Fast RNS Division Algorithms for Fixed Divisors with Application to RSA Encrytion

Residue number systems (RNS) present the advantage of fast addition and multiplication over other number systems, and have thus received much attention for high-throughput computations. Digit-parallel, carry-free, and constant-time multiplication and addition is a unique feature of RNS. However, certain operations such as overflow detection, magnitude comparison, and division are quite difficult in RNS. Thus, RNS is in general limited to applications that do not require extensive use of those difficult operations; for example, liltering in Digital Signal Processing. By improving RNS division, many application areas for which RNS was previously infeasible, such as RSA encryption, can use the fast RNS multiplication without being penalized too much by the slow RNS division.