High Speed Modulo Calculation Algorithm with Radix-2k SD Number

In RSA Cryptograms, many modulo calculations are used, but modulo calculation is based on many subtractions and it takes long time to calculate. In this article, we explain about a new modulo calculation algorithm using table. And we proof that upper 3 digits of Radix-2k SD numbers is enough to specify the answer. In the first section, we prepared some useful theorems for operations of Radix-2k SD Number. In the second section, we defined Upper 3 Digits of Radix-2k SD number and proved that property. In the third section, we proved some property about the minimum digits of Radix-2k SD number. In the fourth section, we identified the range of modulo arithmetic result and proved that the Upper 3 Digits indicate two possible answers. And in the last section, we defined a function to select true answer from the results of Upper 3 Digits.