A Lattice-Based Unordered Aggregate Signature Scheme Based on the Intersection Method

Lu, Xiuhua; Yin, Wei; Wen, Qiaoyan; Jin, Zilong; Li, Wenmin

doi:10.1109/access.2018.2847411

Cited by 15 publications

(4 citation statements)

References 6 publications

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“…How-ever there are no ways to aggregate signatures at the signing simulation of confined guessing in the lattice setting, like Böhl et al's optimized CDH-based and RSA-based signature schemes [9]. On the other hand, many lattice-based aggregate signatures have been proposed so far [5], [26], [30], [40], [41]. There are two types of lattice-based aggregate signatures: sequential aggregate signatures (SAS) specifying the order of aggregation [5], [40] and unordered aggregate signatures (UAS) aggregating in random order [30], [41].…”

Section: Contributionsmentioning

confidence: 99%

“…On the other hand, many lattice-based aggregate signatures have been proposed so far [5], [26], [30], [40], [41]. There are two types of lattice-based aggregate signatures: sequential aggregate signatures (SAS) specifying the order of aggregation [5], [40] and unordered aggregate signatures (UAS) aggregating in random order [30], [41]. When we try to apply the existing aggregation technique to use multiple tags in a signature simulation, it does not work.…”

Section: Contributionsmentioning

confidence: 99%

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Short Lattice Signature Scheme with Tighter Reduction under Ring-SIS Assumption

Kajita

Ohtake

Ogawa

et al. 2023

IEICE Trans. Fundamentals

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We propose a short signature scheme under the ring-SIS assumption in the standard model. Specifically, by revisiting an existing construction [Ducas and Micciancio, CRYPTO 2014], we demonstrate lattice-based signatures with improved reduction loss. As far as we know, there are no ways to use multiple tags in the signature simulation of security proof in the lattice tag-based signatures. We address the tag-collision possibility in the lattice setting, which improves reduction loss. Our scheme generates tags from messages by constructing a scheme under a mild security condition that is existentially unforgeable against random message attack with auxiliary information. Thus our scheme can reduce the signature size since it does not need to send tags with the signatures. Our scheme has short signature sizes of 𝑂 (1) and achieves tighter reduction loss than that of Ducas et al.'s scheme. Our proposed scheme has two variants. Our scheme with one property has tighter reduction and the same verification key size of 𝑂 (log 𝑛) as that of Ducas et al.'s scheme, where 𝑛 is the security parameter. Our scheme with the other property achieves much tighter reduction loss of 𝑂 (𝑄/𝑛) and verification key size of 𝑂 (𝑛), where 𝑄 is the number of signing queries.

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Section: Contributionsmentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

Short Lattice Signature Scheme with Tighter Reduction under Ring-SIS Assumption

Kajita

Ohtake

Ogawa

et al. 2023

IEICE Trans. Fundamentals

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“…In 2016, Bansarkhani et al proposed the first unordered interactive lattice-based aggregate signature scheme that is provably secure in the random oracle model [7], and in 2018, Lu et al proposed an unordered lattice-based aggregate signature scheme based on the intersection method [8]. However, these schemes are not applied to other protocols such as a STARK protocol to produce zero-knowledge proofs that protects the privacy of Bitcoin transaction data.…”

Section: A Related Workmentioning

confidence: 99%

Improving Bitcoin’s Post-Quantum Transaction Efficiency With a Novel Lattice-Based Aggregate Signature Scheme Based on CRYSTALS-Dilithium and a STARK Protocol

