A Post-quantum Digital Signature Scheme Based on Supersingular Isogenies

Yoo, Youngho; Azarderakhsh, Reza; Jalali, Amir; Jao, David; Soukharev, Vladimir

doi:10.1007/978-3-319-70972-7_9

Cited by 74 publications

(26 citation statements)

References 31 publications

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“…Bernstein [6] has questioned the practicality of quantum collision-finding algorithms. Following his arguments, Goldfeder, Chase and Zaverucha [23] chose t = 2λ, and a similar choice was made in Yoo et al [49]. On the other hand, Beals et al [4] suggest there may be a quantum speedup that would require increasing t.…”

Section: Post-quantum Alternatives To Fiat-shamirmentioning

confidence: 99%

“…First we describe their scheme. The independent work [49] presents a signature scheme which is obtained in the same way, by applying the Fiat-Shamir or Unruh transformation to the De Feo-Jao-Plût identification protocol. Nevertheless, in this paper we obtain a smaller signature size.…”

Section: First Signature Schemementioning

confidence: 99%

“…In other words, at first sight, the responses have different lengths. Compression techniques can be used in this case to ensure that responses all have the same length (see Section 4.2 of [49]).…”

Section: De Feo-jao-plût Identification Schemementioning

confidence: 99%

“…We also use a variant of the Fiat-Shamir transform due to Unruh to obtain a post-quantum signature scheme. Essentially the same signature scheme was independently published by Yoo, Azarderakhsh, Jalali, Jao and Soukharev [49], but our version has improved signature size. This scheme has the advantage of being simple to describe, at least to a reader who is familiar with the previous work in the subject, and easy to implement.…”

Section: Introductionmentioning

confidence: 99%

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Identification Protocols and Signature Schemes Based on Supersingular Isogeny Problems

2019

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We present signature schemes whose security relies on computational assumptions relating to isogeny graphs of supersingular elliptic curves. We give two schemes, both of them based on interactive identification protocols. The first identification protocol is due to De Feo, Jao and Plût. The second one, and the main contribution of the paper, makes novel use of an algorithm of Kohel, Lauter, Petit and Tignol for the quaternion version of the -isogeny problem, for which we provide a more complete description and analysis, and is based on a more standard and potentially stronger computational problem. Both identification protocols lead to signatures that are existentially unforgeable under chosen message attacks in the random oracle model using the wellknown Fiat-Shamir transform, and in the quantum random oracle model using another transform due to Unruh. A version of the first signature scheme was independently published by Yoo, Azarderakhsh, Jalali, Jao and Soukharev. This is the full version of a paper published at ASIACRYPT 2017.

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Section: Post-quantum Alternatives To Fiat-shamirmentioning

confidence: 99%

Section: First Signature Schemementioning

confidence: 99%

Section: De Feo-jao-plût Identification Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Identification Protocols and Signature Schemes Based on Supersingular Isogeny Problems

2019

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“…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]. Additionally, after the National Institute of Standards and Technology (NIST) announced a standardization project for PQC, Supersingular Isogeny Key Encapsulation (SIKE) was submitted as one of the candidates [13].…”

Section: Introductionmentioning

confidence: 99%

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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CSIDH: An Efficient Post-Quantum Commutative Group Action

Castryck

Lange

Martindale

et al. 2018

Lecture Notes in Computer Science

341

342

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We propose an efficient commutative group action suitable for non-interactive key exchange in a post-quantum setting. Our construction follows the layout of the Couveignes-Rostovtsev-Stolbunov cryptosystem, but we apply it to supersingular elliptic curves defined over a large prime field Fp, rather than to ordinary elliptic curves. The Diffie-Hellman scheme resulting from the group action allows for publickey validation at very little cost, runs reasonably fast in practice, and has public keys of only 64 bytes at a conjectured AES-128 security level, matching NIST's post-quantum security category I.

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A Post-quantum Digital Signature Scheme Based on Supersingular Isogenies

Cited by 74 publications

References 31 publications

Identification Protocols and Signature Schemes Based on Supersingular Isogeny Problems

Identification Protocols and Signature Schemes Based on Supersingular Isogeny Problems

Efficient Isogeny Computations on Twisted Edwards Curves

CSIDH: An Efficient Post-Quantum Commutative Group Action

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