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Relaxed Lattice-Based Signatures with Short Zero-Knowledge Proofs [chapter]

Cecilia Boschini, Jan Camenisch, Gregory Neven
2018 Lecture Notes in Computer Science  
with zero-knowledge proofs.  ...  most efficient zero-knowledge proofs for lattices.  ...  This work was supported by the ERC under grant #321310 PERCY) and the SNF under grant #200021 157080 (Efficient Lattice-Based Cryptographic Protocols).  ... 
doi:10.1007/978-3-319-99136-8_1 fatcat:rydsvnrfcbh2bewg3zbbuf3cyq

One-Shot Verifiable Encryption from Lattices [chapter]

Vadim Lyubashevsky, Gregory Neven
2017 Lecture Notes in Computer Science  
Existing lattice-based verifiable encryption schemes, and even just proofs of knowledge of the encrypted data, require parallel composition of proofs to reduce the soundness error, resulting in proof sizes  ...  This relaxation is sufficient for many applications and we illustrate this with example usages of our scheme in key escrow and verifiably encrypted signatures.  ...  At the heart of the construction is a zero-knowledge proof of knowledge that, given an s ∈ R k satisfying the relation As = t mod q, (8) Algorithm 1 "Fiat-Shamir with Aborts" zero-knowledge proof of knowledge  ... 
doi:10.1007/978-3-319-56620-7_11 fatcat:7l5izxzvubfqbah2motar5j73u

Better Zero-Knowledge Proofs for Lattice Encryption and Their Application to Group Signatures [chapter]

Fabrice Benhamouda, Jan Camenisch, Stephan Krenn, Vadim Lyubashevsky, Gregory Neven
2014 Lecture Notes in Computer Science  
We then show how our new protocol can be combined with a proof of knowledge for Pedersen commitments in order to prove that the committed value is the same as the encrypted one.  ...  Efficient lattice-based constructions are known for signature and encryption schemes.  ...  Things do not improve for lattice-based proofs of knowledge even if one considers ideal lattices.  ... 
doi:10.1007/978-3-662-45611-8_29 fatcat:pxvk6mwpp5c57dzsf6opwljfda

Efficient Hybrid Exact/Relaxed Lattice Proofs and Applications to Rounding and VRFs [article]

Muhammed F. Esgin, Ron Steinfeld, Dongxi Liu, Sushmita Ruj
2022 IACR Cryptology ePrint Archive  
In this work, we study hybrid exact/relaxed zero-knowledge proofs from lattices, where the proved relation is exact in one part and relaxed in the other.  ...  We first introduce a general framework, LANES + , for realizing such hybrid proofs efficiently by combining standard relaxed proofs of knowledge RPoK and the LANES framework (due to a series of works in  ...  For efficient lattice-based zero-knowledge proofs, it is necessary to relax the opening definition and introduce a relaxation factor f . We let F ⊆ R be the set of acceptable relaxation factors.  ... 
dblp:journals/iacr/EsginSLR22 fatcat:2f4rps2ygzc4rluqo2ggaexip4

Lattice-Based Group Signatures with Logarithmic Signature Size [chapter]

Fabien Laguillaumie, Adeline Langlois, Benoît Libert, Damien Stehlé
2013 Lecture Notes in Computer Science  
(Asiacrypt 2010) suggested the first realization of group signatures based on lattice assumptions in the random oracle model.  ...  with a signature opening oracle).  ...  Statistical zero-knowledge proofs with efficient provers: Lattice problems and more. In Proc. of Crypto, pages 282-298, 2003. 41. C. Peikert.  ... 
doi:10.1007/978-3-642-42045-0_3 fatcat:7lofdls57bdmroxmnfvvnxitai

Efficient and Post-Quantum Zero-Knowledge Proofs for Blockchain Confidential Transaction Protocols [article]

Shang Gao, Tianyu Zheng, Yu Guo, Bin Xiao
2021 IACR Cryptology ePrint Archive  
We propose new zero-knowledge proofs for efficient and postquantum ring confidential transaction (RingCT) protocols based on lattice assumptions in Blockchain systems.  ...  First, we introduce an innerproduct based linear equation satisfiability approach for balance proofs with a wide range (e.g. 64-bit precision).  ...  Xingye LU from the University of Hong Kong for the helpful technical discussions about lattice-based cryptography as well as Dr. Zuoxia Yu from University of Wollongong Dr.  ... 
dblp:journals/iacr/GaoZGX21 fatcat:tuothoh3evgw5lefp2btnks234

On sigma protocols with helper for MQ and PKP, fishy signature schemes and more [article]

Ward Beullens
2019 IACR Cryptology ePrint Archive  
We apply the Fiat-Shamir transform to obtain signature schemes with security proof in the QROM.  ...  ), are more efficient than existing signatures based on the MQ problem and the Permuted Kernel Problem.  ...  Ligero and Aurora proof systems respectively.  ... 
dblp:journals/iacr/Beullens19 fatcat:b44wsexjujad5jesygd6n4z3h4

Practical Post-Quantum Few-Time Verifiable Random Function with Applications to Algorand [article]

