Hacking Cryptographic Protocols with Tensor Network Attacks

TL;DR

This paper explores the use of Tensor Network techniques, including Matrix Product States and a novel quantum circuit simulator, to improve cryptographic attacks on symmetric-key algorithms, demonstrating their efficiency over traditional methods especially for larger keys.

Contribution

It introduces Tensor Network methods, specifically MPS and FQCS, as novel tools for cryptanalysis, outperforming existing quantum attack algorithms in certain scenarios.

Findings

MPS outperforms VQAA and FQCS for small keys in time and iterations.

FQCS becomes more efficient than VQAA as key size increases.

Entanglement is crucial for larger key sizes in Tensor Network attacks.

Abstract

Here we introduce the application of Tensor Networks (TN) to launch attacks on symmetric-key cryptography. Our approaches make use of Matrix Product States (MPS) as well as our recently-introduced Flexible-PEPS Quantum Circuit Simulator (FQCS). We compare these approaches with traditional brute-force attacks and Variational Quantum Attack Algorithm (VQAA) methods also proposed by us. Our benchmarks include the Simplified Data Encryption Standard (S-DES) with 10-bit keys, Simplified Advanced Encryption Standard (S-AES) with 16-bit keys, and Blowfish with 32-bit keys. We find that for small key size, MPS outperforms VQAA and FQCS in both time and average iterations required to recover the key. As key size increases, FQCS becomes more efficient in terms of average iterations compared to VQAA and MPS, while MPS remains the fastest in terms of time. These results highlight the potential of TN methods in advancing quantum cryptanalysis, particularly in optimizing both speed and efficiency. Our results also show that entanglement becomes crucial as key size increases.