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Verification Protocols with Sub-Linear Communication for Polynomial Matrix Operations [article]

David Lucas, Vincent Neiger, Clément Pernet, Daniel S. Roche, Johan Rosenkilde
2019 arXiv   pre-print
The main tools we use are reductions to existing linear algebra verification protocols and a new protocol to verify that a given vector is in the F[x]-row space of a given matrix.  ...  For the sake of efficiency, and because many of the properties we verify are specific to matrices over a principal ideal domain, we cannot simply rely on previously-developed linear algebra protocols for  ...  Horizon 2020 European Research Infrastructures project under award #676541, by the IFD-Science 2017 research program of the Institut Franais du Danemark, and by the CNRS-INS2I Institute through its program for  ... 
arXiv:1807.01272v2 fatcat:fcuqa3x2xva6ldp6qo34nopmp4

Linear Time Interactive Certificates for the Minimal Polynomial and the Determinant of a Sparse Matrix [article]

Jean-Guillaume Dumas, Emmanuel Thomé
2019 arXiv   pre-print
verification complexity requires a single matrix-vector multiplication and a linear number of extra field operations.  ...  We then combine these two techniques to give algorithms that compute certificates for the determinant, and thus for the characteristic polynomial, whose Monte Carlo verification complexity is therefore  ...  The verification procedure for the rank is essentially optimal, it requires two matrix-vector products and n 1+o(1) additional operations; while the verification of the characteristic polynomial after  ... 
arXiv:1602.00810v2 fatcat:5teuh5gy4feqfkty6ivyz7anua

Linear Time Interactive Certificates for the Minimal Polynomial and the Determinant of a Sparse Matrix

Jean-Guillaume Dumas, Erich Kaltofen, Emmanuel Thomé, Gilles Villard
2016 Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16  
verification complexity requires a single matrix-vector multiplication and a linear number of extra field operations.  ...  We then combine these two techniques to give algorithms that compute certificates for the determinant, and thus for the characteristic polynomial, whose Monte Carlo verification complexity is therefore  ...  As this reduction was linear for Victor, this then provides now also a linear time verification procedure for the characteristic polynomial: Figure 1 : 1 A simple sparse determinant protocol Lemma 4  ... 
doi:10.1145/2930889.2930908 dblp:conf/issac/DumasKTV16 fatcat:os5xbgcehvg55chdlsp25ijlju

Certificates for triangular equivalence and rank profiles [article]

Jean-Guillaume Dumas, Clément Pernet
2019 arXiv   pre-print
Then we propose interactive certificates for the same problems whose Monte Carlo verification complexity requires a small constant number of matrix-vector multiplications, a linear space, and a linear  ...  These certificates enable to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a negligible overall overhead.  ...  Table 1 compares linear quadratic volumes of communication, as well as sub-cubic (PLUQ, CHARPOLY) or quadratic matrix operations (one matrix-vector multiplication with a dense matrix is denoted fgemv)  ... 
arXiv:1702.03755v2 fatcat:2bge6osbj5bxrnoaug2ez6puzu

Certificates for Triangular Equivalence and Rank Profiles

Jean-Guillaume Dumas, David Lucas, Clément Pernet
2017 Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17  
Then we propose interactive certificates for the same problems whose Monte Carlo verification complexity requires a small constant number of matrixvector multiplications, a linear space, and a linear number  ...  These certificates enable to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a negligible overall overhead.  ...  Table 1 compares linear quadratic volumes of communication, as well as sub-cubic (PLUQ, CHARPOLY) or quadratic matrix operations (one matrix-vector multiplication with a dense matrix is denoted fgemv)  ... 
doi:10.1145/3087604.3087609 dblp:conf/issac/DumasLP17 fatcat:mkf46nhwuze7feqkfd4mewseaa

Interactive certificate for the verification of Wiedemann's Krylov sequence: application to the certification of the determinant, the minimal and the characteristic polynomials of sparse matrices [article]

Jean-Guillaume Dumas, Erich Kaltofen, Emmanuel Thomé
2015 arXiv   pre-print
For instance, if the n× n input matrix is sparse with n 1+o(1) non-zero entries, the computation of the sequence is quadratic in the dimension of the matrix while the computation of the minimal polynomial  ...  Certificates to a linear algebra computation are additional data structures for each output, which can be used by a-possibly randomized- verification algorithm that proves the correctness of each output  ...  Prover Communications Verifier Z Check Z T Check T 1.8 hours 1.9 GB 5.6 s 14.5 s 7.0 s 6.0 s Table 2 : Verification for a matrix with m = n = 253008, 759022 non-zeroes and of compressed size of 3.8MB.  ... 
arXiv:1507.01083v1 fatcat:o2fnsk2nq5cy3lspd27fgrfzty

Elimination-based certificates for triangular equivalence and rank profiles

Jean-Guillaume Dumas, Erich Kaltofen, David Lucas, Clément Pernet
2019 Journal of symbolic computation  
number of extra field operations , with a linear number of interactions.  ...  Then we propose interactive certificates for the same problems whose Monte Carlo verification complexity requires a small constant number of matrix-vector multiplications, a linear space, and a linear  ...  Table 1 compares linear and quadratic communications, as well as sub-cubic (PLUQ, CharPoly) or quadratic matrix operations.  ... 
doi:10.1016/j.jsc.2019.07.013 fatcat:dfco7vxniratrmum6xydrbpvcq

VESPo: Verified Evaluation of Secret Polynomials [article]