Muhammed F. Esgin, Veronika Kuchta, Amin Sakzad, Ron Steinfeld, Zhenfei Zhang, Shifeng Sun, Shumo Chu
2020 IACR Cryptology ePrint Archive  
We find that, due to the significant increase in the communication size in comparison to classical constructions, which is inherent in all existing lattice-based schemes, the throughput in LB-VRF-based  ...  In particular, in a medium-sized network with 100 nodes, our platform records a 1.14× to 3.4× reduction in throughput, depending on the accompanying signature used.  ...  However, again due to the relaxed nature of the underlying zero-knowledge proof that we use to achieve short proofs, the uniqueness does not immediately follow.  ... 
dblp:journals/iacr/EsginKSSZSC20 fatcat:wy2dj6upmvcb5aejsmqh6rjari

Proof-of-possession for KEM certificates using verifiable generation [article]

Tim Güneysu, Philip Hodges, Georg Land, Mike Ounsworth, Douglas Stebila, Greg Zaverucha
2022 IACR Cryptology ePrint Archive  
interest for improving efficiency of zero-knowledge proofs for other lattice-based statements.  ...  direct lattice-based ZK proofs for Kyber.  ...  Existing Zero-Knowledge Techniques The obvious approach for building a non-interactive proof of possession for a lattice-based KEM key would be to use zero-knowledge tools.  ... 
dblp:journals/iacr/GuneysuHLOSZ22 fatcat:vw2xdavqjngnndnwsnabieskum

CRYSTALS-Dilithium: A Lattice-Based Digital Signature Scheme

Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim Lyubashevsky, Peter Schwabe, Gregor Seiler, Damien Stehlé
2018 Transactions on Cryptographic Hardware and Embedded Systems  
In this paper, we present the lattice-based signature scheme Dilithium, which is a component of the CRYSTALS (Cryptographic Suite for Algebraic Lattices) suite that was submitted to NIST's call for post-quantum  ...  For the same security levels, our scheme has a public key that is 2.5X smaller than the previously most efficient lattice-based schemes that did not use Gaussians, while having essentially the same signature  ...  In that paper, it is actually proved that the underlying zero-knowledge proof is zero-knowledge and then the security of the signature scheme follows via black box transformations.  ... 
doi:10.13154/tches.v2018.i1.238-268 dblp:journals/tches/DucasKLLSSS18 fatcat:skxxtodhvfcwrfb3vq7sqwrjue

A Group Signature Scheme from Lattice Assumptions [chapter]

S. Dov Gordon, Jonathan Katz, Vinod Vaikuntanathan
2010 Lecture Notes in Computer Science  
In this work we give the first construction of a group signature scheme based on lattices (more precisely, the learning with errors assumption), in the random oracle model.  ...  Toward our goal, we construct a new algorithm for sampling a random superlattice of a given modular lattice together with a short basis, that may be of independent interest. * Work done while the authors  ...  A Group Signature Scheme Based on Lattices Definitions We adopt the definition of group signature schemes from the work of Bellare, Micciancio, and Warinschi [7] , with the relaxation suggested by Boneh  ... 
doi:10.1007/978-3-642-17373-8_23 fatcat:xesyps5jyza7vjtgwdbt5dd3gu

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.  ...  Our construction is proved secure in the standard model (assuming interaction in the proving phase) under the Learning-With-Errors (LWE) and Short-Integer-Solution (SIS) assumptions.  ...  We believe our zero-knowledge arguments to be of independent interest as they find applications in other protocols involving zero-knowledge proofs in lattice-based cryptography.  ... 
doi:10.1007/978-3-662-53890-6_4 fatcat:24pjz22dxfgldnyd6e53s2yxpi

Towards Practical Lattice-Based One-Time Linkable Ring Signatures [chapter]

Carsten Baum, Huang Lin, Sabine Oechsner
2018 Lecture Notes in Computer Science  
We show how to instantiate efficient zero-knowledge protocols that can be used to prove a number of relations among these commitments, and apply these in the context of lattice-based threshold cryptosystems  ...  We present an additively homomorphic commitment scheme with hardness based on the Ring-SIS problem.  ...  Fiat-shamir with aborts: Applications to lattice and factoring-based signatures.  ... 
doi:10.1007/978-3-030-01950-1_18 fatcat:ymdodcwgvzeutgenjzqi4g4omu

A code-based group signature scheme

Quentin Alamélou, Olivier Blazy, Stéphane Cauchie, Philippe Gaborit
2016 Designs, Codes and Cryptography  
Along with this work, we also introduce a new kind of proof of knowledge, Testable weak Zero Knowledge (TwZK), implicitly covered in the short version of this paper [1].  ...  Thus, many lattice-based constructions have been proposed such as [14] who first designed a lattice-based group signature scheme with both public key and signature size linear in the number of group members  ...  Proofs of knowledge meeting these requirements will be called Testable weak Zero-Knowledge (TwZK for short).  ... 
doi:10.1007/s10623-016-0276-6 fatcat:dbp7brdbs5hslptj5suxv7765e

A Compressed Σ-Protocol Theory for Lattices [article]

Thomas Attema, Ronald Cramer, Lisa Kohl
2021 IACR Cryptology ePrint Archive  
We show a lattice-based solution for commit-and-prove transparent circuit zero-knowledge (ZK) with polylog-communication, the first not depending on PCPs.  ...  The first gives a tight analysis of efficient knowledge extraction in case of non-constant rounds combined with poly-small challenge space, whereas the second shows that parallel repetition indeed forces  ...  Related Work Circuit ZK with Polylogarithmic Complexity from PCPs. A generic class of (zero-knowledge) proof systems is based on Probabilistically Checkable Proofs (PCPs).  ... 
dblp:journals/iacr/AttemaCK21 fatcat:h4vn55njejcptclyuq7naqjvlu
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