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Lattice-Based commitment scheme for Low Communication Costs

IEEE ACCESS 2024年 12卷 111400-111410页

作者： Miyaji, Hideaki Wang, Yuntao Miyaji, Atsuko Ritsumeikan Univ Coll Informat Sci & Technol Ibaraki Osaka 5678570 Japan Univ Electrocommun Grad Sch Informat & Engn Chofu Tokyo 1828585 Japan Osaka Univ Grad Sch Engn Suita Osaka 5650871 Japan

commitment schemes are cryptographic schemes that can be applied to zero-knowledge proof construction and blockchain construction. Recently, lattice-based cryptography has been intensively investigated due to the promising potential in quantum cryptography. Accordingly, commitment schemes based on lattice assumptions have been studied for practical applications. Notably, applications often require committing an arbitrary message with low communication costs, so commitment schemes must be satisfied with fewer length restrictions and fewer extensions to the messages. Several studies have been conducted to achieve the problem, including the study published by Baum et al. in 2018. However, the output length of their scheme is large in relation to the input length. We design a length-extension-free commitment scheme Com(MWM) in which the length of the message string is large relative to the length of the commitment string, improving on the commitment scheme of Baum et al. Furthermore, we prove that the hiding and binding properties of Com(MWM) are based on the hardness of the decisional search knapsack problem and extended search knapsack problems, respectively. Finally, we evaluate the computation costs of generating commitment value between ours and Baum et al.'s commitment scheme.

关键词： commitment scheme lattice-based protocol hiding property binding property AES-128 commitment scheme lattice-based protocol hiding property binding property AES-128

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Message-Restriction-Free commitment scheme Based on Lattice Assumption 1

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16th International Conference on Information Security Practice and Experience (ISPEC)

作者： Miyaji, Hideaki Wang, Yuntao Miyaji, Atsuko Osaka Univ Grad Sch Engn Suita Osaka Japan Japan Adv Inst Sci & Technol Sch Informat Sci Nomi Japan

ISBN: (数字)9783030932060

ISBN: (纸本)9783030932053;9783030932060

A commitment scheme is a fundamental protocol and an essential component of basic cryptographic tasks, such as zero-knowledge identification. In recent years, lattice-based cryptography has been intensively studied owing to its potential to be promising post-quantum cryptography. Therefore, the commitment schemes based on lattice assumption have been studied for practical applications. Typically, many applications require to commit arbitrary vectors rather than only short ones. In order to send such large messages, one of a crucial challenges of commitment schemes is to increase the size of a message string. Various existing studies have been done to enlarge the size of a message string so far. Baum et al. constructed the commitment scheme, which can allow sending large message size in 2018. However, the domain available for message string is still being used for non-message purposes. In this paper, by improving Baum et al.'s commitment scheme, we propose a commitment scheme that can send a larger message size than Baum et al.'s message string size. Furthermore, we prove that the hiding property of our commitment scheme is based on the hardness of the decisional knapsack problem, and the binding property is based on the hardness of the module small-integer solution problem. We also show how to achieve a statistically hiding commitment scheme by setting appropriate parameters.

关键词： commitment scheme Hash function Lattice-based protocol

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Fuzzy commitment scheme based on Reed Solomon Codes 16

Fuzzy Commitment Scheme based on Reed Solomon Codes

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9th International Conference on Security of Information and Networks (SIN)

作者： Chauhan, Sonam Sharma, Ajay SRM Univ Delhi NCR Sonepat Haryana India

ISBN: (纸本)9781450347648

commitment scheme is the basic element of various cryptographic protocols. The fuzziness introduced in the fuzzy commitment scheme allows small amount of corruptions. The fuzzy commitment scheme based on the cryptographic hash functions suffers security imperfections. Thus, this paper presents a fuzzy commitment scheme with the Reed Solomon error correction codes which is capable of correcting t errors. The proposed scheme explores the different variables involved in the scheme and their effects on the execution time of the scheme.

关键词： Fuzzy commitment scheme (FCS) Fuzzy commitment Key (FCK) Error Correction Codes Reed Solomon Code commitment scheme

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Decreasing Proof Size of BLS scheme

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COMPUTER JOURNAL 2023年第3期67卷 1030-1040页

作者： Fang, Dong Huang, Guifang Wang, Mengfan Hu, Lei Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing 100093 Peoples R China Univ Chinese Acad Sci Sch Cyber Secur Beijing 100093 Peoples R China

Bootle et al. in CRYPTO 2019 proposed a zero knowledge proof for an ISISm,n,q,beta instance A (s) over right arrow= (u) over right arrow mod q with parallel to(s) over right arrow parallel to(infinity) <= beta (BLS scheme). It was implemented by transforming the instance into the form A '(s) over right arrow'= (u) over right arrow mod q, where the coefficients of (s) over right arrow are in {0, 1, 2}, and proved the latter in an exact way. With the concrete parameters m = 1024, n = 2048, beta = 1, q approximate to 2(32), their proof is of length 384.03KB. In this paper, we decrease the proof size of BLS scheme by two techniques. The first one takes effect on some special parameters. For these parameters, using the binary basic set instead of the ternary one results in a shorter proof. The second one deals with the repetition of the lower half in BLS scheme. Observing that what the lower half proves is of form B (r) over right arrow= (t) over right arrow with a short vector (r) over right arrow of polynomials, a variant of parallel repetition can be used to shorten the proof size. Combining these two techniques together, the proof size of the above-mentioned instance can be reduced to 220.01KB, only 57.3% of BLS scheme.

