Title: Fast elliptic curve scalar multiplication for resisting against SPA

Authors: Shuanggen Liu; Huatong Yao; Xu An Wang

Addresses: School of Telecommunication and Information Engineering, Xi'an University of Posts and Telecommunications, Xi'an 710121, China ' School of Telecommunication and Information Engineering, Xi'an University of Posts and Telecommunications, Xi'an 710121, China ' Engineering University of Chinese Armed Police Force, Xi'an 710078, China

Abstract: This paper analyses the computation of symbolic ternary form (STF) elliptic curve scalar multiplication algorithm and binary scalar multiplication algorithm. Compared with binary scalar multiplication algorithm, the efficiency of STF scalar multiplication algorithm is increased by 5.9% on average and has a corresponding advantage. For this reason, we improve the structure of STF scalar multiplication algorithm and make the performance more 'smooth' by constructing indistinguishable operation between points addition (A) and triple point (T) and thus to resist against the simple power analysis attacks. At the same time, we propose highest-weight symbolic ternary form (HSTF), which makes a scalar k transform into the highest-weight form. Thus, every cycle has a fixed pattern to resist against SPA attack. With respect to binary scalar multiplication algorithm with anti-SPA, the average efficiency in enhanced by 17.7%.

Keywords: elliptic curve scalar multiplication; simple power analysis; SPA; highest-weight symbolic ternary form; HSTF.

DOI: 10.1504/IJCSE.2018.095845

International Journal of Computational Science and Engineering, 2018 Vol.17 No.3, pp.343 - 352

Received: 18 Jan 2016
Accepted: 30 Nov 2016
Published online: 25 Oct 2018 *

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