InstaHide's Sample Complexity When Mixing Two Private Images

11/24/2020
∙
by   Baihe Huang, et al.
∙
0
∙

Inspired by InstaHide challenge [Huang, Song, Li and Arora'20], [Chen, Song and Zhuo'20] recently provides one mathematical formulation of InstaHide attack problem under Gaussian images distribution. They show that it suffices to use O(n_𝗉𝗋𝗂𝗏^k_𝗉𝗋𝗂𝗏 - 2/(k_𝗉𝗋𝗂𝗏 + 1)) samples to recover one private image in n_𝗉𝗋𝗂𝗏^O(k_𝗉𝗋𝗂𝗏) + poly(n_𝗉𝗎𝖻) time for any integer k_𝗉𝗋𝗂𝗏, where n_𝗉𝗋𝗂𝗏 and n_𝗉𝗎𝖻 denote the number of images used in the private and the public dataset to generate a mixed image sample. Under the current setup for the InstaHide challenge of mixing two private images (k_𝗉𝗋𝗂𝗏 = 2), this means n_𝗉𝗋𝗂𝗏^4/3 samples are sufficient to recover a private image. In this work, we show that n_𝗉𝗋𝗂𝗏log ( n_𝗉𝗋𝗂𝗏 ) samples are sufficient (information-theoretically) for recovering all the private images.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
∙ 08/16/2022

Private Estimation with Public Data

We initiate the study of differentially private (DP) estimation with acc...
research
∙ 05/17/2021

A Fusion-Denoising Attack on InstaHide with Data Augmentation

InstaHide is a state-of-the-art mechanism for protecting private trainin...
research
∙ 08/11/2023

Private Distribution Learning with Public Data: The View from Sample Compression

We study the problem of private distribution learning with access to pub...
research
∙ 10/25/2019

Limits of Private Learning with Access to Public Data

We consider learning problems where the training set consists of two typ...
research
∙ 07/27/2022

Differentially Private Learning of Hawkes Processes

Hawkes processes have recently gained increasing attention from the mach...
research
∙ 09/12/2023

Public key cryptosystems based on Iterated Functions Systems

Let f=(f_0,f_1,…, f_ν-1) be a collection of one-to-one functions from so...
research
∙ 01/21/2020

batchboost: regularization for stabilizing training with resistance to underfitting overfitting

Overfitting underfitting and stable training are an important challe...

Please sign up or login with your details

Forgot password? Click here to reset