A fast dual-field modular arithmetic logic unit and its hardware implementation

We propose a fast modular arithmetic logic unit (MALU) that is scalable in the digit size (d) and the field size (k). The datapath of MALU has chains of carry save adders (CSAs) to speed up the large integer arithmetic operations over GF(p) and GF(2^m). It is well suited and very efficient for the modular multiplication and addition/subtraction which are the computational kernels of elliptic curve and hyperelliptic curve cryptography (H/ECC). While maintaining the scalability and multi-function, we obtain a throughput of 205 Mbps and 388 Mbps with a clock rate of 110 MHz for 256-bit GF(p) and GF(2²³⁹) respectively on FPGA prototyping