We modify the montgomery modeular multikplication to extract the common parts in common-multiplicand multi-plications. Since the modified method computes the common parts in two modular multiplications once rather than twice, it can speed up the expon...
We modify the montgomery modeular multikplication to extract the common parts in common-multiplicand multi-plications. Since the modified method computes the common parts in two modular multiplications once rather than twice, it can speed up the exponentiations and reduce the amount of storage tables in m-ary or windowexponentiation. It can be also applied to an exponentiation mehod by folding the exponent in half. This method is well-suited to the memory limited environments such as IC card due to its speed and requirement of small memory.