A scalable hardware architecture for prime number validation

This work presents a scalable architecture for prime number validation which targets reconfigurable hardware. The primality test is crucial for security systems, especially for most public-key schemes. The Rabin-Miller Strong Pseudoprime Test has been mapped into hardware, which makes use of a circuit for computing Montgomery modular exponentiation to further speed up the validation and to reduce the hardware cost. A design generator has been developed to generate a variety of scalable and non-scalable Montgomery multipliers based on user-defined parameters. The performance and resource usage of our designs, implemented in Xilinx reconfigurable devices, have been explored using very large prime numbers. Our work demonstrates the flexibility and trade-offs in using reconfigurable platform for prototyping cryptographic hardware in embedded systems. It is shown that, for instance, a 1024-bit primality test can be completed in less than a second, and a low cost XC3S2000 FPGA chip can accommodate a 32k-bit scalable primality test with 64 parallel processing elements.