A unified architecture for a public key cryptographic coprocessor

This paper presents a unified architecture for public key cryptosystems that can support the operations of the Rivest–Shamir–Adleman cryptogram (RSA) and the elliptic curve cryptogram (ECC). A hardware solution is proposed for operations over finite fields GF(p) and GF(2^p). The proposed architecture presents a unified arithmetic unit which provides the functions of dual-field modular multiplication, dual-field modular addition/subtraction, and dual-field modular inversion. A new adder based on the signed-digit (SD) number representation is provided for carry-propagated and carry-less operations. The critical path of the proposed design is reduced compared with previous full adder implementation methods. Experimental results show that the proposed design can achieve a clock speed of 1 GHz using 776 K gates in a 0.09 μm CMOS standard cell technology, or 150 MHz using 5227 CLBs in a Xilinx Virtex 4 FPGA. While the different technologies, platforms and standards make a definitive comparison difficult, based on the performance of our proposed design, we achieve a performance improvement of between 30% and 250% when compared with existing designs.