Cryptanalysis of quantum permutation pad

TL;DR

This paper analyzes the security of the quantum permutation pad (QPP), revealing vulnerabilities where ciphertext can equal plaintext with certain probabilities, and recommends larger permutation matrices for practical security.

Contribution

It provides a cryptanalysis of QPP, identifying specific conditions under which ciphertext equals plaintext, and suggests using larger permutation matrices for enhanced security.

Findings

Instances of ciphertext equal to plaintext with probability 1/N or 1/N^m.

Visual demonstration using cipher images with 256 permutation matrices.

Recommendation to use permutation matrices of size ≥ 2048 for practical security.

Abstract

Cryptanalysis increases the level of confidence in cryptographic algorithms. We analyze the security of a symmetric cryptographic algorithm - quantum permutation pad (QPP) [8]. We found the instances of ciphertext the same as plaintext even after the action of QPP with the probability 1/N when the entire set of permutation matrices of dimension N is used and with the probability 1/N^m when an incomplete set of m permutation matrices of dimension N are used. We visually show such instances in a cipher image created by QPP of 256 permutation matrices of different dimensions. For any practical usage of QPP, we recommend a set of 256 permutation matrices of a dimension more or equal to 2048.