Communication complexity of functions related to set intersection

2016 ◽  
Author(s):  
Ulrich Tamm
Keyword(s):  
Communication Complexity ◽  
Set Intersection

scholarly journals Quantum private set intersection cardinality based on bloom filter

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bai Liu ◽  
Ou Ruan ◽  
Runhua Shi ◽  
Mingwu Zhang
Keyword(s):  
Privacy Protection ◽  
Data Privacy ◽  
Communication Complexity ◽  
Single Photon ◽  
Bloom Filter ◽  
Distributed Database ◽  
Single Photons ◽  
Practical Applications ◽  
Set Intersection ◽  
Private Set Intersection

AbstractPrivate Set Intersection Cardinality that enable Multi-party to privately compute the cardinality of the set intersection without disclosing their own information. It is equivalent to a secure, distributed database query and has many practical applications in privacy preserving and data sharing. In this paper, we propose a novel quantum private set intersection cardinality based on Bloom filter, which can resist the quantum attack. It is a completely novel constructive protocol for computing the intersection cardinality by using Bloom filter. The protocol uses single photons, so it only need to do some simple single-photon operations and tests. Thus it is more likely to realize through the present technologies. The validity of the protocol is verified by comparing with other protocols. The protocol implements privacy protection without increasing the computational complexity and communication complexity, which are independent with data scale. Therefore, the protocol has a good prospects in dealing with big data, privacy-protection and information-sharing, such as the patient contact for COVID-19.

scholarly journals Circuit-PSI With Linear Complexity via Relaxed Batch OPPRF

2021 ◽  
Vol 2022 (1) ◽  
pp. 353-372
Author(s):  
Nishanth Chandran ◽  
Divya Gupta ◽  
Akash Shah
Keyword(s):  
Communication Complexity ◽  
Linear Complexity ◽  
State Of The Art ◽  
The State ◽  
Communication Cost ◽  
Independent Interest ◽  
Pseudorandom Functions ◽  
Long Line ◽  
Set Intersection ◽  
Private Set Intersection

Abstract In 2-party Circuit-based Private Set Intersection (Circuit-PSI), P 0 and P 1 hold sets S0 and S1 respectively and wish to securely compute a function f over the set S0 ∩ S1 (e.g., cardinality, sum over associated attributes, or threshold intersection). Following a long line of work, Pinkas et al. (PSTY, Eurocrypt 2019) showed how to construct a concretely efficient Circuit-PSI protocol with linear communication complexity. However, their protocol requires super-linear computation. In this work, we construct concretely efficient Circuit-PSI protocols with linear computational and communication cost. Further, our protocols are more performant than the state-of-the-art, PSTY – we are ≈ 2.3× more communication efficient and are up to 2.8× faster. We obtain our improvements through a new primitive called Relaxed Batch Oblivious Programmable Pseudorandom Functions (RB-OPPRF) that can be seen as a strict generalization of Batch OPPRFs that were used in PSTY. This primitive could be of independent interest.

Provably Secure Private Set Intersection With Constant Communication Complexity

2019 ◽  
Vol 9 (2) ◽  
pp. 39-64
Author(s):  
Sumit Kumar Debnath
Keyword(s):  
Communication Complexity ◽  
Bloom Filter ◽  
Security And Privacy ◽  
Data Sets ◽  
Indistinguishability Obfuscation ◽  
Security Parameter ◽  
Private Data ◽  
Set Intersection ◽  
Private Set Intersection ◽  
Probabilistic Data Structure

Electronic information is increasingly shared among unreliable entities. In this context, one interesting problem involves two parties that secretly want to determine an intersection of their respective private data sets while none of them wish to disclose the whole set to the other. One can adopt a Private Set Intersection (PSI) protocol to address this problem preserving the associated security and privacy issues. In this article, the authors present the first PSI protocol that incurs constant (p(k)) communication complexity with linear computation overhead and is fast even for the case of large input sets, where p(k) is a polynomial in security parameter k. Security of this scheme is proven in the standard model against semi-honest entities. The authors combine somewhere statistically binding (SSB) hash function with indistinguishability obfuscation (iO) and space-efficient probabilistic data structure Bloom filter to design the scheme.

Oblivious stable sorting protocol and oblivious binary search protocol for secure multi-party computation

2021 ◽  
pp. 1-16
Author(s):  
Ch Koteswara Rao ◽  
Kunwar Singh ◽  
Anoop Kumar
Keyword(s):  
Communication Complexity ◽  
Search Algorithm ◽  
Building Blocks ◽  
Binary Search ◽  
Oblivious Ram ◽  
Detection Systems ◽  
Round Complexity ◽  
Set Intersection ◽  
Private Computation ◽  
Binary Search Algorithm

Multi-party computation (MPC) sorting and searching protocols are frequently used in different databases with varied applications, as in cooperative intrusion detection systems, private computation of set intersection and oblivious RAM. Ivan Damgard et al. have proposed two techniques i.e., bit-decomposition protocol and bit-wise less than protocol for MPC. These two protocols are used as building blocks and have proposed two oblivious MPC protocols. The proposed protocols are based on data-dependent algorithms such as insertion sort and binary search. The proposed multi-party sorting protocol takes the shares of the elements as input and outputs the shares of the elements in sorted order. The proposed protocol exhibits O ( 1 ) constant round complexity and O ( n log n ) communication complexity. The proposed multi-party binary search protocol takes two inputs. One is the shares of the elements in sorted order and the other one is the shares of the element to be searched. If the position of the search element exists, the protocol returns the corresponding shares, otherwise it returns shares of zero. The proposed multi-party binary search protocol exhibits O ( 1 ) round complexity and O ( n log n ) communication complexity. The proposed multi-party sorting protocol works better than the existing quicksort protocol when the input is in almost sorted order. The proposed multi-party searching protocol gives almost the same results, when compared to the general binary search algorithm.

The Probabilistic Communication Complexity of Set Intersection

1992 ◽  
Vol 5 (4) ◽  
pp. 545-557 ◽  
Author(s):  
Bala Kalyanasundaram ◽  
Georg Schintger
Keyword(s):  
Communication Complexity ◽  
Set Intersection
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