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Graphs and cycles in curve-based collision walks
eprint.iacr.orgpaper

Graphs and cycles in curve-based collision walks

Graphs and cycles in curve-based collision walks is an IACR ePrint paper (2026/2560) on van Oorschot-Wiener style collision attacks in the multi-user setting. It covers elliptic curve discrete logarithms and isogeny pathfinding on supersingular F_p^2 and F_p curves, and proposes new pseudorandom walks. For F_p^2 curves, L keys need about L + log(L) useful collisions with no infiltrator. For F_p curves, about 0.75L keys fall to L collisions with an infiltrator.

TL;DR Proposes new pseudorandom walks for multi-user collision attacks on ECDLP and supersingular isogeny pathfinding, with analysis of how many keys L collisions recover.
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Organisations named here

  • infiltrator
  • isogeny pathfinding
  • multi-user attack
  • van Oorschot-Wiener

Technologies named here

  • Isogeny pathfinding problem on supersingular F_{p^2}-curves
  • Isogeny pathfinding problem on supersingular F_p-curves

Techniques named here

  • Meet-in-the-middle collision search on isogeny graphs
  • Discrete logarithm on elliptic curves
  • Supersingular F_{p^2}-curve isogeny pathfinding
  • Supersingular F_p-curve isogeny pathfinding

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