A Review of Techniques for Implementing Elliptic Curve Point Multiplication on Hardware

Lucca, Arielle Verri; Sborz, Guilherme A. M.; Leithardt, Valderi Reis Quietinho; Beko, Marko; Zeferino, Cesar Albenes; Parreira, Wemerson Delcio

doi:10.3390/jsan10010003

Cited by 40 publications

(24 citation statements)

References 38 publications

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“…The algorithm also will allow the implementation of ubiquitous intelligent services for vehicular users [62]. Finally, future work will integrate the algorithm with strategies used to treat Context Histories [63][64][65][66] such as pattern analysis [67], context prediction [68], similarity analysis [69], cryptography [70], and IoT challenges in smart environments [71,72]. This integration will support better solutions; specifically, to routing problems and in general for problems involving context histories.…”

Section: Discussionmentioning

confidence: 99%

A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

et al. 2021

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This work presents a multistart algorithm for solving the capacitated vehicle routing problem with 2D loading constraints (2L-CVRP) allowing for the rotation of goods. Research dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics, such as the Constructive Genetic Algorithm (CGA) to construct promising initial solutions; a Tabu Search (TS) to improve the initial solutions on the routing problem, and a Large Neighborhood Search (LNS) for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multithreading programming to improve the performance. Additionally, memory structures such as hash-tables were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest to the community involved in symmetry studies, such as graph algorithms and graph theory.

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Section: Discussionmentioning

confidence: 99%

A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

et al. 2021

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“…Table 2 summarizes the use intensity of each coordinate system by the different research works published in the literature. From this table, we can find that the majority of the studied works have shown that the Lopez and Dahab coordinates implemented in binary fields are the least expensive in terms of the number of operations required for the scalar multiplication calculation [ 87 ]. For this reason, the Lopez and Dahab coordinates present the best choice to be adopted in order to achieve a scalar multiplication implementation suitable for constrained applications.…”

Section: Elliptic Curve Cryptographymentioning

confidence: 99%

Survey: Vulnerability Analysis of Low-Cost ECC-Based RFID Protocols against Wireless and Side-Channel Attacks

Gabsi

Beroulle

Kieffer

et al. 2021

Sensors

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The radio frequency identification (RFID) system is one of the most important technologies of the Internet of Things (IoT) that tracks single or multiple objects. This technology is extensively used and attracts the attention of many researchers in various fields, including healthcare, supply chains, logistics, asset tracking, and so on. To reach the required security and confidentiality requirements for data transfer, elliptic curve cryptography (ECC) is a powerful solution, which ensures a tag/reader mutual authentication and guarantees data integrity. In this paper, we first review the most relevant ECC-based RFID authentication protocols, focusing on their security analysis and operational performances. We compare the various lightweight ECC primitive implementations designed for RFID applications in terms of occupied area and power consumption. Then, we highlight the security threats that can be encountered considering both network attacks and side-channel attacks and analyze the security effectiveness of RFID authentication protocols against such types of attacks. For this purpose, we classify the different threats that can target an ECC-based RFID system. After that, we present the most promising ECC-based protocols released during 2014–2021 by underlining their advantages and disadvantages. Finally, we perform a comparative study between the different protocols mentioned regarding network and side-channel attacks, as well as their implementation costs to find the optimal one to use in future works.

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“…Security is becoming one of the top concerns in Cyber-Physical Systems and Internet-of-Things (IoT) devices [1]. Therefore, cryptographic algorithms are frequently employed either in symmetric or asymmetric way [2]. The security of symmetric algorithms depends upon the network of the algorithm (e.g.…”

Section: Introductionmentioning

confidence: 99%

An Optimized Architecture for Binary Huff Curves With Improved Security

et al. 2021

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In order to compute the elliptic curve point addition and doubling, the unified point addition law provides better protection against side channel attacks. One of the elliptic curve models, providing the unified point addition, is Binary Huff Curves (BHC). Recently, a new unified method for BHC with improved security against side channel attacks, has been proposed. Therefore, an optimized hardware architecture in terms of higher clock frequency and throughput for the new unified point addition method is required. Consequently, this article has three major contributions: The first contribution is to modify the unified addition law from hardware implementation point of view, resulting 31% decrease in memory requirements. The second contribution is the analysis of memory optimized unified law in the context of pipelining. In this regard, this article proposes an instruction scheduling policy for a 2-stage pipelined architecture which provides 36% reduction in the number of required clock cycles, 14.3% improvement in clock frequency, 53.2% decrease in computation time and 54.5% improvement in throughput/area. Finally, the third contribution is to propose a 4-stage pipelined architecture. The proposed 4-stage pipelined architecture provides an additional 19% improvement in clock frequency and 10% increase in throughput, as compared to the 2-stage pipelined architecture.

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A Review of Techniques for Implementing Elliptic Curve Point Multiplication on Hardware

Cited by 40 publications

References 38 publications

A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

Survey: Vulnerability Analysis of Low-Cost ECC-Based RFID Protocols against Wireless and Side-Channel Attacks

An Optimized Architecture for Binary Huff Curves With Improved Security

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