RNS-modulo reduction upon a restricted base value set and its applicability to RSA cryptography

Abstract

For a modulo reduction scheme in RNS a set of restricted base values is proposed. In RNS, additions and multiplications can be computed in parallel, avoiding carry propagation delays. This advantage enables the implementation of scalable, parallel arithmetic units for computations in very large finite fields. For such a long integer arithmetic unit certain selection criteria for the base value set have been worked out, targeted to optimise the modulo reduction operation on the RNS digit level. As public key cryptography heavily depends on arithmetic in large finite fields, a parallelisable RSA variant is shown as a sample application.