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CLC number: TP309

On-line Access: 2019-11-11

Received: 2018-07-18

Revision Accepted: 2019-04-17

Crosschecked: 2019-10-10

Cited: 0

Clicked: 519

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Naveed Ahmed Azam

http://orcid.org/0000-0002-7941-3419

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Frontiers of Information Technology & Electronic Engineering  2019 Vol.20 No.10 P.1378-1389

10.1631/FITEE.1800434


Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field


Author(s):  Naveed Ahmed Azam, Umar Hayat, Ikram Ullah

Affiliation(s):  Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan; more

Corresponding email(s):   azam@amp.i.kyoto-u.ac.jp, umar.hayat@qau.edu.pk

Key Words:  Substitution box, Finite field, Mordell elliptic curve, Total order, Computational complexity


Naveed Ahmed Azam, Umar Hayat, Ikram Ullah. Efficient construction of a substitution box based on a Mordell elliptic curve over a finite field[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(10): 1378-1389.

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Abstract: 
We study the balance problem caused by forward leaning of the wearer’s upper body during rehabilitation training with a lower limb rehabilitation exoskeleton. The instantaneous capture point is obtained by modeling the human-exoskeleton system and using the capture point theory. By comparing the stability region with instantaneous capture points of different gait phases, the balancing characteristics of different gait phases and changes to the equilibrium state in the gait process are analyzed. Based on a model of the human-exoskeleton system and the condition of balance of different phases, a trajectory correction strategy is proposed for the instability of the human-exoskeleton system caused by forward leaning of the wearer’s upper body. Finally, the reliability of the trajectory correction strategy is verified by carrying out experiments on the Zhejiang University Lower Extremity Exoskeleton. The proposed trajectory correction strategy can respond to forward leaning of the upper body in a timely manner. Additionally, in the process of the center of gravity transferred from a double-support phase to a single-support phase, the ratio of gait cycle to zero moment point transfer is reduced correspondingly, and the gait stability is improved.

高效构造基于有限域上莫德尔椭圆曲线的密码置换盒

摘要:椭圆曲线密码体制与其他密码体制相比有密钥小、安全性高等优点,被广泛应用于各种安全系统。在许多著名安全系统中,仅置换盒是非线性结构。最近研究表明,用动态置换盒代替静态置换盒可提高密码系统安全性,因此需构造新的安全置换盒。提出一种高效构造置换盒方法,该方法基于素数域上的一类莫德尔椭圆曲线,并通过定义不同总阶数实现。对于每个输入,该方法在线性时间与恒定空间内输出一个置换盒。因此,与现有基于椭圆曲线的置换盒生成方法相比,所提方法占用更少时间和空间。计算结果表明,所提方法能生成加密性强的置换盒,且其安全性与现有基于其他数学结构的置换盒相当。

关键词:密码置换盒;有限域;莫德尔椭圆曲线;总阶数;计算复杂度

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