Serial and parallel interleaved modular multipliers on FPGA platform

Abstract

Modular multiplication is a core operation in all public key based cryptosystems. The performance of these cryptosystems can be enhanced substantially by incorporating an optimized modular multiplier. This paper presents serial and parallel radix-4 modular multipliers based on interleaved multiplication algorithm and Montgomery power laddering technique. A serial radix-4 interleaved modular multiplier provides 50% reduction in the required clock cycles. In addition to the reduction in clock cycles, a parallel modular multiplier maintains a critical path delay comparable to the bit serial interleaved multipliers. The proposed designs are implemented in Verilog HDL and synthesized targeting virtex-6 FPGA platform using Xilinx ISE 14.2 Design suite. The serial radix-4 multiplier computes a 256-bit modular multiplication in 1.3μs, occupies 3.9K LUTs, and runs at 96 MHz. The parallel radix-4 multiplier takes 0.77μs, occupies 5.3K LUTs, and runs at 166 MHz. The results show that the parallel radix-4 modular multiplier provides 62% and 49% speed-up over the corresponding bit serial and bit parallel versions, respectively. Thus, these designs are suitable to accelerate modular multiplication in many cryptographic processors.