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From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again

Nir Bitansky, Ran Canetti, Alessandro Chiesa, Eran Tromer
2012 Proceedings of the 3rd Innovations in Theoretical Computer Science Conference on - ITCS '12  
Eran wishes to thank Shai Halevi for early discussions about using extractable collision resistance as a solution approach, and Daniele Micciancio for a discussion of lattice-based Knowledge of Knapsacks  ...  In publicly verifiable SNARGs, this multi-theorem soundness is automatically guaranteed; in designated verifier SNARGs, however, multi-theorem soundness needs to be required explicitly as an additional  ...  in Section 10.) 9.2 NIZK on top of SNARK Theorem 9.2.  ... 
doi:10.1145/2090236.2090263 dblp:conf/innovations/BitanskyCCT12 fatcat:2327yyhwrvgoblswnscyjsdtzm

Secure Multi-party Computation Minimizing Online Rounds [chapter]

Seung Geol Choi, Ariel Elbaz, Tal Malkin, Moti Yung
2009 Lecture Notes in Computer Science  
In this work we ask whether preprocessing can allow low latency (that is, small round) secure multi-party protocols that are universally-composable (UC).  ...  Secure Multi-party Computation (MPC).  ...  Theorem 1.  ... 
doi:10.1007/978-3-642-10366-7_16 fatcat:ol32ppiqynhmjfgxfu24k23whu

Short Non-interactive Zero-Knowledge Proofs [chapter]

Jens Groth
2010 Lecture Notes in Computer Science  
Theorem 2.  ...  Theorem 3.  ...  NIZK proof based on Naccache-Stern encryption. We will now give the full NIZK proof for circuit satisfiability.  ... 
doi:10.1007/978-3-642-17373-8_20 fatcat:3y6n2dqsafbzbacq5uixmvi32u

Threshold Cryptosystems from Threshold Fully Homomorphic Encryption [chapter]

Dan Boneh, Rosario Gennaro, Steven Goldfeder, Aayush Jain, Sam Kim, Peter M. R. Rasmussen, Amit Sahai
2018 Lecture Notes in Computer Science  
In particular, by applying this paradigm to a (non-threshold) lattice signature system, we obtain the first single-round threshold signature scheme from LWE. * This work is a merge of two closely related  ...  We next introduce a new concept, called a universal thresholdizer, from which many threshold systems are possible. We show how to construct a universal thresholdizer from our TFHE.  ...  However, our setting allows the use of NIZK with preprocessing [DMP88, LS90] , which can be constructed from one-way functions and therefore, can be instantiated from lattices.  ... 
doi:10.1007/978-3-319-96884-1_19 fatcat:33c2sxldq5b7xnkm7uigpqk3i4

Two Round Multiparty Computation via Multi-key FHE [chapter]

Pratyay Mukherjee, Daniel Wichs
2016 Lecture Notes in Computer Science  
(EUROCRYPT '12) showed how to achieve three rounds based on LWE and NIZKs, while Garg et al.  ...  honestbut-curious setting we only rely on the learning with errors (LWE) assumption, and in the fully malicious setting we additionally assume the existence of non-interactive zero knowledge arguments (NIZKs  ...  Constructing Threshold Multi-Key FHE We now give a high-level description of the MFHE construction and the threshold decryption protocol.  ... 
doi:10.1007/978-3-662-49896-5_26 fatcat:ylnb3mzo4bbu3douzogbugxqwu

Efficient SMC Protocol Based on Multi-Bit Fully Homomorphic Encryption

Zong-Wu Zhu, Ru-Wei Huang
2021 Applied Sciences  
From the non-interactive zero-knowledge proof, it can be concluded that the protocol is also safe under the malicious model.  ...  homomorphic encryption scheme that supports multi-bit encryption proposed by Chen Li et al. satisfies the key homomorphism.  ...  Preprocessing: Set parameter, ensuring that all participants share parameter settings. Choose a lattice dimension parameter n, where λ is the security parameter.  ... 
doi:10.3390/app112110332 fatcat:chfnpae22fakjfdg2vnbwih3gm

Universal Constructions and Robust Combiners for Indistinguishability Obfuscation and Witness Encryption [chapter]

Prabhanjan Ananth, Aayush Jain, Moni Naor, Amit Sahai, Eylon Yogev
2016 Lecture Notes in Computer Science  
Threshold Multi-key FHE We recall the definition of multi-key fully homomorphic encryption from [LTV12, CM15, MW16].  ...  The proof of the following theorem follows directly from the above lemma. Theorem 7.  ...  By a standard Chernoff bound we get that the probability that more than half are decrypted incorrectly is: Security follows from a standard hybrid argument (see [KMN + 14, Appendix B]).  ... 
doi:10.1007/978-3-662-53008-5_17 fatcat:hodmwzkxl5g47esxgmjuipxzza

