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Quantum security analysis of a lattice-based oblivious transfer protocol

Liu, Mo-meng and Krämer, Juliane and Hu, Yu-pu and Buchmann, Johannes (2018):
Quantum security analysis of a lattice-based oblivious transfer protocol.
In: Frontiers of Information Technology & Electronic Engineering, Springer, pp. 1348-1369, 18, Issue 9, ISSN 2095-9184 (Print) 2095-9230 (Online), [Online-Edition: https://link.springer.com/journal/11714],
[Article]

Abstract

Because of the concise functionality of oblivious transfer (OT) protocols, they have been widely used as building blocks in secure multiparty computation and high-level protocols. The security of OT protocols built upon classical number theoretic problems, such as the discrete logarithm and factoring, however, is threatened as a result of the huge progress in quantum computing. Therefore, post-quantum cryptography is needed for protocols based on classical problems, and several proposals for post-quantum OT protocols exist. However, most post-quantum cryptosystems present their security proof only in the context of classical adversaries, not in the quantum setting. In this paper, we close this gap and prove the security of the lattice-based OT protocol proposed by Peikert et al. (CRYPTO, 2008), which is universally composably secure under the assumption of learning with errors hardness, in the quantum setting. We apply three general quantum security analysis frameworks. First, we apply the quantum lifting theorem proposed by Unruh (EUROCRYPT, 2010) to prove that the security of the lattice-based OT protocol can be lifted into the quantum world. Then, we apply two more security analysis frameworks specified for post-quantum cryptographic primitives, i.e., simple hybrid arguments (CRYPTO, 2011) and game-preserving reduction (PQCrypto, 2014).

Item Type: Article
Erschienen: 2018
Creators: Liu, Mo-meng and Krämer, Juliane and Hu, Yu-pu and Buchmann, Johannes
Title: Quantum security analysis of a lattice-based oblivious transfer protocol
Language: English
Abstract:

Because of the concise functionality of oblivious transfer (OT) protocols, they have been widely used as building blocks in secure multiparty computation and high-level protocols. The security of OT protocols built upon classical number theoretic problems, such as the discrete logarithm and factoring, however, is threatened as a result of the huge progress in quantum computing. Therefore, post-quantum cryptography is needed for protocols based on classical problems, and several proposals for post-quantum OT protocols exist. However, most post-quantum cryptosystems present their security proof only in the context of classical adversaries, not in the quantum setting. In this paper, we close this gap and prove the security of the lattice-based OT protocol proposed by Peikert et al. (CRYPTO, 2008), which is universally composably secure under the assumption of learning with errors hardness, in the quantum setting. We apply three general quantum security analysis frameworks. First, we apply the quantum lifting theorem proposed by Unruh (EUROCRYPT, 2010) to prove that the security of the lattice-based OT protocol can be lifted into the quantum world. Then, we apply two more security analysis frameworks specified for post-quantum cryptographic primitives, i.e., simple hybrid arguments (CRYPTO, 2011) and game-preserving reduction (PQCrypto, 2014).

Journal or Publication Title: Frontiers of Information Technology & Electronic Engineering
Title of Book: https://link.springer.com/journal/11714
Series Name: LNCS
Volume: 18, Issue 9
Publisher: Springer
Uncontrolled Keywords: Primitives; P1; Oblivious transfer; Post-quantum; Lattice-based; Learning with errors; Universally composable
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Theoretical Computer Science - Cryptography and Computer Algebra
DFG-Collaborative Research Centres (incl. Transregio)
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres
Profile Areas
Profile Areas > Cybersecurity (CYSEC)
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1119: CROSSING – Cryptography-Based Security Solutions: Enabling Trust in New and Next Generation Computing Environments
Date Deposited: 06 Sep 2018 11:40
Official URL: https://link.springer.com/journal/11714
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