Paper 2024/1776

An efficient collision attack on Castryck-Decru-Smith’s hash function

Ryo Ohashi, University of Tokyo
Hiroshi Onuki, University of Tokyo
Abstract

In 2020, Castryck-Decru-Smith constructed a hash function, using the (2,2)-isogeny graph of superspecial principally polarized abelian surfaces. In their construction, the initial surface was chosen from vertices very "close" to the square of a supersingular elliptic curve with a known endomorphism ring. In this paper, we introduce an algorithm for detecting a collision on their hash function. Under some heuristic assumptions, the time complexity and space complexity of our algorithm are estimated to be $\widetilde{O}(p^{3/10})$ which are smaller than the complexity $\widetilde{O}(p^{3/2})$ the authors claimed to be necessary to detect a collision, where $p$ is the characteristic of the base field. In particular case where $p$ has a special form, then both the time and space complexities of our algorithm are polynomial in $\log{p}$. We implemented our algorithm in Magma, and succeeded in detecting a collision in 17 hours (using 64 parallel computations) under a parameter setting which the authors had claimed to be 384-bit secure.

Metadata
Available format(s)
PDF
Category
Attacks and cryptanalysis
Publication info
Preprint.
Keywords
Hash functionIsogeny-based cryptographySuperspecial abelian surfaceKani's lemma
Contact author(s)
ryo-ohashi @ g ecc u-tokyo ac jp
hiroshi-onuki @ g ecc u-tokyo ac jp
History
2024-11-01: approved
2024-10-31: received
See all versions
Short URL
https://ia.cr/2024/1776
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/1776,
      author = {Ryo Ohashi and Hiroshi Onuki},
      title = {An efficient collision attack on Castryck-Decru-Smith’s hash function},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1776},
      year = {2024},
      url = {https://eprint.iacr.org/2024/1776}
}
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