Title: Comparison analysis and efficient implementation of reconciliation-based RLWE key exchange protocol

Authors: Xinwei Gao; Jintai Ding; R.V. Saraswathy; Lin Li; Jiqiang Liu

Addresses: Beijing Key Laboratory of Security and Privacy in Intelligent Transportation, Beijing Jiaotong University, No. 3 ShangYuanCun, HaiDian District, Beijing, 100044, China ' Department of Mathematical Sciences, University of Cincinnati, French Hall, West, 2815 Commons Way, Cincinnati, Ohio, 45219, USA ' Department of Mathematical Sciences, University of Cincinnati, French Hall, West, 2815 Commons Way, Cincinnati, Ohio, 45219, USA ' Beijing Key Laboratory of Security and Privacy in Intelligent Transportation, Beijing Jiaotong University, No. 3 ShangYuanCun, HaiDian District, Beijing, 100044, China ' Beijing Key Laboratory of Security and Privacy in Intelligent Transportation, Beijing Jiaotong University, No. 3 ShangYuanCun, HaiDian District, Beijing, 100044, China

Abstract: Error reconciliation is an important technique for learning with error (LWE) and ring-LWE (RLWE)-based constructions. In this paper, we present a comparison analysis on two error reconciliation-based RLWE key exchange protocols: Ding et al. in 2012 (DING12) and Bos et al. in 2015 (BCNS15). We take them as examples to explain the core idea of error reconciliation, building key exchange over RLWE problem, implementation and real-world performance, and compare them comprehensively. We also analyse a LWE key exchange 'Frodo' that uses an improved error reconciliation mechanism in BCNS15. To the best of our knowledge, our work is the first to present at least 128-bit classic (80-bit quantum) and 256-bit classic (> 200-bit quantum) secure parameter choices for DING12 with efficient portable C/C++ implementations. Benchmark shows that our efficient implementation is 11× faster than BCNS15 and one key exchange execution only costs 0.07 ms on a four-year-old middle range CPU. Error reconciliation is 1.57× faster than BCNS15.

Keywords: ring-learning with error; RLWE; post quantum; key exchange; implementation; analysis.

DOI: 10.1504/IJHPCN.2019.097505

International Journal of High Performance Computing and Networking, 2019 Vol.13 No.2, pp.141 - 152

Received: 01 Aug 2017
Accepted: 10 Nov 2017
Published online: 25 Jan 2019 *

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