Parametrized hardware architectures for the Lucas primality test

We present our parametric hardware architecture of the NIST approved Lucas probabilistic primality test. To our knowledge, our work is the first hardware architecture for the Lucas test. Our main contributions are a hardware architecture for calculating the Jacobi symbol based on the binary Jacobi algorithm, a pipelined modular add-shift module for calculating the Lucas sequences, methods for dependence analysis and for scheduling of the Lucas sequences computation. Our architecture implemented on a Virtex-5 FPGA is 30% slower but 3 times more energy efficient than the software version running on a Intel Xeon W3505. Our fastest 45 nm ASIC implementation is 3.6 times faster and 400 times more energy efficient than the optimised software implementation in comparable technology. The performance scaling of our architecture is much better than linear in area. Different speed/area/energy trade-offs are available through parametrization. The cell count and the power consumption of our ASIC implementations make them suitable for integration into an embedded system whereas our FPGA implementation would more likely benefit server applications.