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DOI: 10.4230/LIPIcs.CP.2024.31

Inverting Step-Reduced SHA-1 and MD5 by Parameterized SAT Solvers

Authors: Oleg Zaikin

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract

MD5 and SHA-1 are fundamental cryptographic hash functions proposed in 1990s. Given a message of arbitrary finite size, MD5 produces a 128-bit hash in 64 steps, while SHA-1 produces a 160-bit hash in 80 steps. It is computationally infeasible to invert MD5 and SHA-1, i.e. to find a message given a hash. In 2012, 28-step MD5 and 23-step SHA-1 were inverted by CDCL solvers, yet no progress has been made since then. The present paper proposes to construct 31 intermediate inverse problems for any pair of MD5 or SHA-1 steps (i,i+1), such that the first problem is very close to inverting i steps, while the 31st one is almost inverting i+1 steps. We constructed SAT encodings of intermediate problems for MD5 and SHA-1, and tuned a CDCL solver on the simplest of them. Then the tuned solver was used to design a parallel Cube-and-Conquer solver which for the first time inverted 29-step MD5 and 24-step SHA-1.

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Oleg Zaikin. Inverting Step-Reduced SHA-1 and MD5 by Parameterized SAT Solvers. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{zaikin:LIPIcs.CP.2024.31,
  author =	{Zaikin, Oleg},
  title =	{{Inverting Step-Reduced SHA-1 and MD5 by Parameterized SAT Solvers}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.31},
  URN =		{urn:nbn:de:0030-drops-207165},
  doi =		{10.4230/LIPIcs.CP.2024.31},
  annote =	{Keywords: cryptographic hash function, MD5, SHA-1, preimage attack, SAT, Cube-and-Conquer}
}

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Inverting Step-Reduced SHA-1 and MD5 by Parameterized SAT Solvers

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