Isomorphism classes of Doche–Icart–Kohel curves over finite fields

Farashahi, Reza Rezaeian; Hosseini, Mehran

doi:10.1016/j.ffa.2016.01.008

Cited by 2 publications

(3 citation statements)

References 2 publications

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“…The isomorphism classes of different curve models were first studied in [5]. In [9], Farashahi and Hosseini give explicit formulas for" the number of distinct elliptic curves over a finite field, up to isomorphism, in two families of curves introduced by C. Doche, T. Icart and D.R. Kohel.…”

Section: Original Research Articlementioning

confidence: 99%

Analysis of Isomorphism Classes of a Family of Elliptic Curves Over Finite Fields

Wei

2024

AJOMCOR

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Doche et al. constructed a family of elliptic curves (DIK elliptic curves) and proposed more efficient tripling formulas leading to a fast scalar multiplication algorithm. In this paper we present a direct method to compute the number of \(\bar{F}\)q-isomorphism classes (isomorphism over \(\bar{F}\)q ) and \(\bar{F}\)q isomorphism classes of DIK family of elliptic curves defined over a finite field \(\bar{F}\)q. We give the explicit formulae for the number of \(\bar{F}\)q-isomorphism and an estimate formulae for the number of isomorphism classes. These result can be used in the elliptic curve cryptosystems.

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Section: Original Research Articlementioning

confidence: 99%

Analysis of Isomorphism Classes of a Family of Elliptic Curves Over Finite Fields

Wei

2024

AJOMCOR

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“… Edwards curves: The Edwards model presents an alternative form of elliptic curves, which admits a complete and uniform group law [ 76 ]. Either d or c are two elements of

, with

not squared, the Edwards curves are defined by the following equation [ 76 ]:

The Edwards and Montgomery curves have the advantage of being bi-rational to a Weierstrass curve; this property is important in cryptographic applications, such as IoT [ 77 ]. For example, the calculation of the point exponentiation operation in an Edwards curve is 1.5 times more efficient than that performed in a Weierstrass curve [ 78 ].…”

Section: Elliptic Curve Cryptographymentioning

confidence: 99%

“…The Edwards and Montgomery curves have the advantage of being bi-rational to a Weierstrass curve; this property is important in cryptographic applications, such as IoT [ 77 ]. For example, the calculation of the point exponentiation operation in an Edwards curve is 1.5 times more efficient than that performed in a Weierstrass curve [ 78 ].…”

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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Isomorphism classes of Doche–Icart–Kohel curves over finite fields

Cited by 2 publications

References 2 publications

Analysis of Isomorphism Classes of a Family of Elliptic Curves Over Finite Fields

Analysis of Isomorphism Classes of a Family of Elliptic Curves Over Finite Fields

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

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