Communication Complexity of Private Simultaneous Quantum Messages Protocols

05/15/2021
by   Akinori Kawachi, et al.
0

The private simultaneous messages model is a non-interactive version of the multiparty secure computation, which has been intensively studied to examine the communication cost of the secure computation. We consider its quantum counterpart, the private simultaneous quantum messages (PSQM) model, and examine the advantages of quantum communication and prior entanglement of this model. In the PSQM model, k parties P_1,…,P_k initially share a common random string (or entangled states in a stronger setting), and they have private classical inputs x_1,…, x_k. Every P_i generates a quantum message from the private input x_i and the shared random string (entangled states), and then sends it to the referee R. Receiving the messages, R computes F(x_1,…,x_k). Then, R learns nothing except for F(x_1,…,x_k) as the privacy condition. We obtain the following results for this PSQM model. (1) We demonstrate that the privacy condition inevitably increases the communication cost in the two-party PSQM model as well as in the classical case presented by Applebaum, Holenstein, Mishra, and Shayevitz. In particular, we prove a lower bound (3-o(1))n of the communication complexity in PSQM protocols with a shared random string for random Boolean functions of 2n-bit input, which is larger than the trivial upper bound 2n of the communication complexity without the privacy condition. (2) We demonstrate a factor two gap between the communication complexity of PSQM protocols with shared entangled states and with shared random strings by designing a multiparty PSQM protocol with shared entangled states for a total function that extends the two-party equality function. (3) We demonstrate an exponential gap between the communication complexity of PSQM protocols with shared entangled states and with shared random strings for a two-party partial function.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

11/30/2020

Oblivious Transfer is in MiniQCrypt

MiniQCrypt is a world where quantum-secure one-way functions exist, and ...
01/31/2020

A Private Quantum Bit String Commitment

We propose an entanglement-based quantum bit string commitment protocol ...
03/20/2021

Round and Communication Balanced Protocols for Oblivious Evaluation of Finite State Machines

We propose protocols for obliviously evaluating finite-state machines, i...
07/25/2021

Tight Bounds for the Randomized and Quantum Communication Complexities of Equality with Small Error

We investigate the randomized and quantum communication complexities of ...
01/15/2020

Exponential quantum communication reductions from generalizations of the Boolean Hidden Matching problem

In this work we revisit the Boolean Hidden Matching communication proble...
05/27/2020

Security Improvements of Several Basic Quantum Private Query Protocols with O(log N) Communication Complexity

New quantum private database (with N elements) query protocols are prese...
05/01/2019

On a conditional inequality in Kolmogorov complexity and its applications in communication complexity

Romashchenko and Zimand rom-zim:c:mutualinfo have shown that if we parti...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.