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Open Physics

Quantum grover attack on MIBS

Hasan Özgür Çıldıroğlu, Harun Basmaci, Oğuz Yayla

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Abstract The advent of quantum computing necessitates a rigorous reassessment of classical cryptographic primitives, particularly lightweight block ciphers (LBCs) deployed in resource-constrained environments. This work presents a comprehensive quantum implementation and security analysis of the Feistel-based LBC MIBS against quantum cryptanalysis. Using the inherent reversibility of its structure, we develop a novel ancilla-free quantum circuit that optimizes qubit count and depth. For MIBS-64 and MIBS-80, our implementation achieves quantum costs of 23,371 and 24,363, requiring 128 and 144 qubits, respectively, with a depth of 4,768. We subsequently quantify the cipher’s vulnerability to Grover’s key-search algorithm under the NIST PQC security constraint M A X D E P T H $\mathtt{M}\mathtt{A}\mathtt{X}\mathtt{D}\mathtt{E}\mathtt{P}\mathtt{T}\mathtt{H}$ . By constructing Grover oracles using inner parallelization with multiple plaintext-ciphertext pairs to suppress false positives, we demonstrate total quantum attack costs of approximately 2 94 for MIBS-64 and 2 111 for MIBS-80. These values fall below NIST’s Level-1 security threshold (2 170 ), confirming the susceptibility of both MIBS variants to quantum key-recovery attacks despite their classical lightweight efficiency.

