CSIDH: An efficient post-quantum commutative group action

Wouter Castryck; Tanja Lange; Chloe Martindale; Lorenz Panny; Joost Renes

doi:10.1007/978-3-030-03332-3_15

CSIDH: An efficient post-quantum commutative group action

Wouter Castryck, Tanja Lange, Chloe Martindale, Lorenz Panny, Joost Renes

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

56 Citations (Scopus)

Abstract

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 F_p, rather than to ordinary elliptic curves. The Diffie–Hellman scheme resulting from the group action allows for public-key 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.

Original language	English
Title of host publication	Advances in Cryptology – ASIACRYPT 2018 - 24th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings
Editors	Thomas Peyrin, Steven Galbraith
Place of Publication	Berlin
Publisher	Springer
Pages	395-427
Number of pages	33
ISBN (Print)	9783030033316
DOIs	https://doi.org/10.1007/978-3-030-03332-3_15
Publication status	Published - 1 Jan 2018
Event	24th Annual International Conference on Theory and Application of Cryptology and Information Security, (ASIACRYPT 2018) - Brisbane, Australia Duration: 2 Dec 2018 → 6 Dec 2018 https://asiacrypt.iacr.org/2018/

Publication series

Name	Lecture Notes in Computer Science
Volume	11274
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	24th Annual International Conference on Theory and Application of Cryptology and Information Security, (ASIACRYPT 2018)
Abbreviated title	ASIACRYPT2018
Country/Territory	Australia
City	Brisbane
Period	2/12/18 → 6/12/18
Internet address	https://asiacrypt.iacr.org/2018/

Keywords

Class-group action
Isogeny-based cryptography
Key confirmation
Non-interactive key exchange
Post-quantum cryptography

Access to Document

10.1007/978-3-030-03332-3_15

Cite this

Castryck, W., Lange, T., Martindale, C., Panny, L., & Renes, J. (2018). CSIDH: An efficient post-quantum commutative group action. In T. Peyrin, & S. Galbraith (Eds.), Advances in Cryptology – ASIACRYPT 2018 - 24th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings (pp. 395-427). (Lecture Notes in Computer Science; Vol. 11274). Springer. https://doi.org/10.1007/978-3-030-03332-3_15

Castryck, Wouter ; Lange, Tanja ; Martindale, Chloe ; Panny, Lorenz ; Renes, Joost. / CSIDH : An efficient post-quantum commutative group action. Advances in Cryptology – ASIACRYPT 2018 - 24th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. editor / Thomas Peyrin ; Steven Galbraith. Berlin : Springer, 2018. pp. 395-427 (Lecture Notes in Computer Science).

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Castryck, W, Lange, T , Martindale, C , Panny, L & Renes, J 2018, CSIDH: An efficient post-quantum commutative group action. in T Peyrin & S Galbraith (eds), Advances in Cryptology – ASIACRYPT 2018 - 24th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. Lecture Notes in Computer Science, vol. 11274, Springer, Berlin, pp. 395-427, 24th Annual International Conference on Theory and Application of Cryptology and Information Security, (ASIACRYPT 2018), Brisbane, Australia, 2/12/18. https://doi.org/10.1007/978-3-030-03332-3_15

CSIDH : An efficient post-quantum commutative group action. / Castryck, Wouter; Lange, Tanja ; Martindale, Chloe ; Panny, Lorenz; Renes, Joost.

Advances in Cryptology – ASIACRYPT 2018 - 24th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. ed. / Thomas Peyrin; Steven Galbraith. Berlin : Springer, 2018. p. 395-427 (Lecture Notes in Computer Science; Vol. 11274).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - 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 public-key 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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KW - Isogeny-based cryptography

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Castryck W, Lange T , Martindale C , Panny L, Renes J. CSIDH: An efficient post-quantum commutative group action. In Peyrin T, Galbraith S, editors, Advances in Cryptology – ASIACRYPT 2018 - 24th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. Berlin: Springer. 2018. p. 395-427. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-030-03332-3_15

CSIDH: An efficient post-quantum commutative group action

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