elliptic curve
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Paul Alexander Helminck

AbstractIn this paper we generalize the j-invariant criterion for the semistable reduction type of an elliptic curve to superelliptic curves X given by $$y^{n}=f(x)$$ y n = f ( x ) . We first define a set of tropical invariants for f(x) using symmetrized Plücker coordinates and we show that these invariants determine the tree associated to f(x). This tree then completely determines the reduction type of X for n that are not divisible by the residue characteristic. The conditions on the tropical invariants that distinguish between the different types are given by half-spaces as in the elliptic curve case. These half-spaces arise naturally as the moduli spaces of certain Newton polygon configurations. We give a procedure to write down their equations and we illustrate this by giving the half-spaces for polynomials of degree $$d\le {5}$$ d ≤ 5 .

2022 ◽  
Vol 2 (14) ◽  
pp. 18-25
Vu Thi Van ◽  
Luong The Dung ◽  
Hoang Van Quan ◽  
Tran Thi Luong

The secure scalar product protocol is widely applied to solve practical problems such as privacy-preserving data mining, secure auction, secure electronic voting, privacy-preserving recommendation system, privacy-preserving statistical data analysis, etc.. In this paper, we propose an efficient multi-party secure computation protocol using Elliptic curve cryptography, which allows to compute the sum value of multi-scalar products without revealing about the input vectors. Moreover, theoretical and experimental analysis shows that the proposed method is more efficient than others in both computation and communication.

2022 ◽  
Vol 32 (3) ◽  
Ching-Hao Chang ◽  
Jih-Hsin Cheng ◽  
I-Hsun Tsai

Sensors ◽  
2022 ◽  
Vol 22 (1) ◽  
pp. 336
Shahzad Khan ◽  
Waseem Iqbal ◽  
Abdul Waheed ◽  
Gulzar Mehmood ◽  
Shawal Khan ◽  

The ever-growing ecosystem of the Internet of Things (IoT) integrating with the ever-evolving wireless communication technology paves the way for adopting new applications in a smart society. The core concept of smart society emphasizes utilizing information and communication technology (ICT) infrastructure to improve every aspect of life. Among the variety of smart services, eHealth is at the forefront of these promises. eHealth is rapidly gaining popularity to overcome the insufficient healthcare services and provide patient-centric treatment for the rising aging population with chronic diseases. Keeping in view the sensitivity of medical data, this interfacing between healthcare and technology has raised many security concerns. Among the many contemporary solutions, attribute-based encryption (ABE) is the dominant technology because of its inherent support for one-to-many transfer and fine-grained access control mechanisms to confidential medical data. ABE uses costly bilinear pairing operations, which are too heavy for eHealth’s tiny wireless body area network (WBAN) devices despite its proper functionality. We present an efficient and secure ABE architecture with outsourcing intense encryption and decryption operations in this work. For practical realization, our scheme uses elliptic curve scalar point multiplication as the underlying technology of ABE instead of costly pairing operations. In addition, it provides support for attribute/users revocation and verifiability of outsourced medical data. Using the selective-set security model, the proposed scheme is secure under the elliptic curve decisional Diffie–Hellman (ECDDH) assumption. The performance assessment and top-ranked value via the help of fuzzy logic’s evaluation based on distance from average solution (EDAS) method show that the proposed scheme is efficient and suitable for access control in eHealth smart societies.

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