Jean-Guillaume Dumas, Daniel S. Roche
2022 arXiv   pre-print
Our methods rely only on linearly homomorphic encryption and pairings, and preliminary timing results indicate reasonable performance for polynomials with millions of coefficients, and efficient DPoR with  ...  Our protocols support two important features: the polynomial itself can be encrypted on the server, and it can be dynamically updated by changing individual coefficients cheaply without redoing the entire  ...  Acknowledgments We thank Gaspard Anthoine for providing us with some preliminary comparisons with the PBC and libpaillier libraries and Anthony Martinez for the libsnark baseline benchmarking.  ... 
arXiv:2110.02022v4 fatcat:elzgs5pnc5h5lp245vz3ubuawm

On Information-Theoretic Classical Verification of Quantum Computers [article]

Ayal Green
2021 arXiv   pre-print
We define a family of protocols which seem natural for verifying quantum computations and generalizes such known protocols, namely those of [AAV13,AG17].  ...  Quantum inspired protocols e.g.  ...  Also, many thanks to Dorit Aharonov for useful discussions both during and prior to this work, and to Zuzana Gavorova for useful discussions.  ... 
arXiv:2105.05942v1 fatcat:p2geistetjfofmzbhrrshuwpre

A chaotic based integrity verification and encryption model for real-time VANET

Kareemulla Shaik, Dr. Md. Ali Hussain
2019 Indonesian Journal of Electrical Engineering and Computer Science  
In this paper, an integrity verification model and non-linear double encryption model were proposed and implemented on large geographical VANET map.  ...  Experimental results proved that the proposed security model has less computation cost for encryption model and higher bit change during integrity verification compared to the existing approaches.</p>  ...  Step 6: In the transformation box, the following operations are performed Initialize randomized permutation matrix as pkey. Partition the byte array block into sub-blocks of 32 bits each.  ... 
doi:10.11591/ijeecs.v14.i3.pp1425-1432 fatcat:d52fz46xozbflhfzx4fjkiqj4u

Essentially optimal interactive certificates in linear algebra [article]

Jean-Guillaume Dumas, Erich Kaltofen
2019 arXiv   pre-print
For example, if the n× n input matrix is sparse with n^1+o(1) non-zero entries, our rank certificate can be verified in n^1+o(1) field operations.  ...  All our certificates are based on interactive verification protocols with the interaction removed by a Fiat-Shamir identification heuristic.  ...  For instance, if the matrix is sparse with only n1+o(1) non- zero elements, then the certificate verification is essentially linear. 2 Notions of certificate The ideas in this paper arise from linear  ... 
arXiv:1401.4567v3 fatcat:5crvg3ov4zcorcoizxhdmjqwfa

Efficient Arguments without Short PCPs

Yuval Ishai, Eyal Kushilevitz, Rafail Ostrovsky
2007 Proceedings - IEEE Conference on Computational Complexity  
Current constructions of efficient argument systems combine a short (polynomial size) PCP with a cryptographic hashing technique.  ...  (JACM 1998) yields a simple argument system for NP in which the communication from the prover to the verifier only includes a constant number of short encryptions.  ...  We are grateful to Eli Ben-Sasson and Prahladh Harsha for enlightening discussions on the efficiency of short PCPs, and to Rafael Pass for pointing out the relevance of [33] .  ... 
doi:10.1109/ccc.2007.10 dblp:conf/coco/IshaiKO07 fatcat:cxpvnlwrw5clnmll6yhgmhuyse

Breaking Blockchain's Communication Barrier with Coded Computation [article]

Canran Wang, Netanel Raviv
2022 arXiv   pre-print
With limited bandwidth, the communication complexity for nodes to process a block scales with the growing network size and hence becomes the limiting factor of blockchain's performance.  ...  Third, we propose a novel 2-dimensional sharding strategy, which inherently supports cross-shard transactions, alleviating the need for complicated communication protocols between shards, while keeping  ...  Although it is a promising platform for various applications, its performance is sub-optimal due to the limited bandwidth and the scaling communication complexity, in terms of message complexity and bit  ... 
arXiv:2204.00979v1 fatcat:r23g6gn255cjfgojxtlv6vcbbi

Essentially optimal interactive certificates in linear algebra

Jean-Guillaume Dumas, Erich Kaltofen
2014 Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14  
For example, if the n × n input matrix is sparse with n 1+o(1) non-zero entries, our rank certificate can be verified in n 1+o(1) field operations.  ...  All our certificates are based on interactive verification protocols with the interaction removed by a Fiat-Shamir identification heuristic.  ...  Acknowledgments We thank Brice Boyer , Shafi Goldwasser , Clément Pernet , Jean-Louis Roch , Guy Rothblum , Justin Thaler and the referees for their helpful comments.  ... 
doi:10.1145/2608628.2608644 dblp:conf/issac/DumasK14 fatcat:kaa52pbrwvao7itggjkhqbpof4

Sub-linear Lattice-Based Zero-Knowledge Arguments for Arithmetic Circuits [chapter]

Carsten Baum, Jonathan Bootle, Andrea Cerulli, Rafael del Pino, Jens Groth, Vadim Lyubashevsky
2018 Lecture Notes in Computer Science  
For a circuit with N gates, the communication complexity of our protocol is O N λ log 3 N , where λ is the security parameter.  ...  A key component of our construction is a surprisingly simple zero-knowledge proof for pre-images of linear relations whose amortized communication complexity depends only logarithmically on the number  ...  Sub-linear communication is achieved by setting parameters as in Table 2 Linear Constraint Argument Description.  ... 
doi:10.1007/978-3-319-96881-0_23 fatcat:ico53lgysjeodg4v3c5b37juwe
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