@article {IOPORT.00720641, author = {Ko\c{c}, \c{C}.K.}, title = {Montgomery reduction with even modulus.}, year = {1994}, journal = {IEE Proceedings. Computers and Digital Techniques}, volume = {141}, number = {5}, issn = {1350-2387}, pages = {314-316}, publisher = {Institution of Electrical Engineers (IEE), London}, doi = {10.1049/ip-cdt:19941291}, abstract = {Montgomery's fast algorithm for computing $c=a.b\pmod n$ requires that the modulus $n$ is an odd integer. This technical note shows that when $n$ is even, by applying the Chinese remainder theorem to break the modular exponentiation $a\sp e\pmod n$ into two independent modular exponentiation operations with respect to moduli $q$ and $2\sp j$ respectively, where $n= q\cdot 2\sp j$, this restriction can be lifted. This is a simple method to make Montgomery's algorithm applicable for both odd and even modulus, and is similar to Quisquater and Couvreur's algorithm.}, reviewer = {H.Shen (Nathan)}, identifier = {00720641}, }