Locating modifications in signed data for partial data integrity

TL;DR

This paper introduces an efficient scheme for detecting and locating modifications in signed data, supporting partial data integrity by identifying up to a threshold number of altered blocks using combinatorial group testing.

Contribution

It presents a novel algorithmic approach combining nonadaptive combinatorial group testing and cover-free families for partial data integrity verification.

Findings

Signature size increases by O(log n) for fixed d

Supports identification of up to d modified blocks

Efficient algorithms for signature and verification

Abstract

We consider the problem of detecting and locating modifications in signed data to ensure partial data integrity. We assume that the data is divided into $n$ blocks (not necessarily of the same size) and that a threshold $d$ is given for the maximum amount of modified blocks that the scheme can support. We propose efficient algorithms for signature and verification steps which provide a reasonably compact signature size, for controlled sizes of $d$ with respect to $n$. For instance, for fixed $d$ the standard signature size gets multiplied by a factor of $O(\log n)$, while allowing the identification of up to $d$ modified blocks. Our scheme is based on nonadaptive combinatorial group testing and cover-free families.