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npj Quantum Information

Quantum cryptanalysis of SPN ciphers with known plaintext

Uroosa Kiran, Aneela Safdar, Saif Ullah Khalid, Hammad Tanveer Butt, Zunera Jalil

Published Apr 1, 2026• 0 citations
Publisher

Abstract

Key recovery attack on SPN ciphers such as AES is NP hard in complexity. Previous studies have estimated the quantum resources required for implementing Grover’s key search for AES, but these are largely theoretical in nature. The key challenges to implement Grover’s algorithm on current quantum hardware include the number of available qubits, noise, and decoherence. However, the rapid advancement of hardware has brought us closer to practical realization for the cryptanalysis of light-weight SPN ciphers. This study presents an efficient quantum circuit implementation of Mini-AES, a 16-bit variant of AES, employing standard CNOT and Toffoli gates. To the best of our knowledge, our work provides the first complete quantum implementations of all core Mini-AES components for the quantum oracle. The effects of noise are emulated for each module of the quantum oracle and quantified. Furthermore, Grover’s algorithm is applied to Mini-AES to perform successful key recovery through a known-plaintext attack, demonstrating significant amplitude amplification while using near-optimal Grover’s iterations, thereby reducing the total quantum volume. The optimal Grover’s iterations have been obtained empirically as well as validated with finite-shot analysis. Notably, the application of Grover’s algorithm reveals key clustering behavior in Mini-AES, which has been corroborated through classical simulation.

DOI
10.1038/s41534-026-01218-x

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Key recovery attack on SPN ciphers such as AES is NP hard in complexity. Previous studies have estimated the quantum resources required for implementing Grover’s key search for AES, but these are largely theoretical in nature. The key challenges to implement Grover’s algorithm on current quantum hardware include the number of available qubits, noise, and decoherence. However, the rapid advancement of hardware has brought us closer to practical realization for the cryptanalysis of light-weight SPN ciphers. This study presents an efficient quantum circuit implementation of Mini-AES, a 16-bit variant of AES, employing standard CNOT and Toffoli gates. To the best of our knowledge, our work provides the first complete quantum implementations of all core Mini-AES components for the quantum oracle. The effects of noise are emulated for each module of the quantum oracle and quantified. Furthermore, Grover’s algorithm is applied to Mini-AES to perform successful key recovery through a known-plaintext attack, demonstrating significant amplitude amplification while using near-optimal Grover’s iterations, thereby reducing the total quantum volume. The optimal Grover’s iterations have been obtained empirically as well as validated with finite-shot analysis. Notably, the application of Grover’s algorithm reveals key clustering behavior in Mini-AES, which has been corroborated through classical simulation.
Quantum search algorithms, such as Grover's algorithm, will soon pose a threat to current encryption standards as quantum computing advances toward practical implementation. These algorithms rely on quantum circuits that map cryptographic algorithms into appropriate Hilbert spaces, thus linking algorithmic inputs and outputs through quantum superposition. However, implementing and testing such circuits on existing quantum simulators, such as Qiskit, encounters significant memory and computational bottlenecks that limit research progress. To address these simulation constraints, we present a resource-optimized quantum circuit implementation of a complete two-round Mini-AES encryption algorithm. Our approach systematically converts the cipher's algebraic structure using algebraic normal form (ANF) equations, mapping XOR operations to CNOT gates and AND operations to Toffoli gates. To reduce memory overhead, we implement an ancilla-reuse strategy utilizing mid-circuit measurements and resets. Additionally, we introduce an automated procedure that generates Qiskitcompatible quantum circuits for arbitrary S-boxes and cryptographic primitives, streamlining the development of quantum cryptanalysis implementations. Our implementation achieves full encryption and decryption in a quantum circuit with modest gate requirements that can be achieved by the current or near-future state of the art quantum computers. In addition, we provide system utilization metrics to validate our resource-constrained implementation. This compact and pedagogically accessible implementation establishes a practical foundation for quantum cryptanalysis research and post-quantum cryptographic analysis.
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The Advanced Encryption Standard (AES) is one of the most widely used symmetric block cipher cryptography algorithms. Simplified-AES (S-AES) retains the structural framework of AES, making it an ideal model for elucidating the mechanism of symmetric cryptography. In this paper, we investigate potential quantum attacks on S-AES, utilizing both Grover-based algorithms and variational quantum algorithms (VQAs). For Grover-based attacks, we introduce an optimized oracle for implementing S-AES, reducing the complexity from 160 Toffoli gates to 120 by refining the SubNibble operation. Additionally, we propose a general Variational Quantum Attack Algorithm (VQAA) for any type of symmetric encryption that does not require the quantum implementation of the encryption procedure, which reduces the gate complexity substantially. These improvements enable the implementation of both Grover-based attacks and VQAA on superconducting quantum computers. The results demonstrate the feasibility of cryptographic analysis on currently available quantum hardware. Our findings also underscore the challenges of parameter optimization for S-AES, attributing the difficulty to the design of efficient parameterized quantum circuits, which constrain the effectiveness of variational algorithms. Despite these advancements, significant challenges remain in achieving quantum attacks on AES.
Advanced Encryption Standard is one of the most widely used and important symmetric ciphers for today. It well known, that it can be subjected to the quantum Grover's attack that twice reduces its key strength. But full AES attack requires hundreds of qubits and circuit depth of thousands, that makes impossible not only experimental research but also numerical simulations of this algorithm. Here we present an algorithm for optimized Grover's attack on downscaled Simplifed-AES cipher. Besides full attack we present several approaches that allows to reduce number of required qubits if some nibbles of the key are known as a result of side-channel attack. For 16-bit S-AES the proposed attack requires 23 qubits in general case and 19, 15 or 11 if 4, 8 or 12 bits were leaked in specifc confguration. Comparing to previously known 32-qubits algorithm this approach potentially allows to run the attack on today's NISQ-devices and perform numerical simulations with GPU, that may be useful for further research of problem-specifc error mitigation and error correction techniques.
NIST(National Institute of Standards and Technology) estimates the Grover key search cost required for symmetric key cryptography as the postquantum security strength. The Grover search algorithm is applicable to key recovery in symmetric key cryptography, and for this, the target encryption process must be implemented as a quantum circuit. In this paper, we present an optimized implementation of Simplified AES as a quantum circuit. Substitution, Mix Columns, and Key Expansion are implemented efficiently, and as a result of resource analysis, qubits, quantum gates, and circuit depth are significantly reduced compared to the previous result.
In this study, we present in detail the application of Grover's quantum algorithm to the searching problem of the secret key of a simple SPN (Substitution–permutation network) block cipher called Yo-yo. The main goal of the paper is to clarify the construction of the quantum circuit and the operation phases of Grover's algorithm to find the secret key with the condition of knowing at least 1 pair of plaintext-ciphertext. To achieve this goal, we consider 2 cases: the case where there is a unique key that satisfies and the case where there are 2 keys that satisfy at the same time. As a result, our implementation technique, implemented in the Qiskit programming language, requires only 17 qubits to find the key of the Yo-yo block cipher correctly. This technique can be effectively applied on IBM quantum computers for large-scale SPN block ciphers, such as AES and GOST R.34.10.2015, which are widely used today.