Paper 2021/372

Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees

Laia Amorós, Annamaria Iezzi, Kristin Lauter, Chloe Martindale, and Jana Sotáková


We give an exposition of supersingular isogeny graphs, quaternion ideal graphs and Bruhat–Tits trees, and of their connections. Bruhat–Tits trees are combinatorial objects whose vertices and edges have a very simple representation as two-by-two matrices, which, as we show, is useful for understanding certain aspects of the corresponding elliptic curves and isogenies. Moreover Bruhat–Tits trees can be given an orientation and a notion of depth that we translate into the setting of supersingular isogeny graphs. We give some suggestions towards using Bruhat–Tits trees as a tool for cryptanalysis of certain cryptosystems based on supersingular isogeny graphs.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Minor revision. Women in Numbers Europe III: Research Directions in Number Theory.
isogenySIKESIDHquaternionsBruhat-Titselliptic curves
Contact author(s)
laia ac @ protonmail com
annamaria iezzi @ gmail com
kristinelauter @ gmail com
chloe martindale @ bristol ac uk
ja sotakova @ gmail com
2021-03-22: received
Short URL
Creative Commons Attribution


      author = {Laia Amorós and Annamaria Iezzi and Kristin Lauter and Chloe Martindale and Jana Sotáková},
      title = {Explicit connections between supersingular isogeny graphs and Bruhat–Tits trees},
      howpublished = {Cryptology ePrint Archive, Paper 2021/372},
      year = {2021},
      note = {\url{}},
      url = {}
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