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- Article name
- Combinatorial model for estimating the number of feasible routes with an arbitrary number of intermediate nodes, allowing source and destination to appear as hops
- Authors
- Zyuzin V. D., , v.d.zyuzin@gmail.com, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
- Keywords
- peer-to-peer networks / combinatorial model / route enumeration / anonymity / traffic analysis / virtual private network / routing
- Year
- 2025 Issue 2 Pages 25 - 33
- Code EDN
- VGLBCS
- Code DOI
- 10.52190/2073-2600_2025_2_25
- Abstract
- The article presents a combinatorial model is introduced for estimating the number of feasible routes in a peer-to-peer network comprising n nodes with an arbitrary number of intermediate hops j. The source and destination nodes are allowed to appear at internal positions of the chain, while each node can be used at most once. The resulting system of formulae generalises previously known special cases and reveals how the size of the routing space depends on the relation between n and j. The derivation has been validated by a Python implementation and a computational experiment whose outcomes confirm a polynomial growth in the number of paths and a sharp rise in route entropy for j ³ 4. The model enables quick a priori assessments of the cryptographic resilience of overlay networks and supports the optimisation of hop-selection algorithms in VPN tunnels, mix networks, and blockchain gateways, thereby improving their resistance to modern traffic-analysis attacks.
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