arXiv subjects

Jan Willemson

Publications and source records attributed to Jan Willemson.

6 recordsLinked to original sources

arXiv2026

Pythagorean walks on $\mathbb{Z}^2$

We consider an infinite graph with the vertex set $\mathbb{Z}^2$ and edges connecting the vertices iff the Euclidean distance between the respective points is an integer, and the points do not lie on the same horizontal or vertical. Equivalently, there must exist a Pythagorean triangle with the hypotenuse corresponding to the graph edge and the legs parallel to the axes. We prove that the diameter of this graph is $3$, but surprisingly it appears that the nodes at the maximal (graph) distance of $3$ apart seem to be only those that are geometrically very close to each other. It also appears that the paths of length $2$ connecting geometrically close nodes may need to go through geometrically very distant points. We prove a general relation that generates infinite series of length-$2$ paths, and present the results of our computer experiments. We conclude the paper with a general conjecture about the length-$2$ and length-$3$ paths. We have posed this conjecture to several of the current leading AI models. Remarkably, none of them managed to make any significant progress in proving it.

math.CO↗

arXiv2025

Recommendations to OSCE/ODIHR (on how to give better recommendations for Internet voting)

This paper takes a critical look at the recommendations OSCE/ODIHR has given for the Estonian Internet voting over the 20 years it has been running. We present examples of recommendations that can not be fulfilled at all, but also examples where fulfilling a recommendation requires a non-trivial trade-off, potentially weakening the system in some other respect. In such cases OSCE/ODIHR should take an explicit position which trade-off it recommends. We also look at the development of the recommendation to introduce end-to-end verifiability. In this case we expect OSCE/ODIHR to define what it exactly means by this property, as well as to give explicit criteria to determine whether and to which extent end-to-end verifiability has been achieved.

cs.CR↗

arXiv2023

Trust assumptions in voting systems

Assessing and comparing the security level of different voting systems is non-trivial as the technical means provided for and societal assumptions made about various systems differ significantly. However, trust assumptions concerning the involved parties are present for all voting systems and can be used as a basis for comparison. This paper discusses eight concrete voting systems with different properties, 12 types of parties involved, and seven general security goals set for voting. The emerging trust relations are assessed for their criticality, and the result is used for comparison of the considered systems.

cs.CR↗

arXiv2023

Analyzing and Improving Eligibility Verifiability of the Proposed Belgian Remote Voting System

This paper discusses several recent electronic-paper remote voting hybrid schemes, concentrating more specifically on the proposal put forward for Belgian elections. We point to some problems in the proposal, and consider addition of blind signatures as one possible approach to dealing with the identified shortcomings. We discuss the concomitant updates from both the protocol and electoral processes point of view, arguing that our proposal would strike a better balance between different requirements. To the best of our knowledge, this is also the first proposal to use blind signatures in a paper-based voting system.

cs.CR↗

arXiv2021

UC Modelling and Security Analysis of the Estonian IVXV Internet Voting System

Estonian Internet voting has been used in national-wide elections since 2005. However, the system was initially designed in a heuristic manner, with very few proven security guarantees. The Estonian Internet voting system has constantly been evolving throughout the years, with the latest version (code-named IVXV) implemented in 2018. Nevertheless, to date, no formal security analysis of the system has been given. In this work, for the first time, we provide a rigorous security modeling for the Estonian IVXV system as a ceremony, attempting to capture the effect of actual human behavior on election verifiability in the universal composability (UC) framework. Based on the voter behavior statistics collected from three actual election events in Estonia, we show that IVXV achieves end-to-end verifiability in practice despite the fact that only $4\%$ (on average) of the Estonian voters audit their ballots.

cs.CR↗

arXiv1999

Certificate Revocation Paradigms

Research in the field of electronic signature confirmation has been active for some 20 years now. Unfortunately present certificate-based solutions also come from that age when no-one knew about online data transmission. The official standardized X.509 framework also depends heavily on offline operations, one of the most complicated ones being certificate revocation handling. This is done via huge Certificate Revocation Lists which are both inconvenient and expencive. Several improvements to these lists are proposed and in this report we try to analyze them briefly. We conclude that although it is possible to do better than in the original X.509 setting, none of the solutions presented this far is good enough.

cs.CR↗