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Lattice-Based Zero-Knowledge Arguments for Integer Relations [chapter]

Benoît Libert, San Ling, Khoa Nguyen, Huaxiong Wang
2018 Lecture Notes in Computer Science  
We provide lattice-based protocols allowing to prove relations among committed integers.  ...  While our protocol for additive relations only handles nonnegative integers, it suffices for many applications, such as arguments of inequalities among committed integers, range membership for public/hidden  ...  Zero-Knowledge Arguments for Integer Additions This section presents our lattice-based ZK argument system for additive relation among committed integers.  ... 
doi:10.1007/978-3-319-96881-0_24 fatcat:5nlajnkxqfdy5ffnitomdhh5jm

Implementing confidential transactions with lattice techniques

Huang Zhang, Fangguo Zhang, Baodian Wei, Yusong Du
2019 IET Information Security  
In this study, inspired by the notion of commitments to polynomials and zero-knowledge arguments of knowledge for the inhomogeneous short integer solution problem, the authors give an approach to implement  ...  confidential transactions using lattice techniques.  ...  Acknowledgments The authors are grateful to the anonymous reviewers for their valuable suggestions and comments on this paper.  ... 
doi:10.1049/iet-ifs.2018.5491 fatcat:rhtzdh4u5jelvhu7t3ju7wlhjm

Lattice-Based Simulatable VRFs: Challenges and Future Directions

Carlo Brunetta, Bei Liang, Aikaterini Mitrokotsa
2018 Journal of Internet Services and Information Security  
In this short paper, we provide our insights on constructing a lattice-based simulatable verifiable random function (sVRF) using non interactive zero knowledge arguments and dual-mode commitment schemes  ...  Lattice-based cryptography is evolving rapidly and is often employed to design cryptographic primitives that hold a great promise to be post-quantum resistant and can be employed in multiple application  ...  We are grateful to the anonymous reviewers for their insightful comments, suggestions, discussions and the new literature-directions provided.  ... 
doi:10.22667/jisis.2018.11.30.057 dblp:journals/jisis/BrunettaLM18 fatcat:y2vfafveezftljtg33beq3uh2u

A Lattice-Based Group Signature Scheme with Message-Dependent Opening [chapter]

Benoît Libert, Fabrice Mouhartem, Khoa Nguyen
2016 Lecture Notes in Computer Science  
These components are tied together using suitable zero-knowledge argument systems. Lattice-based cryptography.  ...  One of the cited reasons explaining this efficiency gap is the fact that zero-knowledge proofs [21] for lattice-related languages [21, 33, 6] remain less effective than those in groups with a bilinear  ...  The supporting zero-knowledge argument system is constructed in Section 3. In Section 4, we present our lattice-based GS-MDO scheme. Background Notations.  ... 
doi:10.1007/978-3-319-39555-5_8 fatcat:lmkrdymtnfewpbncemsu6wrbwm

Zero-Knowledge Password Policy Check from Lattices [chapter]

Khoa Nguyen, Benjamin Hong Meng Tan, Huaxiong Wang
2017 Lecture Notes in Computer Science  
To this end, we introduce a new randomised password hashing scheme for ASCII-based passwords and design an accompanying zero-knowledge protocol for policy compliance.  ...  In this work, we construct the first post-quantum ZKPPC using lattice-based tools.  ...  We would like to thank the anonymous reviewers of ISC 2017 for helpful comments.  ... 
doi:10.1007/978-3-319-69659-1_6 fatcat:jwjf3mwq7zdc5mzub7oq4xygzu

Zero-Knowledge Password Policy Check from Lattices [article]

Khoa Nguyen and Benjamin Hong Meng Tan and Huaxiong Wang
2018 arXiv   pre-print
To this end, we introduce a new randomised password hashing scheme for ASCII-based passwords and design an accompanying zero-knowledge protocol for policy compliance.  ...  In this work, we construct the first post-quantum ZKPPC using lattice-based tools.  ...  We would like to thank the anonymous reviewers of ISC 2017 for helpful comments.  ... 
arXiv:1802.05004v1 fatcat:kjv243zjpzdjlbrloidua4cf4e

Practical UC-Secure Zero-Knowledge Smart Contracts [article]

Jayamine Alupotha, Xavier Boyen
2022 IACR Cryptology ePrint Archive  
Problem (DLP) targeting Ring/Aggregable CT like Monero and Mimblewimble, and (2) "CIP-SIS" from Approximate (Ring-Modular-) Shortest Integer Solution Problem (Approx-SIS) aiming at lattice-based Ring/  ...  Zero-knowledge defines that verifier(s) learns nothing but predefined statement(s); e.g., verifiers learn nothing except the program's path for the respective transaction in a zero-knowledge contract program  ...  Zero-Knowledge and Intra-Privacy. Theorem 6 proves zero-knowledge of CIP-DLP's range proofs. We prove zero-knowledge and intra-privacy by contradiction for the rest of primitive relations.  ... 
dblp:journals/iacr/AlupothaB22 fatcat:krt6twb7c5g5zg4luuluuyuot4

Noninteractive Zero Knowledge Proof System for NP from Ring LWE [article]

