Modular multiplication in the residue number system with application to massively-parallel public-key cryptography systems

Modular multiplication is a fundamental operation in many public-key cryptography systems including RSA. Residue number system (RNS) implementation of modular multiplication has been of recent interest due to inherent RNS properties of multiplicative complexity reduction and digit independence over addition and multiplication. In this paper, a new RNS modular multiplication technique is introduced which relies solely upon modular arithmetic. The overhead formerly associated with such methods is rendered negligible, and the complexity roughly matches that of the most efficient mixed-arithmetic method. Application to massively-parallel systems is examined, revealing significant advantages over weighted number system counterparts.