An Optimized Montgomery Modular Multiplication Algorithm for Cryptography

Montgomery modular multiplication is one of the fundamental operations used in cryptographic algorithms, such as RSA and Elliptic Curve Cryptosystems. The previous Montgomery multipliers perform a single Montgomery multiplication in approximately 2n clock cycles and it requires more number of addition stages for large word length additions, where n is the size of operands in bits. In this paper, new Montgomery modular multiplier is proposed which performs the same operation in approximately n clock cycles with almost same clock period. The proposed multiplier uses carry select adders (CSLAs) to perform large word length additions. Carry select adder is based on the concept of Binary to Excess-1convertor (BEC). The proposed algorithm using the concept of precomputing partial results using two possible assumptions regarding the most significant bit of the previous word. The optimized algorithm is simulated using Xilinx ISE 12.1i and it is implemented using Virtex5 FPGA device. Keyword Rivest, Shamir, Adleman(RSA), Carry Select Adders (CSLAs) and Binary to Excess-1convertor (BEC).