, a new class of cylindrical array is proposed, the ring-planarized cylindrical array, which overcomes the barrier to efficient, fully-pipelined arrays projected in directions having diametric signal paths. In contrast to standard cylindrical arrays, processors from each cylinder row are distributed along planar ring structures rather than lines. This construction inherently constrains maximum signal path length to a constant, permitting efficient scalability. Application to the cryptographically relevant modular multiplication problem is demonstrated.