Wenping Ma
2019 IACR Cryptology ePrint Archive  
to a non-interactive argument.  ...  Our construction can also be instantiated in two possible modes, yielding a NIZK that is either computationally sound and statistically zero knowledge in the common random string model, or vice-versa in  ...  A noninteractive zero knowledge (NIZK) argument system Π for an NP relation R is a tuple of PPT algorithms (Setup, Prove, Verify) having the following interfaces: 1.  ... 
dblp:journals/iacr/Ma19 fatcat:quzs7obywvhrfddq3ttxieydmm

A lattice-based batch identification scheme

Rosemberg Silva, Pierre-Louis Cayrel, Richard Lindner
2011 2011 IEEE Information Theory Workshop  
This paper presents a batch version of the lattice-based identification scheme known as CLRS.  ...  We use the hardness of a lattice problem, namely the Inhomogeneous Small Integer Solution problem (I-SIS), as security assumption.  ...  Given a lattice L, the Shortest Vector Problem consists in finding a non-zero lattice vector with the minimum norm. Definition 2.3 (Small Integer Solution -SIS).  ... 
doi:10.1109/itw.2011.6089381 dblp:conf/itw/SilvaCL11 fatcat:ot5zcjzxfracdm3bcn6vregzkq

Post-quantum cryptography: lattice identification schemes

ROSEMBERG SILVA, PIERRE-LOUIS CAYREL, JOHANNES BUCHMANN
2011 Publicationes mathematicae (Debrecen)  
This survey presents an overview and a comparative analysis of the state of art in post-quantum identification schemes based on lattices.  ...  Furthermore, we propose an adaptation of the HB family of identification in a lattice context.  ...  Zero-knowledge proof of knowledge.  ... 
doi:10.5486/pmd.2011.5311 fatcat:qynhz2ewlzaznnxbb4h6cclbuu

Improved Zero-Knowledge Identification with Lattices [chapter]

Pierre-Louis Cayrel, Richard Lindner, Markus Rückert, Rosemberg Silva
2010 Lecture Notes in Computer Science  
Efficiency improvement for NTRU. In A. Alkassar and J. H. Siekmann, editors, Sicherheit 2008: Sicherheit, Schutz und Zuverlässigkeit. Konferenzband der 4.  ...  Lattice-Based Zero-Knowledge Identification.  ...  In contrast to typical zero-knowledge schemes, Lyubashevsky's construction is based on a witness-indistinguishable (not zero-knowledge) proof of knowledge.  ... 
doi:10.1007/978-3-642-16280-0_1 fatcat:qphlhyww45avzim6wyo7bvnira

Zero-Knowledge Arguments for Matrix-Vector Relations and Lattice-Based Group Encryption [chapter]

Benoît Libert, San Ling, Fabrice Mouhartem, Khoa Nguyen, Huaxiong Wang
2016 Lecture Notes in Computer Science  
We believe our proof system to be useful in other applications involving zero-knowledge proofs in the lattice setting.  ...  As a crucial component of our system, we describe a new zero-knowledge argument system allowing to demonstrate that a given ciphertext is a valid encryption under some hidden but certified public key,  ...  Acknowledgements We thank Damien Stehlé for useful discussions and the reviewers for useful comments.  ... 
doi:10.1007/978-3-662-53890-6_4 fatcat:24pjz22dxfgldnyd6e53s2yxpi

Improved Zero-Knowledge Identification with Lattices

Pierre-Louis Cayrel, Richard Lindner, Markus Rückert, Rosemberg Silva
2012 Tatra Mountains Mathematical Publications  
One of the main hardness assumption for ID schemes based on lattices is the short integer solution (SIS) problem.  ...  In contrast to typical zero-knowledge schemes, Lyubashevsky's construction is based on a witness-indistinguishable (not zero-knowledge) proof of knowledge. Furthermore, it has no soundness error.  ...  We are grateful to an anonymous referee for helpful comments.  ... 
doi:10.2478/v10127-012-0038-4 fatcat:xt42dbd7dvg4lhycgdg7slux3e

Cuproof: Range Proof with Constant Size

Cong Deng, Lin You, Xianghong Tang, Gengran Hu, Shuhong Gao
2022 Entropy  
Zero-Knowledge Proof is widely used in blockchains. For example, zk-SNARK is used in Zcash as its core technology to identifying transactions without the exposure of the actual transaction values.  ...  Bootle et al. used the inner product method and recursion to construct an efficient Zero-Knowledge Proof in 2016.  ...  Acknowledgments: We thank the anonymous referees for their valuable comments for the improvement of this paper. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e24030334 pmid:35327845 pmcid:PMC8947667 fatcat:vwjmt73ryjbulac2td4pc5pi4y

Zero-Knowledge Arguments for Lattice-Based Accumulators: Logarithmic-Size Ring Signatures and Group Signatures Without Trapdoors [chapter]

Benoît Libert, San Ling, Khoa Nguyen, Huaxiong Wang
2016 Lecture Notes in Computer Science  
Under the Small Integer Solution assumption, we provide zero-knowledge arguments showing possession of a hash chain.  ...  In the lattice setting, currently known instantiations of the primitive are based on Merkle trees, which do not interact well with zero-knowledge proofs.  ...  Acknowledgements We thank Damien Stehlé for useful discussions and the anonymous reviewers of EUROCRYPT 2016 for helpful comments.  ... 
doi:10.1007/978-3-662-49896-5_1 fatcat:oyaa6tifrra75jt6dwhgfarm5e
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