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From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again
2012
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference on - ITCS '12
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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]
2009
Lecture Notes in Computer Science
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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]
2010
Lecture Notes in Computer Science
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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]
2018
Lecture Notes in Computer Science
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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]
2016
Lecture Notes in Computer Science
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(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
2021
Applied Sciences
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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]
2016
Lecture Notes in Computer Science
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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
2018
Innovations in Theoretical Computer Science
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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]
2019
arXiv
pre-print
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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
2022
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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]
2018
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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
2019
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(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
2014
IEEE Access
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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]
2021
arXiv
pre-print
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2021 pre-print arXiv:1912.04977v2 fatcat:iu324p2v7nfqnkfnxbvpu4omuyOther Versions
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
1994
ACM Computing Surveys
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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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