Flexible Composite Galois Field GF((2^m)^2) Multiplier Designs

Composite Galois Field GF ((2)) multiplications denote the multiplication with extension field over the ground field GF (2), that are used in cryptography and error correcting codes. In this paper, composite versatile and vector GF ((2)) multipliers are proposed. The proposed versatile GF ((2)) multiplier design is used to perform the GF ((2)) multiplication, where 2 ≤ x ≤ m. The proposed vector GF ((2)) multiplier design is used to perform 2 numbers of GF ((2 m 2k )) multiplications in parallel, where throughput is comparatively higher than other designs and k ∈ {0, 1, ...(log2m)− 1)}. In both the works, the hardware cost is the trade-off while the flexibility is high. The proposed and existing multipliers are synthesised and compared using 45 nm CMOS technology. The throughputs of the proposed parallel and serial vector GF ((2)) multipliers are 72.7% and 53.62% greater than Karatsuba based multiplier design [11] respectively. Mohamed Asan Basiri M and Sandeep K Shukla, Department of Computer Science and Engineering, Indian Institute of Technology Kanpur, Utter Pradesh 208016, India