High-Performance Elliptic Curve Cryptography by Using the CIOS Method for Modular Multiplication

Mrabet, Amine; Mrabet, Nadia El; Lashermes, Ronan; Rigaud, Jean-Baptiste; Bouallègue, Belgacem; Mesnager, Sihem; Machhout, Mohsen

doi:10.1007/978-3-319-54876-0_15

Cited by 6 publications

(3 citation statements)

References 20 publications

(32 reference statements)

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“…Therefore, the operation dG is the d doubling time for G, which results in another point (x j , y j ), known as the public key. The security of ECC is based on the hardness of the mathematical problem [38], which indicates that in knowing the public key point and the base point G, it is impossible to find d in polynomial time. This is referred to in the literature as the elliptic curve discrete logarithm problem (ECDLP) [39].…”

Section: B Elliptic Curve Cryptography (Ecc)mentioning

confidence: 99%

SE-Enc: A Secure and Efficient Encoding Scheme Using Elliptic Curve Cryptography

Almajed

Almogren

2019

IEEE Access

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Many applications use asymmetric cryptography to secure communications between two parties. One of the main issues with asymmetric cryptography is the need for vast amounts of computation and storage. While this may be true, elliptic curve cryptography (ECC) is an approach to asymmetric cryptography used widely in low computation devices due to its effectiveness in generating small keys with a strong encryption mechanism. The ECC decreases power consumption and increases device performance, thereby making it suitable for a wide range of devices, ranging from sensors to the Internet of things (IoT) devices. It is necessary for the ECC to have a strong implementation to ensure secure communications, especially when encoding a message to an elliptic curve. It is equally important for the ECC to secure the mapping of the message to the curve used in the encryption. This work objective is to propose a trusted and proofed scheme that offers authenticated encryption (AE) for both encoding and mapping a message to the curve. In addition, this paper provides analytical results related to the security requirements of the proposed scheme against several encryption techniques. Additionally, a comparison is undertaken between the SE-Enc and other state-of-the-art encryption schemes to evaluate the performance of each scheme.

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Section: B Elliptic Curve Cryptography (Ecc)mentioning

confidence: 99%

SE-Enc: A Secure and Efficient Encoding Scheme Using Elliptic Curve Cryptography

Almajed

Almogren

2019

IEEE Access

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“…The public key is the product of the operation dG, which is the d doubling times for the base point G. This operation results in point (x j , y j ). ECC's security stems from the computational hardness associated with finding d when the adversary has the base point G and the public key [17]. The abovementioned ECDLP stipulates that there is no efficient algorithm that yields d in polynomial time.…”

Section: Preliminary: Elliptic Curve Cryptography (Ecc)mentioning

confidence: 99%

“…If no such y exists, then x is not mapped to the elliptic curve. The crucial advantage associated with mapping points to an elliptic curve stems from an exploitation of the elliptic curve discrete logarithm problem (ECDLP) [17], which constitutes the base of ECC. However, if a message M, encrypted using ECC, did not map to an elliptic curve (i.e., the x value of M has no corresponding y), then it is necessary to increment x and recalculate until y is found [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

iTrust—A Trustworthy and Efficient Mapping Scheme in Elliptic Curve Cryptography

Almajed

Almogren

Alabdulkareem

2020

Sensors

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Recently, many platforms have outsourced tasks to numerous smartphone devices known as Mobile Crowd-sourcing System (MCS). The data is collected and transferred to the platform for further analysis and processing. These data needs to maintain confidentiality while moving from smartphones to the platform. Moreover, the limitations of computation resources in smartphones need to be addressed to balance the confidentiality of the data and the capabilities of the devices. For this reason, elliptic curve cryptography (ECC) is accepted, widespread, and suitable for use in limited resources environments such as smartphone devices. ECC reduces energy consumption and maximizes devices’ efficiency by using small crypto keys with the same strength of the required cryptography of other cryptosystems. Thus, ECC is the preferred approach for many environments, including the MCS, Internet of Things (IoT) and wireless sensor networks (WSNs). Many implementations of ECC increase the process of encryption and/or increase the space overhead by, for instance, incorrectly mapping points to EC with extra padding bits. Moreover, the wrong mapping method used in ECC results in increasing the computation efforts. This study provides comprehensive details about the mapping techniques used in the ECC mapping phase, and presents performance results about widely used elliptic curves. In addition, it suggests an optimal enhanced mapping method and size of padding bit to secure communications that guarantee the successful mapping of points to EC and reduce the size of padding bits.

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Optimized Algorithms and Architectures for Montgomery Multiplication for Post-quantum Cryptography

Khatib

Azarderakhsh

Kermani

2019

Cryptology and Network Security

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High-Performance Elliptic Curve Cryptography by Using the CIOS Method for Modular Multiplication

Cited by 6 publications

References 20 publications

SE-Enc: A Secure and Efficient Encoding Scheme Using Elliptic Curve Cryptography

SE-Enc: A Secure and Efficient Encoding Scheme Using Elliptic Curve Cryptography

iTrust—A Trustworthy and Efficient Mapping Scheme in Elliptic Curve Cryptography

Optimized Algorithms and Architectures for Montgomery Multiplication for Post-quantum Cryptography

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