# Secure Multiparty Computation of the Laplace Mechanism

### Amir Zarei, Staal Vinterbo

#### 2024

#### Abstract

Differential Privacy (DP) employs perturbation mechanisms to protect individual data, formulated as Y = q(D) + i, where q(D) is a query result from dataset D and i is random noise. Adjusting the variance of i ensures that an adversary cannot discern if Y originates from D or its neighboring D′. Complications arise when computing Y using floating-point (FL) or fixed-point (FP) arithmetic. Such approximations mean not every potential output for Y is feasible, leading to a mismatch between the output of q(D) + i and q(D′) + i that allows the adversary to breach DP. One solution is to approximate Y as Y˜ = qr(D) + ir, where qr(D) is q(D) rounded to a discretization factor r = 2−k. However, integrating this solution into secure multiparty computation (MPC) is still unexplored. Our work addresses this challenge by proposing an MPC protocol that rounds an FL number to the nearest multiple of r. We show how this protocol enables secure MPC of Y˜ by introducing two Laplace mechanisms. These are then specifically adapted for linear queries. Importantly, our protocols support real-valued query functions on FL inputs and are not limited to integer-valued ones. The first protocol uses FL arithmetic to generate the noise for DP, while the second utilizes integer arithmetic. Both offer information-theoretical security against passive adversaries and can be extended for protection against malicious adversaries. We also analyze the complexity of our protocols to evaluate their performance. Our protocols represent the first provably secure MPC for the Laplace mechanism managing real-valued queries.

Download#### Paper Citation

#### in Harvard Style

Zarei A. and Vinterbo S. (2024). **Secure Multiparty Computation of the Laplace Mechanism**. In *Proceedings of the 10th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP*; ISBN 978-989-758-683-5, SciTePress, pages 582-593. DOI: 10.5220/0012453700003648

#### in Bibtex Style

@conference{icissp24,

author={Amir Zarei and Staal Vinterbo},

title={Secure Multiparty Computation of the Laplace Mechanism},

booktitle={Proceedings of the 10th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP},

year={2024},

pages={582-593},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012453700003648},

isbn={978-989-758-683-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 10th International Conference on Information Systems Security and Privacy - Volume 1: ICISSP

TI - Secure Multiparty Computation of the Laplace Mechanism

SN - 978-989-758-683-5

AU - Zarei A.

AU - Vinterbo S.

PY - 2024

SP - 582

EP - 593

DO - 10.5220/0012453700003648

PB - SciTePress