Integer mapping architectures for the polynomial ring engine

A finite polynomial ring structure for mapping inner product computations to parallel independent ring computations over 3-b moduli has been introduced by N.M. Wigley et al. (1992). The main algorithmic computation architecture can be implemented using well-established systolic array mapping principles, and a project to construct a Polynomial Ring Engine (PRE) is underway to exploit the VLSI implementation properties of such computations. A semi-systolic architecture for the input and output conversion mappings that are required in the engine is introduced here. It is shown that the entire mappings procedure can be carried out with pipelined six-input logic blocks and small, fast, binary adders. CMOS implementation techniques for the pipelined blocks are discussed, and the design procedure is illustrated with results from a recently completed module generator