FPGA-based multipliers for elliptic curve cryptography

This paper presents an approach to build large-integer multipliers for Elliptic Curve Cryptography (ECC). Compared to the traditional divide and conquer method, our method introduces the 𝑛-term Karatsuba-like algorithm and adopts a cascaded structure for integer multiplications, which simplifies the complexity of the whole structure and contributes to a fine-grained multiplier design. Target at the required width of random elliptic curves over prime fields, we implement the design on virtex-7 FPGA and utilize internal DSPs as the fundamental multiplier resources. The synthesis results are compared quantitatively in terms of designs with different parameters and demonstrate the flexibility of our method.