Foundations of Homomorphic Secret Sharing

Elette Boyle, Niv Gilboa, Yuval Ishai, Huijia Lin, Stefano Tessaro, Marc Herbstritt
2018 Innovations in Theoretical Computer Science  
We establish limitations on information-theoretic multi-input HSS with short output shares via a relation with communication complexity.  ...  We prove Theorem 16 by combining the following steps; see full version for details. Step 1: (3,2)-HSS for 3Mult-Plus.  ...  Using the HSS-based worst-case to average-case reduction from Theorem 23, we get checkers M with the following feature: after an input-independent polynomial-time preprocessing, any computation f (x) can  ... 
doi:10.4230/lipics.itcs.2018.21 dblp:conf/innovations/BoyleGILT18 fatcat:g7bcmnhplvavri4eqzhkith6ce

Proof of All: Verifiable Computation in a Nutshell [article]

Mario Alessandro Barbara
2019 arXiv   pre-print
Furthermore, I expand on the future of Verifiable Computation, Universal proof compilers and "Proofs of All", by approaching the state-of-the-art zk-STARK construction from a more accessible and informal  ...  Post-Quantum Multi-Party a single proof can be generated using multiple inputs taken from different Provers.  ...  Flawed NIZK Zero-Knowledge and Non-Deniability The last remark noted that we're preventing Provers from being able to simulate protocol runs.  ... 
arXiv:1908.02327v2 fatcat:fdhmpzpnqfhprhijoy3zdradze

Post-quantum Privacy-Preserving Primitives Constructed with Symmetric Primitives

Maxime Buser
Theorem 3 (Anonymity).  ...  Theorem 9 (Anonymity).  ...  Additional definitions 111 • M − τ : number of preprocessing computations revealed.  ... 
doi:10.26180/19672167.v1 fatcat:5qpngs5nnrcd7ef23hbj53pl6i

Verifiable Computation in Practice: Tools and Protocols [article]

Ahmed Kosba
The challenges we address include the proof computation overhead at the prover's side, and the level of expertise expected from the programmers to write secure and efficient programs for VC.  ...  The case of multi-target contracts.  ...  However, existing estimates of concrete security for such schemes only extend to lattices over small finite fields, but do not a priori apply to lattices constructed over a SNARK's (much larger) native  ... 
doi:10.13016/5m0g-pw8a fatcat:537mkrooezfl7dw55bqct56oqa

On Improving Communication Complexity in Cryptography

Lisa Maria Kohl
(Gay, Hofheinz, Kohl, and Pan, EUROCRYPT, 2018) Another important area of cryptography is secure multi-party computation, where the goal [...]  ...  Cryptography from Lattices A lattice is a discrete subgroup of R n (for n ∈ N).  ...  Cryptography from Lattices. A lattice is a discrete subgroup of the n-dimensional space of real numbers.  ... 
doi:10.5445/ir/1000100363 fatcat:prdzjb46pbforgmk2uq225t7wq

Information Security in Big Data: Privacy and Data Mining

Lei Xu, Chunxiao Jiang, Jian Wang, Jian Yuan, Yong Ren
2014 IEEE Access  
In this paper, we view the privacy issues related to data mining from a wider perspective and investigate various approaches that can help to protect sensitive information.  ...  • Step 1: Data preprocessing.  ...  b: NAÏVE BAYESIAN CLASSIFICATION Naïve Bayesian classification is based on Bayes' theorem of posterior probability.  ... 
doi:10.1109/access.2014.2362522 fatcat:oxnmv2kjy5bllhotbkqvxd5rfu

Advances and Open Problems in Federated Learning [article]

Peter Kairouz, H. Brendan McMahan, Brendan Avent, Aurélien Bellet, Mehdi Bennis, Arjun Nitin Bhagoji, Kallista Bonawitz, Zachary Charles, Graham Cormode, Rachel Cummings, Rafael G.L. D'Oliveira, Hubert Eichner (+47 others)
2021 arXiv   pre-print
FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science  ...  from multi-task learning [506] immediately become relevant.  ...  In such a setting, NIZKs may enable to prove to the server properties about the client's inputs.  ... 
arXiv:1912.04977v3 fatcat:efkbqh4lwfacfeuxpe5pp7mk6a

On randomization in sequential and distributed algorithms

Rajiv Gupta, Scott A. Smolka, Shaji Bhaskar
1994 ACM Computing Surveys  
i will contain a small number of points within any lattice square.  ...  Ben-Or et al. [1988a] propose a multi- prover interactive proof model.  ...  A preliminary version of this paper appeared in Proceedings the use of zero-knowledge proofs on proving the completeness theorem for protocols with honest majority.  ... 
doi:10.1145/174666.174667 fatcat:mwufckvt5vawlostdlhcv7rxwm
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