Quantum Circuit Realization and Grover Cryptanalysis of the Hybrid ARX-SPN Cipher GFSPX
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Quantum Physics arXiv:2605.27443 (quant-ph) [Submitted on 23 May 2026] Title:Quantum Circuit Realization and Grover Cryptanalysis of the Hybrid ARX-SPN Cipher GFSPX Authors:Ibrahim Ulgen (1 and 3), Hasan Ozgur Cildiroglu (2), Oğuz Yayla (1) ((1) Institute of Applied Mathematics, Middle East Technical University, Ankara/Türkiye, (2) Physics Department, Ankara University, Ankara/Türkiye, (3) Department of Mathematics, Siirt University, Siirt/Türkiye) View a PDF of the paper titled Quantum Circuit Realization and Grover Cryptanalysis of the Hybrid ARX-SPN Cipher GFSPX, by Ibrahim Ulgen (1 and 3) and 9 other authors View PDF HTML (experimental) Abstract: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 $1.12 \times 2^{159}$ quantum gates. Although this cost falls below the NIST Level 1 security threshold of $2^{170}$, 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. Comments: Subjects: Quantum Physics (quant-ph) ACM classes: E.3; J.2 Cite as: arXiv:2605.27443 [quant-ph] (or arXiv:2605.27443v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.27443 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ibrahim Ulgen [view email] [v1] Sat, 23 May 2026 12:38:46 UTC (1,466 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Circuit Realization and Grover Cryptanalysis of the Hybrid ARX-SPN Cipher GFSPX, by Ibrahim Ulgen (1 and 3) and 9 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)