Efficient Algorithms for Supersingular Isogeny Diffie-Hellman

Costello, Craig; Longa, Patrick; Naehrig, Michael

doi:10.1007/978-3-662-53018-4_21

Cited by 183 publications

(171 citation statements)

References 33 publications

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“…This method was proposed by Jao and De Feo and later optimized by Costello et al [5,10]. The main processes for deriving 4-isogeny are illustrated in projective coordinates.…”

Section: Vélu's Formulas On Montgomery Curvesmentioning

confidence: 99%

“…The main processes for deriving 4-isogeny are illustrated in projective coordinates. For odd-degree isogenies, refer to [10]. Let , be a Montgomery curve defined in (2).…”

Section: Vélu's Formulas On Montgomery Curvesmentioning

confidence: 99%

“…The birational map that maps twisted Edwards curve , to Montgomery curve , sends as follows: (34) Let = ( : ) be the corresponding 4-torsion point on , . The evaluation of 4-isogeny = 1 ∘ on , with kernel ⟨ ⟩ is defined as in [10].…”

Section: Isogenies On Twisted Edwards Curves Computingmentioning

confidence: 99%

“…Azarderakhsh et al also implemented key exchange protocol on ARM-NEON and FPGA devices [8,9]. Costello et al proposed faster computation methods and library for supersingular isogeny key exchange [10]. In 2017, isogeny-based digital signature schemes were proposed by Galbraith et al and Yoo et al, which brought diversity in the isogeny-based cryptography [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Efficient Isogeny Computations on Twisted Edwards Curves

Kim

Yoon

Kwon

et al. 2018

Security and Communication Networks

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The isogeny-based cryptosystem is the most recent category in the field of postquantum cryptography. However, it is widely studied due to short key sizes and compatibility with the current elliptic curve primitives. The main building blocks when implementing the isogeny-based cryptosystem are isogeny computations and point operations. From isogeny construction perspective, since the cryptosystem moves along the isogeny graph, isogeny formula cannot be optimized for specific coefficients of elliptic curves. Therefore, Montgomery curves are used in the literature, due to the efficient point operation on an arbitrary elliptic curve. In this paper, we propose formulas for computing 3 and 4 isogenies on twisted Edwards curves. Additionally, we further optimize our isogeny formulas on Edwards curves and compare the computational cost of Montgomery curves. We also present the implementation results of our isogeny computations and demonstrate that isogenies on Edwards curves are as efficient as those on Montgomery curves.

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“…This method was proposed by Jao and De Feo and later optimized by Costello et al [5,10]. The main processes for deriving 4-isogeny are illustrated in projective coordinates.…”

Section: Vélu's Formulas On Montgomery Curvesmentioning

confidence: 99%

“…The main processes for deriving 4-isogeny are illustrated in projective coordinates. For odd-degree isogenies, refer to [10]. Let , be a Montgomery curve defined in (2).…”

Section: Vélu's Formulas On Montgomery Curvesmentioning

confidence: 99%

Section: Isogenies On Twisted Edwards Curves Computingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient Isogeny Computations on Twisted Edwards Curves

Kim

Yoon

Kwon

et al. 2018

Security and Communication Networks

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“…Recently, cryptosystems based on supersingular elliptic curve isogenies were proposed by De Feo, Jao, and Plût [15], who gave protocols for key exchange, zeroknowledge proof of identity, and public key encryption. With small key sizes and efficient implementations [10,23], isogenies provide a promising candidate for post-quantum key establishment.…”

Section: Introductionmentioning

confidence: 99%

A Post-quantum Digital Signature Scheme Based on Supersingular Isogenies

Yoo

Azarderakhsh

Jalali

et al. 2017

Lecture Notes in Computer Science

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Post‐quantum cryptography techniques for secure communication in resource‐constrained Internet of Things devices: A comprehensive survey

Kumari

Singh

et al. 2022

Softw Pract Exp

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As the number and characteristics of smart devices change, the concept of the Internet of Things (IoT) emerges. The IoT provides the connected devices with a variety of resources that enable effective communication. At this point, several security issues arise to get the sensitive information behind every communication in the IoT. To provide users with security and privacy, cryptographic schemes are adopted, the most popular being public key cryptographic systems (PKC). However, with the advent of quantum computing, the level of security that can be provided by the PKC schemes is a big question. Another important issue is that the IoT environment is resource-constrained, which necessitates the implementation of lightweight cryptographic algorithms for better security. In response to these issues, the post-quantum cryptographic (PQC) schemes are one of the significant developments contributing to IoT security in the post-quantum world. This article examines the key security issues in the IoT environment and examines the effective solutions found in the literature. The problems in IoT in the quantum era are discussed and appropriate solutions by PKC schemes under limited resources in IoT are focused. As the lattice-based cryptosystems are more effective, the importance of these schemes

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Efficient Algorithms for Supersingular Isogeny Diffie-Hellman

Cited by 183 publications

References 33 publications

Efficient Isogeny Computations on Twisted Edwards Curves

Efficient Isogeny Computations on Twisted Edwards Curves

A Post-quantum Digital Signature Scheme Based on Supersingular Isogenies

Post‐quantum cryptography techniques for secure communication in resource‐constrained Internet of Things devices: A comprehensive survey

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