Implementations of Montgomery Multiplication Algorithms in Machine Languages

Software implementations of public-key algorithms such RSA and Diffie-Hellman are often desired because of their flexibility and cost effectiveness. In order to obtain the required level of performance on a selected platform, developers turn to implement efficient algorithms in machine (assembly) languages for basic (kernel) operations. Among these basic operations, modular multiplication and exponentiation operations play an important role. This paper concerns with fast software implementations of the montgomery multiplication algorithms. Montgomery multiplication algorithms, which are the most popular algorithms used in public-key cryptography, serve as efficient algorithms for modular multiplication and exponentiation operations.