Paper 2016/280 Original: eprint.iacr.org/2016/280 ↗

Low Power Montgomery Modular Multiplication on Reconfigurable Systems

Abstract

This paper presents an area-optimized FPGA architecture of the Montgomery modular multiplication algorithm on a low power reconfigurable IGLOO® 2 FPGA of Microsemi®. Our contributions consist of the mapping of the Montgomery algorithm to the specific architecture of the target FPGA, using the pipelined Math blocks and the embedded memory blocks. We minimize the occupation of these blocks as well as the usage of the regular FPGA cells (LUT4 and Flip Flops) through an dedicated scheduling algorithm. The obtained results suggest that a 224-bit modular multiplication can be computed in 2.42 µs, at a cost of 444 LUT4, 160 Flip Flops, 1 Math Block and 1 64x18 RAM, with a power consumption of 25.35 mW. If more area resources are considered, modular multiplication can be performed in 1.30 µs at a cost of 658 LUT4, 268 Flip Flops, 2 Math Blocks, 2 64x18 RAMs and a power consumption of 36.02 mW.