A high-speed low-cost modulo Pimultiplier with RNS arithmetic applications

Modulo P
i
multipliers are implemented by look-up tables when P
i
is small (5 bits or less) and by index calculus if P
i
is larger (6 bits or more). However, index calculus only works for prime moduli P
i
. In this letter, we introduce a new square-law multiplier that is useful for modulo P
i
multiplication where P
i
is any modulus. It is expected that this will have important applications in RNS arithmetic computing hardware.