An Optimized Montgomery Modular Multiplication Algorithm for Cryptography

Montgomery modular multiplication is one of the fundamental operations used in cryptographicalgorithms, such as RSA andElliptic Curve Cryptosystem. The previous Montgomery multipliers perform a single Montgomery multiplication in approximately 2n clock cycles and it requires more numberof addition stages for large word length addition, where nis the size of of operandsoperands inbits. Inthis paper, new Montgomery modularmultiplier isproposed whichperformsthesame operationin approximatelyn clock cycles with almostsameclockperiod. The proposed multiplieruses carry selectadders (CSLAs) to perform largewordlengthadditions. Carry selectaddersis based on the concept of Binary to Excess-1convertor (BEC). The proposed algorithmusing the concept ofprecomputing partialresultsusingtwopossible assumptionseither zero or oneregarding the most significant bit of the previous word.The optimized algorithm is simulated using Xilinx ISE 12.1i and itis implemented using Virtex5 FPGA device. Keyword Rivest, Shamir, Adleman(RSA), Carry Select Adders (CSLAs) and Binary to Excess-1convertor (BEC).