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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

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Citations:  Bibtex RefMan EndNote GB/T7714


Naveed Ahmed Azam


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


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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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.




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