关键词： zero knowledge proof ISIS commitment scheme

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Privacy-Preserving Social Media With Unlinkability and Disclosure

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IEEE ACCESS 2023年 11卷 28955-28965页

作者： Miyaji, Hideaki Hsu, Po-Chu Miyaji, Atsuko Osaka Univ Grad Sch Engn Suita Osaka 0650871 Japan JAIST Nomi Ishikawa 9231292 Japan

Social media (SM) has become a primary communication tool in the modern world, with an ever-increasing volume of users. Many SM users use anonymous nicknames as their public usernames. However, Zhang et al. (2018) were able to demonstrate an attack that can identify users from the contents of their posts. This attack is caused by the fact that two different posts can be guessed to be the same user. Such linking of different posts is called a linkable feature. On the other hand, usually post under an anonymous nickname, but when a post is thrust into the limelight, we may want to claim the post as our own. Unfortunately, however, current SM offers only two options: using an anonymous nickname or publishing under our own name. In other words, the function of disclosure, which is to make some posts public even though they are usually anonymous, has not been realized in existing SM. In this paper, we propose a SM with unlinkability and disclosure simultaneously, which is achieved by applying a commitment scheme. A commitment scheme consists of commitment and decommitment phases. As for unlinkability, we newly introduce a one-time post name, which is a commitment value of nickname and post. As for disclosure, we use a decommitment phase to one-time post name. We also have demonstrated that our SM is practically feasible.

关键词： Social networking (online) Security Privacy Probabilistic logic Public key Blogs Servers Homomorphic encryption Cryptography Cryptographic scheme commitment scheme homomorphic encryption ring signature unlinkable posts social media

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Somewhere Statistically Binding commitment schemes with Applications 25th

Somewhere Statistically Binding Commitment Schemes with Appl...

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25th International Conference on Financial Cryptography and Data Security (FC)

作者： Fauzi, Prastudy Lipmaa, Helger Pindado, Zaira Siim, Janno Simula UiB Bergen Norway Univ Tartu Tartu Estonia Univ Pompeu Fabra Barcelona Spain

ISBN: (纸本)9783662643228;9783662643211

We define a new primitive that we call a somewhere statistically binding (SSB) commitment scheme, which is a generalization of dual-mode commitments but has similarities with SSB hash functions (Hubacek and Wichs, ITCS 2015) without local opening. In (existing) SSB hash functions, one can compute a hash of a vector v that is statistically binding in one coordinate of v. Meanwhile, in SSB commitment schemes, a commitment of a vector v is statistically binding in some coordinates of v and is statistically hiding in the other coordinates. The set of indices where binding holds is predetermined but known only to the commitment key generator. We show that the primitive can be instantiated by generalizing the succinct Extended Multi-Pedersen commitment scheme (Gonzalez et al., Asiacrypt 2015). We further introduce the notion of functional SSB commitment schemes and, importantly, use it to get an efficient quasi-adaptive NIZK for arithmetic circuits and efficient oblivious database queries.

关键词： commitment scheme Oblivious transfer QA-NIZK SSB

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commitments via Physically Related Functions

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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2023年 18卷 1497-1508页

作者： Boyapally, Harishma Patranabis, Sikhar Mukhopadhyay, Debdeep Indian Inst Technol Kharagpur Kharagpur 721302 India Swiss Fed Inst Technol CH-8092 Zurich Switzerland IBM Res Bengaluru 560045 India

commitment schemes are one of the basic building blocks to construct secure protocols for multi party computation. Many recent works are exploring hardware primitives like physically unclonable functions to build keyless cryptographic protocols, with minimal assumptions. The asymmetric nature and non-invertibility property of PUFs are widely exploited to build oblivious transfer protocols that are extended to build bit-commitment schemes. However, these schemes require the physical transfer of the PUF device between the interacting parties. In this work, we introduce a new class of hardware-based primitives called physically related functions that enable hardware circuits to securely communicate with each other over insecure channels. We propose a bit-commitment protocol based on this hardware primitive without needing any physical transfer. Our scheme is statistically hiding and computationally binding, requiring only one round of communication while being practically deployable. We explore the security properties of physically related functions, under which we prove the security of our scheme. We experimentally show that it is impossible to break the security of the scheme with more than negligible probability.

