Residue multipliers using factored decomposition

A technique for residue multiplication is described where the modulus is a non-prime integer. If the modulus m can be decomposed into two or more relatively prime factors, then multiplication can be done as a set of concurrent multiplication operations using the relatively prime factors as moduli. If a factor is prime, then multiplication is performed with an index calculus technique, otherwise a direct table look-up is used. An all ROM table look-up implementation of this technique is considered and a specific example is given for a modulo-28 multiplier. Hardware requirements for non-prime moduli up to 1024 are calculated and analyzed and compared with those for prime moduli of similar magnitude. Finally, an extension of the decomposition technique is discussed which allows further levels of modulus decomposition