Private Simultaneous Messages Based on Quadratic Residues

by   Kazumasa Shinagawa, et al.

Private Simultaneous Messages (PSM) model is a minimal model for secure multiparty computation. Feige, Kilian, and Naor (STOC 1994) and Ishai (Cryptology and Information Security Series 2013) constructed PSM protocols based on quadratic residues. In this paper, we define QR-PSM protocols as a generalization of these protocols. A QR-PSM protocol is a PSM protocol whose decoding function outputs the quadratic residuosity of what is computed from messages. We design a QR-PSM protocol for any symmetric function f: {0,1}^n →{0,1} of communication complexity O(n^2). As far as we know, it is the most efficient PSM protocol since the previously known best PSM protocol was of O(n^2log n) (Beimel et al., CRYPTO 2014). We also study the sizes of the underlying finite fields 𝔽_p in the protocols since the communication complexity of a QR-PSM protocol is proportional to the bit length of the prime p. In particular, we show that the N-th Peralta prime P_N, which is used for general QR-PSM protocols, can be taken as at most (1+o(1))N^2 2^2N-2, which improves the Peralta's known result (Mathematics of Computation 1992) by a constant factor (1+√(2))^2.


page 1

page 2

page 3

page 4


Differentially Private Summation with Multi-Message Shuffling

In recent work, Cheu et al. (Eurocrypt 2019) proposed a protocol for n-p...

Communication Complexity of Private Simultaneous Quantum Messages Protocols

The private simultaneous messages model is a non-interactive version of ...

Mistakes of A Popular Protocol Calculating Private Set Intersection and Union Cardinality and Its Corrections

In 2012, De Cristofaro et al. proposed a protocol to calculate the Priva...

Simultaneous Multiparty Communication Complexity of Composed Functions

In the Number On the Forehead (NOF) multiparty communication model, k pl...

Maximum Production of Transmission Messages Rate for Service Discovery Protocols

Minimizing the number of dropped User Datagram Protocol (UDP) messages i...

Instability of backoff protocols with arbitrary arrival rates

In contention resolution, multiple processors are trying to coordinate t...

SNPSFuzzer: A Fast Greybox Fuzzer for Stateful Network Protocols using Snapshots

Greybox fuzzing has been widely used in stateless programs and has achie...

Please sign up or login with your details

Forgot password? Click here to reset