The Brave New World of Global Generic Groups and UC-Secure Zero-Overhead SNARKs

Jan Bobolz; Pooya Farshim; Markulf Kohlweiss; Akira Takahashi

doi:10.1007/978-3-031-78011-0_4

The Brave New World of Global Generic Groups and UC-Secure Zero-Overhead SNARKs

Jan Bobolz, Pooya Farshim, Markulf Kohlweiss, Akira Takahashi

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

Abstract

The universal composability (UC) model provides strong security guarantees for protocols used in arbitrary contexts. While these guarantees are highly desirable, in practice, schemes with a standalone proof of security, such as the Groth16 proof system, are preferred. This is because UC security typically comes with undesirable overhead, sometimes making UC-secure schemes significantly less efficient than their standalone counterparts.

We establish the UC security of Groth16 without any significant overhead. In the spirit of global random oracles, we design a global (restricted) observable generic group functionality that models a natural notion of observability: computations that trace back to group elements derived from generators of other sessions are observable. This notion turns out to be surprisingly subtle to formalize. We provide a general framework for proving protocols secure in the presence of global generic groups, which we then apply to Groth16.

Original language	English
Title of host publication	Theory of Cryptography
Subtitle of host publication	22nd International Conference, TCC 2024, Milan, Italy, December 2–6, 2024, Proceedings, Part I
Publisher	Springer
Pages	90-124
Number of pages	35
ISBN (Electronic)	9783031780110
ISBN (Print)	9783031780103
DOIs	https://doi.org/10.1007/978-3-031-78011-0_4
Publication status	Published - 2 Dec 2024
Event	Theory of Cryptography Conference: 22nd International Conference - Milan, Italy Duration: 2 Dec 2024 → 6 Dec 2024 Conference number: 22 https://tcc.iacr.org/2024/

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	15364
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	Theory of Cryptography Conference
Abbreviated title	TCC 2024
Country/Territory	Italy
City	Milan
Period	2/12/24 → 6/12/24
Internet address	https://tcc.iacr.org/2024/

Access to Document

10.1007/978-3-031-78011-0_4

BobolzEtalTCC24TheBraveNewWorldofGlobalGenericGroupsAccepted author manuscript, 717 KBLicence: Creative Commons: Attribution (CC-BY)

https://eprint.iacr.org/2024/818Licence: Creative Commons: Attribution (CC-BY)

Cite this

Bobolz, J., Farshim, P., Kohlweiss, M., & Takahashi, A. (2024). The Brave New World of Global Generic Groups and UC-Secure Zero-Overhead SNARKs. In Theory of Cryptography: 22nd International Conference, TCC 2024, Milan, Italy, December 2–6, 2024, Proceedings, Part I (pp. 90-124). (Lecture Notes in Computer Science; Vol. 15364). Springer. https://doi.org/10.1007/978-3-031-78011-0_4

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author = "Jan Bobolz and Pooya Farshim and Markulf Kohlweiss and Akira Takahashi",

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Bobolz, J, Farshim, P, Kohlweiss, M & Takahashi, A 2024, The Brave New World of Global Generic Groups and UC-Secure Zero-Overhead SNARKs. in Theory of Cryptography: 22nd International Conference, TCC 2024, Milan, Italy, December 2–6, 2024, Proceedings, Part I. Lecture Notes in Computer Science, vol. 15364, Springer, pp. 90-124, Theory of Cryptography Conference, Milan, Italy, 2/12/24. https://doi.org/10.1007/978-3-031-78011-0_4

The Brave New World of Global Generic Groups and UC-Secure Zero-Overhead SNARKs. / Bobolz, Jan; Farshim, Pooya; Kohlweiss, Markulf et al.
Theory of Cryptography: 22nd International Conference, TCC 2024, Milan, Italy, December 2–6, 2024, Proceedings, Part I. Springer, 2024. p. 90-124 (Lecture Notes in Computer Science; Vol. 15364).

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

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T1 - The Brave New World of Global Generic Groups and UC-Secure Zero-Overhead SNARKs

AU - Bobolz, Jan

AU - Farshim, Pooya

AU - Kohlweiss, Markulf

AU - Takahashi, Akira

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N2 - The universal composability (UC) model provides strong security guarantees for protocols used in arbitrary contexts. While these guarantees are highly desirable, in practice, schemes with a standalone proof of security, such as the Groth16 proof system, are preferred. This is because UC security typically comes with undesirable overhead, sometimes making UC-secure schemes significantly less efficient than their standalone counterparts. We establish the UC security of Groth16 without any significant overhead. In the spirit of global random oracles, we design a global (restricted) observable generic group functionality that models a natural notion of observability: computations that trace back to group elements derived from generators of other sessions are observable. This notion turns out to be surprisingly subtle to formalize. We provide a general framework for proving protocols secure in the presence of global generic groups, which we then apply to Groth16.

AB - The universal composability (UC) model provides strong security guarantees for protocols used in arbitrary contexts. While these guarantees are highly desirable, in practice, schemes with a standalone proof of security, such as the Groth16 proof system, are preferred. This is because UC security typically comes with undesirable overhead, sometimes making UC-secure schemes significantly less efficient than their standalone counterparts. We establish the UC security of Groth16 without any significant overhead. In the spirit of global random oracles, we design a global (restricted) observable generic group functionality that models a natural notion of observability: computations that trace back to group elements derived from generators of other sessions are observable. This notion turns out to be surprisingly subtle to formalize. We provide a general framework for proving protocols secure in the presence of global generic groups, which we then apply to Groth16.

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M3 - Conference contribution

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T2 - Theory of Cryptography Conference

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The Brave New World of Global Generic Groups and UC-Secure Zero-Overhead SNARKs

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