High-Speed and Unified ECC Processor for Generic Weierstrass Curves over GF(p) on FPGA

In this paper, we present a high-speed, unified elliptic curve cryptography (ECC) processor for arbitrary Weierstrass curves over GF(p), which to the best of our knowledge, outperforms other similar works in terms execution time. Our approach employs combination schoolbook long and Karatsuba multiplication algorithm point (ECPM) achieve better parallelization while retaining low complexity. hardware implementation, substantial gain speed is also contributed by n-bit pipelined Montgomery Modular Multiplier (pMMM), constructed from multiplier-accumulators that utilizes digital signal (DSP) primitives as digit multipliers. Additionally, introduce unified, modular adder/subtractor (pMAS) underlying field arithmetic, leverage more efficient yet compact scheduling ladder algorithm. The implementation 256-bit modulus size on 7-series FPGA: Virtex-7, Kintex-7, XC7Z020 yields 0.139, 0.138, 0.206 ms time, respectively. Furthermore, since pMMM module generic any form, support multi-curve parameters, resulting ECC architecture. Lastly, method constant making it suitable applications requiring high SCA-resistant characteristics.