Semi-commutative masking: A framework for isogeny-based protocols, with an application to fully secure two-round isogeny-based OT

Cyprien Delpech de Saint Guilhem; Emmanuela Orsini; Christophe Petit; Nigel P. Smart

doi:10.1007/978-3-030-65411-5_12

Semi-commutative masking: A framework for isogeny-based protocols, with an application to fully secure two-round isogeny-based OT

Cyprien Delpech de Saint Guilhem, Emmanuela Orsini, Christophe Petit, Nigel P. Smart^*

^*Corresponding author for this work

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We define semi-commutative invertible masking structures which aim to capture the methodology of exponentiation-only protocol design (such as discrete logarithm and isogeny-based cryptography). We give an instantiation based on the semi-commutative action of isogenies of supersingular elliptic curves, in the style of the SIDH key-exchange protocol. We then construct an oblivious transfer protocol using this new structure and prove that it UC-securely realises the oblivious transfer functionality in the random-oracle-hybrid model against passive adversaries with static corruptions. Moreover, we show that it satisfies the security properties required by the compiler of Döttling et al. (Eurocrypt 2020), achieving the first fully UC-secure two-round OT protocol based on supersingular isogenies.

Original language	English
Title of host publication	Cryptology and Network Security - 19th International Conference, CANS 2020, Vienna, Austria, December 14–16, 2020, Proceedings
Editors	Stephan Krenn, Haya Shulman, Serge Vaudenay
Publisher	Springer
Pages	235-258
Number of pages	24
ISBN (Print)	9783030654108
DOIs	https://doi.org/10.1007/978-3-030-65411-5_12
Publication status	Published - 2020
Event	19th International Conference on Cryptology and Network Security, CANS 2020 - Vienna, Austria Duration: 14 Dec 2020 → 16 Dec 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12579 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	19th International Conference on Cryptology and Network Security, CANS 2020
Country/Territory	Austria
City	Vienna
Period	14/12/20 → 16/12/20

Bibliographical note

Funding Information:
Acknowledgements. This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by CyberSecurity Research Flanders with reference number VR20192203, by the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contracts No. N66001-15-C-4070 and No. HR001120C0085, by the FWO under an Odysseus project GOH9718N and by EPSRC grant EP/S01361X/1

Publisher Copyright:
© Springer Nature Switzerland AG 2020.

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-030-65411-5_12

Cite this

de Saint Guilhem, C. D., Orsini, E., Petit, C., & Smart, N. P. (2020). Semi-commutative masking: A framework for isogeny-based protocols, with an application to fully secure two-round isogeny-based OT. In S. Krenn, H. Shulman, & S. Vaudenay (Eds.), Cryptology and Network Security - 19th International Conference, CANS 2020, Vienna, Austria, December 14–16, 2020, Proceedings (pp. 235-258). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12579 LNCS). Springer. https://doi.org/10.1007/978-3-030-65411-5_12

de Saint Guilhem, Cyprien Delpech ; Orsini, Emmanuela ; Petit, Christophe et al. / Semi-commutative masking : A framework for isogeny-based protocols, with an application to fully secure two-round isogeny-based OT. Cryptology and Network Security - 19th International Conference, CANS 2020, Vienna, Austria, December 14–16, 2020, Proceedings. editor / Stephan Krenn ; Haya Shulman ; Serge Vaudenay. Springer, 2020. pp. 235-258 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{b00704b07d6c430289d1dda5e641dba4,

title = "Semi-commutative masking: A framework for isogeny-based protocols, with an application to fully secure two-round isogeny-based OT",

abstract = "We define semi-commutative invertible masking structures which aim to capture the methodology of exponentiation-only protocol design (such as discrete logarithm and isogeny-based cryptography). We give an instantiation based on the semi-commutative action of isogenies of supersingular elliptic curves, in the style of the SIDH key-exchange protocol. We then construct an oblivious transfer protocol using this new structure and prove that it UC-securely realises the oblivious transfer functionality in the random-oracle-hybrid model against passive adversaries with static corruptions. Moreover, we show that it satisfies the security properties required by the compiler of D{\"o}ttling et al. (Eurocrypt 2020), achieving the first fully UC-secure two-round OT protocol based on supersingular isogenies.",

author = "{de Saint Guilhem}, {Cyprien Delpech} and Emmanuela Orsini and Christophe Petit and Smart, {Nigel P.}",

note = "Funding Information: Acknowledgements. This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by CyberSecurity Research Flanders with reference number VR20192203, by the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contracts No. N66001-15-C-4070 and No. HR001120C0085, by the FWO under an Odysseus project GOH9718N and by EPSRC grant EP/S01361X/1 Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.; 19th International Conference on Cryptology and Network Security, CANS 2020 ; Conference date: 14-12-2020 Through 16-12-2020",

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de Saint Guilhem, CD, Orsini, E, Petit, C & Smart, NP 2020, Semi-commutative masking: A framework for isogeny-based protocols, with an application to fully secure two-round isogeny-based OT. in S Krenn, H Shulman & S Vaudenay (eds), Cryptology and Network Security - 19th International Conference, CANS 2020, Vienna, Austria, December 14–16, 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12579 LNCS, Springer, pp. 235-258, 19th International Conference on Cryptology and Network Security, CANS 2020, Vienna, Austria, 14/12/20. https://doi.org/10.1007/978-3-030-65411-5_12

Semi-commutative masking: A framework for isogeny-based protocols, with an application to fully secure two-round isogeny-based OT. / de Saint Guilhem, Cyprien Delpech; Orsini, Emmanuela; Petit, Christophe et al.
Cryptology and Network Security - 19th International Conference, CANS 2020, Vienna, Austria, December 14–16, 2020, Proceedings. ed. / Stephan Krenn; Haya Shulman; Serge Vaudenay. Springer, 2020. p. 235-258 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12579 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N1 - Funding Information: Acknowledgements. This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by CyberSecurity Research Flanders with reference number VR20192203, by the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contracts No. N66001-15-C-4070 and No. HR001120C0085, by the FWO under an Odysseus project GOH9718N and by EPSRC grant EP/S01361X/1 Publisher Copyright: © Springer Nature Switzerland AG 2020.

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AB - We define semi-commutative invertible masking structures which aim to capture the methodology of exponentiation-only protocol design (such as discrete logarithm and isogeny-based cryptography). We give an instantiation based on the semi-commutative action of isogenies of supersingular elliptic curves, in the style of the SIDH key-exchange protocol. We then construct an oblivious transfer protocol using this new structure and prove that it UC-securely realises the oblivious transfer functionality in the random-oracle-hybrid model against passive adversaries with static corruptions. Moreover, we show that it satisfies the security properties required by the compiler of Döttling et al. (Eurocrypt 2020), achieving the first fully UC-secure two-round OT protocol based on supersingular isogenies.

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de Saint Guilhem CD, Orsini E, Petit C, Smart NP. Semi-commutative masking: A framework for isogeny-based protocols, with an application to fully secure two-round isogeny-based OT. In Krenn S, Shulman H, Vaudenay S, editors, Cryptology and Network Security - 19th International Conference, CANS 2020, Vienna, Austria, December 14–16, 2020, Proceedings. Springer. 2020. p. 235-258. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-65411-5_12

Semi-commutative masking: A framework for isogeny-based protocols, with an application to fully secure two-round isogeny-based OT

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus subject areas

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