A Faster Way to the CSIDH

Meyer, Michaël; Reith, Steffen

doi:10.1007/978-3-030-05378-9_8

Cited by 54 publications

(46 citation statements)

References 12 publications

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“…With this choice, the implementation of [6] computes one class group action in 40 ms on average. Meyer and Reith [22] further improved this to 36 ms on average. Neither implementation is constant-time.…”

Section: Inputmentioning

confidence: 94%

“…The first implementation of CSIDH completed a key exchange in less than 0.1 seconds, and its performance has been further improved by Meyer and Reith [22]. However, both [6] and [22] recognized the difficulty of implementing CSIDH with constant-time algorithms, that is, algorithms whose running time, sequence of operations, and memory access patterns do not depend on secret data. The implementations of [6] and [22] are thus vulnerable to simple timing attacks.…”

Section: Introductionmentioning

confidence: 99%

“…However, both [6] and [22] recognized the difficulty of implementing CSIDH with constant-time algorithms, that is, algorithms whose running time, sequence of operations, and memory access patterns do not depend on secret data. The implementations of [6] and [22] are thus vulnerable to simple timing attacks.…”

Section: Introductionmentioning

confidence: 99%

“…Meyer et al take a different path: the running time of their algorithm is independent of the secret key, but not of the output of an internal random number generator. They claim a speed only 3.10 times slower than the unprotected algorithm in [22]. Onuki et al introduced new improvements, claiming a speed-up of 27.35% over Meyer et al, i.e., a net slow-down factor of 2.25 compared to [22].…”

Section: Introductionmentioning

confidence: 99%

“…They claim a speed only 3.10 times slower than the unprotected algorithm in [22]. Onuki et al introduced new improvements, claiming a speed-up of 27.35% over Meyer et al, i.e., a net slow-down factor of 2.25 compared to [22].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stronger and Faster Side-Channel Protections for CSIDH

Cervantes-Vázquez

Chenu

Chi-Domínguez

et al. 2019

Lecture Notes in Computer Science

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CSIDH is a recent quantum-resistant primitive based on the difficulty of finding isogeny paths between supersingular curves. Recently, two constant-time versions of CSIDH have been proposed: first by Meyer, Campos and Reith, and then by Onuki, Aikawa, Yamazaki and Takagi. While both offer protection against timing attacks and simple power consumption analysis, they are vulnerable to more powerful attacks such as fault injections. In this work, we identify and repair two oversights in these algorithms that compromised their constant-time character. By exploiting Edwards arithmetic and optimal addition chains, we produce the fastest constant-time version of CSIDH to date. We then consider the stronger attack scenario of fault injection, which is relevant for the security of CSIDH static keys in embedded hardware. We propose and evaluate a dummy-free CSIDH algorithm. While these CSIDH variants are slower, their performance is still within a small constant factor of lessprotected variants. Finally, we discuss derandomized CSIDH algorithms.Note: A previous version of this article incorrectly claimed that a test in Algorithm 2 leaks information through the timing channel. We are grateful to Prof. Onuki for point out our mistake.

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Section: Inputmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stronger and Faster Side-Channel Protections for CSIDH

Cervantes-Vázquez

Chenu

Chi-Domínguez

et al. 2019

Lecture Notes in Computer Science

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Towards Optimized and Constant-Time CSIDH on Embedded Devices

Jalali

Azarderakhsh

Kermani

et al. 2019

Constructive Side-Channel Analysis and Secure Design

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Quantum Circuits for the CSIDH: Optimizing Quantum Evaluation of Isogenies

Bernstein

Lange

Martindale

et al. 2019

Lecture Notes in Computer Science

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show abstract

A Faster Way to the CSIDH

Cited by 54 publications

References 12 publications

Stronger and Faster Side-Channel Protections for CSIDH

Stronger and Faster Side-Channel Protections for CSIDH

Towards Optimized and Constant-Time CSIDH on Embedded Devices

Quantum Circuits for the CSIDH: Optimizing Quantum Evaluation of Isogenies

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