Rate-1 Trapdoor Functions from the Diffie-Hellman Problem

Nico Döttling; Sanjam Garg; Mohammad Hajiabadi; Kevin Liu; Giulio Malavolta

doi:10.1007/978-3-030-34618-8_20

Rate-1 Trapdoor Functions from the Diffie-Hellman Problem

Nico Döttling, Sanjam Garg, Mohammad Hajiabadi, Kevin Liu, Giulio Malavolta

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

Abstract

Trapdoor functions (TDFs) are one of the fundamental building blocks in cryptography. Studying the underlying assumptions and the efficiency of the resulting instantiations is therefore of both theoretical and practical interest. In this work we improve the input-to-image rate of TDFs based on the Diffie-Hellman problem. Specifically, we present: (a)A rate-1 TDF from the computational Diffie-Hellman (CDH) assumption, improving the result of Garg, Gay, and Hajiabadi [EUROCRYPT 2019], which achieved linear-size outputs but with large constants. Our techniques combine non-binary alphabets and high-rate error-correcting codes over large fields.(b)A rate-1 deterministic public-key encryption satisfying block-source security from the decisional Diffie-Hellman (DDH) assumption. While this question was recently settled by Döttling et al. [CRYPTO 2019], our scheme is conceptually simpler and concretely more efficient. We demonstrate this fact by implementing our construction.

Original language	English (US)
Title of host publication	Advances in Cryptology – ASIACRYPT 2019 - 25th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings
Editors	Steven D. Galbraith, Shiho Moriai
Publisher	Springer
Pages	585-606
Number of pages	22
ISBN (Print)	9783030346171
DOIs	https://doi.org/10.1007/978-3-030-34618-8_20
State	Published - 2019
Event	25th Annual International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2019 - Kobe, Japan Duration: Dec 8 2019 → Dec 12 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11923 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	25th Annual International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2019
Country	Japan
City	Kobe
Period	12/8/19 → 12/12/19

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-030-34618-8_20

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Döttling, N., Garg, S., Hajiabadi, M., Liu, K., & Malavolta, G. (2019). Rate-1 Trapdoor Functions from the Diffie-Hellman Problem. In S. D. Galbraith, & S. Moriai (Eds.), Advances in Cryptology – ASIACRYPT 2019 - 25th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings (pp. 585-606). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11923 LNCS). Springer. https://doi.org/10.1007/978-3-030-34618-8_20

Döttling, Nico ; Garg, Sanjam ; Hajiabadi, Mohammad ; Liu, Kevin ; Malavolta, Giulio. / Rate-1 Trapdoor Functions from the Diffie-Hellman Problem. Advances in Cryptology – ASIACRYPT 2019 - 25th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. editor / Steven D. Galbraith ; Shiho Moriai. Springer, 2019. pp. 585-606 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Trapdoor functions (TDFs) are one of the fundamental building blocks in cryptography. Studying the underlying assumptions and the efficiency of the resulting instantiations is therefore of both theoretical and practical interest. In this work we improve the input-to-image rate of TDFs based on the Diffie-Hellman problem. Specifically, we present: (a)A rate-1 TDF from the computational Diffie-Hellman (CDH) assumption, improving the result of Garg, Gay, and Hajiabadi [EUROCRYPT 2019], which achieved linear-size outputs but with large constants. Our techniques combine non-binary alphabets and high-rate error-correcting codes over large fields.(b)A rate-1 deterministic public-key encryption satisfying block-source security from the decisional Diffie-Hellman (DDH) assumption. While this question was recently settled by D{\"o}ttling et al. [CRYPTO 2019], our scheme is conceptually simpler and concretely more efficient. We demonstrate this fact by implementing our construction.",

author = "Nico D{\"o}ttling and Sanjam Garg and Mohammad Hajiabadi and Kevin Liu and Giulio Malavolta",

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Döttling, N, Garg, S, Hajiabadi, M, Liu, K & Malavolta, G 2019, Rate-1 Trapdoor Functions from the Diffie-Hellman Problem. in SD Galbraith & S Moriai (eds), Advances in Cryptology – ASIACRYPT 2019 - 25th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11923 LNCS, Springer, pp. 585-606, 25th Annual International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2019, Kobe, Japan, 12/8/19. https://doi.org/10.1007/978-3-030-34618-8_20

Rate-1 Trapdoor Functions from the Diffie-Hellman Problem. / Döttling, Nico; Garg, Sanjam; Hajiabadi, Mohammad; Liu, Kevin; Malavolta, Giulio.

Advances in Cryptology – ASIACRYPT 2019 - 25th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. ed. / Steven D. Galbraith; Shiho Moriai. Springer, 2019. p. 585-606 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11923 LNCS).

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

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Döttling N, Garg S, Hajiabadi M, Liu K, Malavolta G. Rate-1 Trapdoor Functions from the Diffie-Hellman Problem. In Galbraith SD, Moriai S, editors, Advances in Cryptology – ASIACRYPT 2019 - 25th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. Springer. 2019. p. 585-606. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-34618-8_20