Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks

TL;DR

This paper introduces an optimal cryptanalysis method for permutation-only multimedia ciphers, significantly reducing complexity and applicable to various encryption schemes, with practical implications for security assessment.

Contribution

It presents a novel, efficient attack method on permutation-only encryption algorithms, extending to multiple levels of plaintext values and analyzing specific encryption scheme performance.

Findings

The attack has spatial complexity O(32·MN) and computational complexity O(16·n₀·MN).

It can break any permutation-only scheme with complexity O(MN) and O(⌈log_L(MN)⌉·MN).

The method effectively analyzes image scrambling encryption performance.

Abstract

Recently, an image scrambling encryption algorithm of pixel bit based on chaos map was proposed. Considering the algorithm as a typical binary image scrambling/permutation algorithm exerting on plaintext of size $M\times (8N)$, this paper proposes a novel optimal method to break it with some known/chosen-plaintexts. The spatial complexity and computational complexity of the attack are only $O(32\cdot MN)$ and $O(16\cdot n_0\cdot MN)$ respectively, where $n_0$ is the number of known/chosen-plaintexts used. The method can be easily extended to break any permutation-only encryption scheme exerting on plaintext of size $M\times N$ and with $L$ different levels of values. The corresponding spatial complexity and computational complexity are only $O(MN)$ and $O(\lceil\log_L(MN)\rceil \cdot MN)$ respectively. In addition, some specific remarks on the performance of the image scrambling encryption algorithm are presented.