A High-Speed, High-Radix, Processor Array Architecture for Real-Time Elliptic Curve Cryptography Over GF(2m)

This paper presents a high-radix elliptic curve cryptographic architecture that performs a scalar multiple of an elliptic curve point operations over GF(2
^𝓂
). The proposed architecture is based on a new algorithm, which is a modified version of the sliding window scalar multiplication algorithm. We speed-up the scalar multiplication by merging the point doubling and adding operations into a single step, which decreases the scalar multiplication critical path delay at the expense of a larger look-up table. The proposed architecture utilizes an optimized processor array-based field ALU that efficiently implements addition, squaring, multiplication and division over GF(2
^𝓂
). The proposed architecture is implemented for 𝓂 ϵ {163, 283, 571} on a Xilinx XC4VFX100-12 device. We achieved a frequency of 253 MHz, which allows the architecture to calculate GF(2
¹⁶³
) scalar multiplication for radix 2
⁸
in 9μs. Our results for GF(2
¹⁶³
) show a speed-up that ranges from 1.5 to 326 in comparison to previous FPGA implementations and a speed-up ranges from 1.1 to 5.6 in comparison to previous ASIC implementations.