关键词： Physical unclonable function physically related function (PReF) multi-party computation (MPC) commitment scheme

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A verifiable scheme for differential privacy based on zero-knowledge proofs

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JOURNAL OF KING SAUD UNIVERSITY-COMPUTER AND INFORMATION SCIENCES 2025年第3期37卷 1-15页

作者： Wei, Jianqi Chen, Yuling Yang, Xiuzhang Luo, Yun Pei, Xintao Guizhou Univ State Key Lab Publ Big Data Guiyang 550025 Peoples R China Guizhou Univ Coll Comp Sci & Technol Guiyang 550025 Peoples R China

The protection of personal privacy has become a paramount issue in the field of data science, with its significance continuously rising. Differential privacy technology has garnered significant attention for its effectiveness in preserving individual privacy. However, the implementation of differential privacy relies on a degree of trust in the entities or individuals executing the algorithms. This paper proposes an innovative solution: a verifiable differential privacy mechanism based on zero-knowledge proofs. This approach integrates differential privacy with zero-knowledge proof technology to not only verify the correctness of the differential privacy techniques but also enhance the transparency and reliability of the algorithms. Additionally, we have designed a publicly verifiable data release scheme that integrates commitment mechanisms and range proofs, ensuring that the range of published data noise does not exceed predetermined thresholds, thereby ensuring the utility of the data. Compared to other verifiable differential privacy solutions, our approach is unique in that it does not rely on the number of participants but is solely dependent on the precision of the data. This means that our computational cost will not increase with the addition of more participants. Finally, we conducted a performance evaluation of the solution, which only took 700ms to complete a single verification. On average, there was a 6% reduction in expectation and a 40% reduction in variance, demonstrating the enhancement of its data utility and the feasibility and effectiveness in practical applications.

关键词： Differential privacy commitment scheme Zero-knowledge proofs Verifiable Data utility

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Avoiding trusted setup in isogeny-based commitments

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DESIGNS CODES AND CRYPTOGRAPHY 2025年 1-19页

作者： Saah, Gustave Tchoffo Fouotsa, Tako Boris Fouotsa, Emmanuel Nkuimi-Jugnia, Celestin Univ Yaounde I Dept Math Yaounde Cameroon Univ Bamenda Ctr Cybersecur & Math Cryptol Bamenda Cameroon Ecole Polytech Fed Lausanne Lausanne Switzerland

In 2021, Sterner proposed a commitment scheme based on supersingular isogenies. For this scheme to be binding, one relies on a trusted party to generate a starting supersingular elliptic curve of unknown endomorphism ring. In fact, the knowledge of the endomorphism ring allows one to compute an endomorphism of degree a power of a given small prime. Such an endomorphism can then be split into two to obtain two different messages with the same commitment. This is the reason why one needs a curve of unknown endomorphism ring, and the only known way to generate such supersingular curves is to rely on a trusted party or on some expensive multiparty computation. We observe that if the degree of the endomorphism in play is well chosen, then the knowledge of the endomorphism ring is not sufficient to efficiently compute such an endomorphism and in some particular cases, one can even prove that endomorphism of a certain degree do not exist. Leveraging these observations, we adapt Sterner's commitment scheme in such a way that the endomorphism ring of the starting curve can be known and public. This allows us to obtain isogeny-based commitment schemes which can be instantiated without trusted setup requirements.

关键词： Supersingular isogenies Post-quantum cryptography Isogeny-based cryptography commitment scheme

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Toothpicks: More Efficient Fork-Free Two-Round Multi-signatures 43rd

Toothpicks: More Efficient Fork-Free Two-Round Multi-signatu...

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43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT)

作者： Pan, Jiaxin Wagner, Benedikt Univ Kassel Kassel Germany Saarland Univ CISPA Helmholtz Ctr Informat Secur Saarbrucken Germany

ISBN: (纸本)9783031587153;9783031587160

Tightly secure cryptographic schemes can be implemented with standardized parameters, while still having a sufficiently high security level backed up by their analysis. In a recent work, Pan and Wagner (Eurocrypt 2023) presented the first tightly secure two-round multi-signature scheme without pairings, called Chopsticks. While this is an interesting first theoretical step, Chopsticks is much less efficient than its non-tight counterparts. In this work, we close this gap by proposing a new tightly secure two-round multi-signature scheme that is as efficient as non-tight schemes. Our scheme is based on the DDH assumption without pairings. Compared to Chopsticks, we reduce the signature size by more than a factor of 3 and the communication complexity by more than a factor of 2. Technically, we achieve this as follows: (1) We develop a new pseudorandom path technique, as opposed to the pseudorandom matching technique in Chopsticks. (2) We construct a more efficient commitment scheme with suitable properties, which is an important primitive in both our scheme and Chopsticks. Surprisingly, we observe that the commitment scheme does not have to be binding, enabling our efficient construction.

关键词： Multi-Signatures Tightness commitment scheme Lossy Identification

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