Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Asep Muhamad Awaludin * , Harashta Tatimma Larasati , Howon Kim *
Version 1 : Received: 12 January 2021 / Approved: 13 January 2021 / Online: 13 January 2021 (13:03:15 CET)

A peer-reviewed article of this Preprint also exists.

Awaludin, A.M.; Larasati, H.T.; Kim, H. High-Speed and Unified ECC Processor for Generic Weierstrass Curves over GF(p) on FPGA. Sensors 2021, 21, 1451. Awaludin, A.M.; Larasati, H.T.; Kim, H. High-Speed and Unified ECC Processor for Generic Weierstrass Curves over GF(p) on FPGA. Sensors 2021, 21, 1451.

Journal reference: Sensors 2021, 21, 1451
DOI: 10.3390/s21041451

Abstract

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

Subject Areas

elliptic curves cryptography (ECC); high speed implementation; unified; Montgomery multiplication; field-programmable gate array (FPGA)

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