An efficient polynomial-modulus based technique for multiplication of large integers

This paper proposes a computational method for polynomial-modulus residue number system (PMRNS), a system in which residue is calculated after decomposing the numbers into polynomial of desired radix. This residue can be used to find product, sum, and difference so that different steps (e.g. finding the residue, addition/subtraction etc. of residues, conversion of result into an integer) can be performed in parallel to enhance the speed of operation. The advantages of the proposed method are: i) it does not need to calculate multiplicative inverse for conversion from the residue product to the number; and ii) it does not need to increase the number of modulus as the number gets larger, instead radix can be increased to meet the computational need.