Fast modular multiplications based on precomputations with less memory

A fast modular multiplication method based on precomputation is proposed for use in public-key cryptosystems. The proposed method can compute the Montgomery reduction TR¹ mod N only through additions. Furthermore, this is 6.4 times faster than the Montgomery method implemented in modular reduction with a 512 bit modulus when 2.1 MB of memory is used. This memory size is also only 1/4 of that required in the method proposed by Takenaka et al