A State-of-the-art Elliptic Curve Cryptographic Processor Operating in the Frequency Domain

We propose a novel area/time efficient elliptic curve cryptography (ECC) processor architecture which performs all finite field arithmetic operations in the discrete Fourier domain. The proposed architecture utilizes a class of optimal extension fields (OEF) GF(qm) where the field characteristic is a Mersenne prime q = 2n - 1 and m = n. The main advantage of our architecture is that it achieves extension field modular multiplication in the discrete Fourier domain with only a linear number of base field GF(q) multiplications in addition to a quadratic number of simpler operations such as addition and bitwise rotation. We achieve an area between 25k and 50k equivalent gates for the implementations over OEFs of size 169, 289 and 361 bits. With its low area and high speed, the proposed architecture is well suited for ECC in small device environments such as sensor networks. The work at hand presents the first hardware implementation of a frequency domain multiplier suitable for ECC and the first hardware implementation of ECC in the frequency domain.