An Integrated Radix-4 Modular Divider/Multiplier Hardware Architecture for Cryptographic Applications

The increasing importance of security in computers and communication systems introduces the need for several public-key cryptosystems. The modular division and multiplication arithmetic operations in GF (p) and GF (2n) are extensively used in many public key cryptosystems, such as El-Gamal cryptosystem, Elliptic Curve Cryptography (ECC), and the Elliptic Curve Digital Signature Algorithm (ECDSA). Processing these cryptosystems involves complicated computations, therefore, it is recommended to develop specialized hardware to speed up these computations. In this work, we propose efficient hardware design to compute both operations (division and multiplication) in the binary extension finite filed (GF (2n). The common points in both operations are utilized in our design to reduce the design area and delay. making the proposed architecture faster than other previously proposed designs. The FPGA implementation of the proposed design shows better results compared with other designs in this field.