Post-quantum cryptography: lattice signatures

Buchmann, Johannes; Lindner, Richard; Rückert, Markus; Schneider, Michael

doi:10.1007/s00607-009-0042-y

Cited by 11 publications

(6 citation statements)

References 29 publications

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“…Since Nguyen and Regev categorically show (without perturbation) NTRUSign to be absolutely insecure and Ducas and Nguyen [2012b] even broke further countermeasures and a version with perturbations, the descriptions will not be covered since implementation results currently do not have practical applications. However, interested readers are referred to a survey by Buchmann et al [2009]. Recent research such as Melchor et al [2014] holds some promise for the future of these DSSs, such that someday the security and efficiency issues of NTRUSign may be amended.…”

Section: Ggh and Ntrusign Signaturesmentioning

confidence: 98%

Practical Lattice-Based Digital Signature Schemes

Howe

Pöppelmann

O’Neill

et al. 2015

ACM Trans. Embed. Comput. Syst.

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Digital signatures are an important primitive for building secure systems and are used in most real-world security protocols. However, almost all popular signature schemes are either based on the factoring assumption (RSA) or the hardness of the discrete logarithm problem (DSA/ECDSA). In the case of classical cryptanalytic advances or progress on the development of quantum computers, the hardness of these closely related problems might be seriously weakened. A potential alternative approach is the construction of signature schemes based on the hardness of certain lattice problems that are assumed to be intractable by quantum computers. Due to significant research advancements in recent years, lattice-based schemes have now become practical and appear to be a very viable alternative to number-theoretic cryptography. In this article, we focus on recent developments and the current state of the art in lattice-based digital signatures and provide a comprehensive survey discussing signature schemes with respect to practicality. Additionally, we discuss future research areas that are essential for the continued development of lattice-based cryptography.

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Section: Ggh and Ntrusign Signaturesmentioning

confidence: 98%

Practical Lattice-Based Digital Signature Schemes

Howe

Pöppelmann

O’Neill

et al. 2015

ACM Trans. Embed. Comput. Syst.

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“…Here, we present some fundamental notions and properties of lattices that we will need. We refer to for a detailed introduction to lattices. Integer Lattices .…”

Section: Preliminariesmentioning

confidence: 99%

A post‐quantum provable data possession protocol in cloud

Chen¹,

Han

Jing

et al. 2013

Security Comm Networks

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Provable data possession (PDP) is a model for efficiently checking the integrity of data in cloud storage. Most previous PDP protocols are insecure when quantum computers are considered. In this paper, we propose a homomorphic hash‐based PDP (HH‐PDP) protocol from ideal lattice assumptions. Firstly, we prove that a collision‐resistant hash function family is homomorphic. Then, we use the homomorphism to generate homomorphic verification tags and further construct a new PDP protocol. The security of the proposed protocol relies on the assumed worst‐case hardness of ideal lattice problems, which hold a great promise for post‐quantum cryptography. We prove that the proposed protocol guarantees data possession in the standard model if the shortest polynomial problem is hard. As the main operations in our construction are addition and multiplication on small integers, the proposed protocol is more efficient than previous protocols. Experimental result shows that HH‐PDP is approximately five times cheaper in preprocessing and checking proof, half cost in generating proof compared with the most efficient PDP protocol proposed by Ateniese et al. in 2011. Copyright © 2013 John Wiley & Sons, Ltd.

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“…For details on the topic of latticebased cryptography, see, e.g. [10,11,12,13]. In 2008, Gentry et al proposed a simple and efficient signature scheme [14] (GPV's scheme) from their new trapdoor functions based on lattice assumption.…”

Section: Introductionmentioning

confidence: 99%

Public verifiable proof of storage protocol from lattice assumption

Feng

Liu

2012

2012 IEEE International Conference on Intelligent Control, Automatic Detection and High-End Equipment

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Proof of storage (PoS) is an interactive protocol allowing a client to verify that the server possesses the original data without retrieving it. All of the existed PoS protocols are based on the hardness of factoring or discrete-log problems, which cannot resist quantum attacks. In this paper, we first propose a linearly homomorphic signature scheme(LHHS) from lattice assumption, and generate HTVs from LHSS. Then we construct the first lattice-based PoS protocol from the new HTVs. Our PoS protocol is public verifiable and can be proved unforgeable in random oracle model assuming that SIS problem is hard. Complexity analysis shows that the mainly computation cost in LPoS are occur in Encode phase. The communication cost in prove and verify phases is independent to the scale of the file. The client or the verifier only needs to store the verifiable tags rather than the original file blocks.

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Post-quantum cryptography: lattice signatures

Abstract: This survey provides a comparative overview of lattice-based signature schemes with respect to security and performance. Furthermore, we explicitly show how to construct a competitive and provably secure Merkle-tree signature scheme solely based on worst-case lattice problems.

Cited by 11 publications

References 29 publications

Practical Lattice-Based Digital Signature Schemes

Practical Lattice-Based Digital Signature Schemes

A post‐quantum provable data possession protocol in cloud

Public verifiable proof of storage protocol from lattice assumption

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