DOI
10.1515/phys-2025-0297

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Abstract The advent of quantum computing necessitates a rigorous reassessment of classical cryptographic primitives, particularly lightweight block ciphers (LBCs) deployed in resource-constrained environments. This work presents a comprehensive quantum implementation and security analysis of the Feistel-based LBC MIBS against quantum cryptanalysis. Using the inherent reversibility of its structure, we develop a novel ancilla-free quantum circuit that optimizes qubit count and depth. For MIBS-64 and MIBS-80, our implementation achieves quantum costs of 23,371 and 24,363, requiring 128 and 144 qubits, respectively, with a depth of 4,768. We subsequently quantify the cipher’s vulnerability to Grover’s key-search algorithm under the NIST PQC security constraint M A X D E P T H MAXDEPTH\mathtt{M}\mathtt{A}\mathtt{X}\mathtt{D}\mathtt{E}\mathtt{P}\mathtt{T}\mathtt{H}MAXDEPTH . By constructing Grover oracles using inner parallelization with multiple plaintext-ciphertext pairs to suppress false positives, we demonstrate total quantum attack costs of approximately 2 94 for MIBS-64 and 2 111 for MIBS-80. These values fall below NIST’s Level-1 security threshold (2 170 ), confirming the susceptibility of both MIBS variants to quantum key-recovery attacks despite their classical lightweight efficiency.
The emergence of quantum computing demands rigorous reassessment of classical cryptographic primitives, particularly lightweight block ciphers (LBCs). This work addresses this critical need by presenting the first comprehensive quantum implementation and security analysis of the Feistel-based LBCs SLIM and MIBS against quantum cryptanalysis. Leveraging the inherent reversibility of the ciphers, we develop novel ancilla-free quantum circuits optimizing qubit utilization and depth. For SLIM-80, our design achieves 30,404 quantum cost with 112 qubits and depth of 4,066. For MIBS-64 and MIBS-80, we implement circuits with 23,371 and 24,363 quantum costs requiring 128 and 144 qubits, respectively, and a uniform depth of 4,768. We then quantify vulnerability to Grover’s key-search under the NIST PQC security constraint MAXDEPTH. By constructing Grover oracles under inner parallelization with multiple plaintext-ciphertext pairs to suppress false positives, we demonstrate total attack costs of 2^111 for SLIM-80 and MIBS-80, and 2^94 for MIBS-64. These costs fall below NIST’s Level-1 security threshold 2^170, confirming both ciphers’ susceptibility to quantum threats despite their lightweight efficiency. Our methodology establishes a quantum implementation framework for Feistel ciphers, revealing critical trade-offs among qubit efficiency, depth, and quantum resilience.
Abstract We present a novel quantum implementation of SLIM, a lightweight 32/80-bit Feistel cipher. By inverting its Key addition-Substitution-Permutation (KSP) layers without ancillary qubits, we construct the full quantum circuit using 112 qubits with quantum cost 30,404 and depth 4,066. To assess quantum resilience, we implement Grover’s algorithm with three plaintext-ciphertext pairs (r = 3; 337 qubits), yielding an attack cost of 2 111 under NIST’s MAXDEPTH constraints—below the Level-1 threshold 2 170 . While SLIM falls short of NIST’s security threshold for near-term quantum attacks, among other lightweight BCs, its efficient architecture retains practical advantages for constrained applications.
The security of classical symmetric-key primitives is fundamentally challenged by the emergence of quantum computing, necessitating a rigorous evaluation of their post-quantum resilience. This paper presents a comprehensive quantum circuit realization and Grover cryptanalysis of GFSPX, a lightweight block cipher featuring a 64-bit data block and a 128-bit secret key. GFSPX utilizes a unique hybrid architecture that integrates a 4-branch generalized Feistel structure with both Addition-Rotation-XOR (ARX) and Substitution-Permutation Network (SPN) components. Our quantum implementation optimizes resource distribution by exploiting the inherent reversibility of the Feistel network and employing a compact ripple-carry adder for the ARX layers. The proposed architecture achieves a qubit-optimized footprint of 209 qubits with a baseline quantum cost of 32,498 and a circuit depth of 7,617. To evaluate the cipher's resistance against quantum adversaries, we construct a parallelized Grover oracle using three plaintext-ciphertext pairs to eliminate spurious matches. Our analysis reveals that the total quantum cost of a key-recovery attack on GFSPX is 1.12×21591.12 \times 2^{159}1.12×2159 quantum gates. Although this cost falls below the NIST Level 1 security threshold of 21702^{170}2170, the hybrid ARX-SPN design demonstrates a higher quantum attack resistance among other lightweight designs. These findings provide critical insights into the balance between classical efficiency and quantum resilience in next-generation cryptographic designs for resource-constrained environments.
Because of the substantial progress in quantum computing technology, the safety of traditional cryptologic schemes is facing serious challenges. In this study, we explore the quantum safety of the lightweight cipher MIBS and propose quantum key-recovery attacks on the MIBS cipher by utilizing Grover’s algorithm and Bernstein–Vazirani algorithm. We first construct linear-structure functions based on the 5-round MIBS cipher according to the characteristics of the linear transformations, and then we obtain a quantum distinguisher of the 5-round MIBS cipher by applying Bernstein–Vazirani algorithm to the constructed functions. Finally, utilizing this distinguisher and Grover’s algorithm, we realize a 7-round key-recovery attack on the MIBS cipher, and then we expand the attack to more rounds of MIBS based on a similar idea. The quantum attack on the 7-round MIBS requires 156 qubits and has a time complexity of 210.5. An 8-round attack requires 179 qubits and has a time complexity of 222. Compared with existing quantum attacks, our attacks have better time complexity when attacking the same number of rounds.
Extensive research is currently underway to determine the security of existing ciphers in light of the advancements in quantum computing. Against symmetric key cryptography, Grover’s search algorithm is a prominent attack, capable of reducing search costs to the square root. For using Grover’s algorithm, it is imperative to embed the target cipher into a quantum circuit. Even so, this area of research is relatively new; it has garnered significant attention from the research community. In this study, we provide the first estimation of the cost of Grover’s key search attack against the AES-based AEAD schemes Rocca-S, AEGIS-128, and Tiaoxin-346. Our analysis considers circuit depth restrictions specified in NIST’s PQC standardization process. Considering NIST’s maximum depth constraints, We present the overall cost of these attacks using gate count and depth-times-width metrics. We observed that for MAXDEPTH=240\textsf{MAXDEPTH} = 2^{40}MAXDEPTH=240 , Rocca-S, AEGIS-128, and Tiaoxin-346 can be retrieved using Grover’s search algorithm with gate count of 1.09 × 2253, 1.14 × 2124, and 1.22 × 2124 respectively. Concerning the current updated values by NIST, these ciphers are secure in terms of the cost of implementing Grover’s attack for key recovery. The quantum circuits of these ciphers are implemented using QISKIT, an open-source software development kit (SDK) designed for working with quantum computers running on the IBM Quantum Experience platform.
Abstract Grover’s algorithm reduces the security level of the target cipher from n-bit to n/2-bit. To implement Grover’s algorithm, a quantum circuit capable of performing the target cipher operations must be constructed. In this paper, we propose a quantum circuit implementation scheme for the involutive lightweight block cipher (IVLBC) block cipher. We utilized the DORCIS tool to implement the quantum circuit for the S-box and applied Gaussian elimination to construct the quantum circuit for matrix multiplication. Subsequently, we evaluated the overall quantum resource consumption required for the implementation. Based on this, we performed a quantum attack on IVLBC using Grover’s algorithm, calculating the attack cost using the NCT gate library, and further analyzed its security. Finally, we conducted a comparative analysis of the classical attack complexity and quantum attack complexity of IVLBC, highlighting the potential of using quantum complexity as a standard for future security assessments.