Algorithm Exploration for Long Integer Modular Arithmetic on a SPARC V8 Processor with Cryptography Extensions

In recent years, public-key cryptography has emerged to become an important workload for embedded processors, driven by a number of factors such as the need for securing wireless communication. The computational requirements of public-key cryptosystems are often beyond the modest capabilities of embedded processors, which motivated the development of architectural enhancements and instruction set extensions to accelerate cryptographic operations like long integer modular multiplication. Such instruction set extensions make it necessary to explore different algorithms for modular multiplication in order to determine the most suitable one for the given custom instructions. In this paper we analyze and compare the performance of two modular multiplication algorithms on a SPARC V8 processor with cryptography extensions. These algorithms are the Montgomery multiplication according to the product scanning (FIPS) technique and the Karatsuba-Comba-Montgomery (KCM) multiplication. Our experimental results show that the FIPS technique outperforms the KCM multiplication for typical operand lengths used in cryptography. We also compare our results with the performance figures of the GNU Multiple Precision Arithmetic Library (GMP).