Modular multiplication is the core arithmetic for most of the Cryptographic applications. Montgomery multiplication is one of the fastest methods available for performing modular multiplication. A k - partition method for Montgomery multiplication is thoroughly studied and analysed. This method reduces the time complexity of multiplication from O (n) to O (n/k). Another method for modular exponentiation - Square and Multiply method is implemented. As the name suggests, squaring is the main principle behind this method. The implementation results are compared with that of an ordinary Montgomery multiplier and the k - partition method in terms of power and area constraints. Results for 128, 256, 512 and 1024 bit input operands show that the Square and Multiply method is more power efficient than the other two
P. R. Gokul, Prabhu E., and Mangalam, H., “Performance comparison of multipliers based on Square and Multiply and montgomery algorithms”, in Green Computing Communication and Electrical Engineering (ICGCCEE), 2014 International Conference on, 2014.