A comment on “An efficient common-multiplicand-multiplication method to the Montgomery algorithm for speeding up exponentiation”

In 2009, Wu proposed a fast modular exponentiation algorithm and claimed that the proposed algorithm on average saved about 38.9% and 26.68% of single-precision multiplications as compared to Dussé–Kaliski’s Montgomery algorithm and Ha–Moon’s Montgomery algorithm, respectively. However, in this comment, we demonstrate that Wu’s algorithm on average reduces the number of single-precision multiplications by at most 22.43% and 6.91%, when respectively compared with Dussé–Kaliski’s version and Ha–Moon’s version. That is, the computational efficiency of Wu’s algorithm is obviously overestimated.