Isogeny Graphs in Superposition and Quantum Onion Routing
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908803986882560 |
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| author | Agathocleous, Eleni Hartung, Tobias Jansen, Karl Mansour, Lukas |
| author_facet | Agathocleous, Eleni Hartung, Tobias Jansen, Karl Mansour, Lukas |
| contents | Onion routing provides anonymity by layering encryption so that no relay can link sender to destination. A quantum analogue faces a core obstacle: layered quantum encryption generally requires symmetric encryption schemes, whereas classically one would rely on public-key encryption. We propose a symmetric-encryption-based quantum onion routing (QOR) scheme by instantiating each layer with the abelian ideal class group action from the Theory of Complex Multiplication. Session keys are established locally via a Diffie-Hellman key exchange between neighbors in the chain of communication. Furthermore, we propose a novel ''non-local'' key exchange between the sender and receiver. The underlying problem remains hard even for quantum adversaries and underpins the security of current post-quantum schemes. We connect our construction to isogeny graphs and their association schemes, using the Bose-Mesner algebra to formalize commutativity and guide implementation. We give two implementation paths: (i) a universal quantum oracle evaluating the class group action with polynomially many quantum resources, and (ii) an intrinsically quantum approach via continuous-time quantum walks (CTQWs), outlined here and developed in a companion paper. A small Qiskit example illustrates the mechanics (by design, not the efficiency) of the QOR. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_01464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isogeny Graphs in Superposition and Quantum Onion Routing Agathocleous, Eleni Hartung, Tobias Jansen, Karl Mansour, Lukas Quantum Physics Information Theory 11G15, 05E30, 81P45, 81P94, 68Q12, 94A60, 11R29, 14K02 C.2.2; E.3; F.1.2 Onion routing provides anonymity by layering encryption so that no relay can link sender to destination. A quantum analogue faces a core obstacle: layered quantum encryption generally requires symmetric encryption schemes, whereas classically one would rely on public-key encryption. We propose a symmetric-encryption-based quantum onion routing (QOR) scheme by instantiating each layer with the abelian ideal class group action from the Theory of Complex Multiplication. Session keys are established locally via a Diffie-Hellman key exchange between neighbors in the chain of communication. Furthermore, we propose a novel ''non-local'' key exchange between the sender and receiver. The underlying problem remains hard even for quantum adversaries and underpins the security of current post-quantum schemes. We connect our construction to isogeny graphs and their association schemes, using the Bose-Mesner algebra to formalize commutativity and guide implementation. We give two implementation paths: (i) a universal quantum oracle evaluating the class group action with polynomially many quantum resources, and (ii) an intrinsically quantum approach via continuous-time quantum walks (CTQWs), outlined here and developed in a companion paper. A small Qiskit example illustrates the mechanics (by design, not the efficiency) of the QOR. |
| title | Isogeny Graphs in Superposition and Quantum Onion Routing |
| topic | Quantum Physics Information Theory 11G15, 05E30, 81P45, 81P94, 68Q12, 94A60, 11R29, 14K02 C.2.2; E.3; F.1.2 |
| url | https://arxiv.org/abs/2510.01464 |