Star-specific Key-homomorphic PRFs from Linear Regression and Extremal Set Theory

05/02/2022
by   Vipin Singh Sehrawat, et al.
0

We introduce a novel method to derandomize the learning with errors (LWE) problem by generating deterministic yet sufficiently independent LWE instances, that are constructed via special linear regression models. We also introduce star-specific key-homomorphic (SSKH) pseudorandom functions (PRFs), which are defined by the respective sets of parties that construct them. We use our derandomized variant of LWE to construct a SSKH PRF family. The sets of parties constructing SSKH PRFs are arranged as star graphs with possibly shared vertices, i.e., some pair of sets have non-empty intersections. We reduce the security of our SSKH PRF family to the hardness of LWE. To establish the maximum number of SSKH PRFs that can be constructed – by a set of parties – in the presence of passive/active and external/internal adversaries, we prove several bounds on the size of maximally cover-free at most t-intersecting k-uniform family of sets ℋ, where the three properties are defined as: (i) k-uniform: ∀ A ∈ℋ: |A| = k, (ii) at most t-intersecting: ∀ A, B ∈ℋ, B ≠ A: |A ∩ B| ≤ t, (iii) maximally cover-free: ∀ A ∈ℋ: A ⊈⋃_B ∈ℋ B ≠ A B. For the same purpose, we define and compute the mutual information between different linear regression hypotheses that are generated via overlapping training datasets.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/03/2019

Approximating Star Cover Problems

Given a metric space (F ∪ C, d), we consider star covers of C with balan...
research
04/04/2021

D-optimal designs for the Mitscherlich non-linear regression function

Mitscherlich's function is a well-known three-parameter non-linear regre...
research
07/09/2022

Confidence Sets for a level set in linear regression

Regression modeling is the workhorse of statistics and there is a vast l...
research
02/20/2020

Total tessellation cover and quantum walk

We propose the total staggered quantum walk model and the total tessella...
research
10/05/2019

A new family of maximum scattered linear sets in PG(1,q^6)

We generalize the example of linear set presented by the last two author...
research
03/02/2017

Small Superposition Dimension and Active Set Construction for Multivariate Integration Under Modest Error Demand

Constructing active sets is a key part of the Multivariate Decomposition...

Please sign up or login with your details

Forgot password? Click here to reset