Quan

2022

IEEE Access

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This paper proposes a novel lattice-based aggregate signature (LAS) scheme that bring postquantum security to the Bitcoin system without sacrificing its transaction efficiency. Bitcoin currently employs Elliptic Curve Digital Signature Algorithm (ECDSA), which is insecure against the emerging quantum technology, so post-quantum signature schemes like the proposed LAS will become necessary in the near future. However, most of the post-quantum signatures schemes have large signature sizes which decrease Bitcoin's efficiency while our proposed scheme does not have this negative side effect. Our LAS scheme is based on CRYSTALS-Dilithium and a zero-knowledge Scalable Transparent Arguments of Knowledge (STARK) protocol. CRYSTALS-Dilithium is the most prominent algorithm chosen by the National Institute of Standards and Technology (NIST), yet it still has an adverse limitation: it would cause Bitcoin's transaction efficiency to fall by 17 times due to its relatively large signature size. On the other hand, the proposed LAS scheme takes full advantage of signature aggregation using the STARK protocol and Dilithium's easy and fast implementation, thus generating signatures with post-quantum security and small signature sizes which are critical to transaction efficiency. Our proofs convey the correctness, compactness, and post-quantum security of our construction in the quantum random oracle model, and our implementation conveyed that the proposed scheme would only decrease Bitcoin's transaction efficiency by 3 times, a significant improvement from using Dilithium and other lattice-based aggregate signature schemes. Our proposed scheme has many advantages over the existing schemes and may become very valuable to Bitcoin.

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“…Partially inspired by collusion-resistant broadcast encryption scheme [4], Chu et al [5] introduced key-aggregate encryption schemes in which an aggregate key is generated for the authorized user to decrypt all the shared files. Recently, key aggregate signatures [10], [13], [20], [24] also have been studied.…”

Section: Introductionmentioning

confidence: 99%

Lattice-Based Key-Aggregate (Searchable) Encryption in Cloud Storage

et al. 2019

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In cloud storage, selectively sharing encrypted data is becoming increasingly important. One key design challenge is the management of encryption keys. Traditionally, a large quantity of encryption keys have to be managed by the data owner, and an equally large number of keyword trapdoors must be sent to the cloud for the purpose of searching over the shared data, which are cumbersome in terms of secure communication and management. Recently, key-aggregate (searchable) encryption schemes have been introduced to alleviate the problem. However, they were only designed under the Bilinear Diffie-Hellman Exponent assumption in the prior works. Lattice-based key-aggregate (searchable) encryption schemes are valuable, because they have security against quantum computing attacks, average-case to worse-case equivalence as well as simplicity and potential efficiency. Here we propose a key-aggregate encryption scheme and a key-aggregate searchable encryption scheme which are both based on a lattice problem (i.e., the Learning with Errors problem). Some key techniques are employed during the construction of the schemes. A basis delegation algorithm is designed to generate the aggregate key without increasing the lattice dimension. The encryption algorithms of the two schemes are trickily devised to make the encrypted files decryptable or searchable. To overcome the problem of general matrix multiplication failing to satisfy commutative law, a hash function is designed by using diagonalizable matrices to make the encrypted file decryptable and the trapdoor adjustable. We present the schemes' correctness proof, formal security analysis as well as performance analysis, which confirm that they are provably secure and practically efficient. To the best of our knowledge, the former is the first lattice-based key-aggregate encryption scheme and the latter is the first lattice-based key-aggregate searchable encryption scheme. We also demonstrate their application to cloud storage for searchable group data sharing by combining the two schemes. INDEX TERMS Cloud storage, searchable data sharing, key-aggregate encryption, key-aggregate searchable encryption, lattice-based problem, the learning with errors problem.

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A Lattice-Based Unordered Aggregate Signature Scheme Based on the Intersection Method

Cited by 15 publications

References 6 publications

Short Lattice Signature Scheme with Tighter Reduction under Ring-SIS Assumption

Short Lattice Signature Scheme with Tighter Reduction under Ring-SIS Assumption

Improving Bitcoin’s Post-Quantum Transaction Efficiency With a Novel Lattice-Based Aggregate Signature Scheme Based on CRYSTALS-Dilithium and a STARK Protocol

Lattice-Based Key-Aggregate (Searchable) Encryption in Cloud Storage

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