Until now the use of high radices to implement modular multiplication has been questioned, because it involves complex determination of quotient digits for the modulo reduction. This paper presents algorithms that are obtained through rewriting of Montgomery's algorithm. The determination of quotients becomes trivial and the cycle time becomes independent of the choice of radix. It is discussed how the critical path in the loop can be reduced to a single shift-and-add operation. This implies that a true speed up is achieved by choosing higher radices.