Paper 2014/041

Cryptanalysis via algebraic spans

Adi Ben-Zvi, Arkadius Kalka, and Boaz Tsaban


We introduce a method for obtaining provable polynomial time solutions of problems in nonabelian algebraic cryptography. This method is widely applicable, easier to apply, and more efficient than earlier methods. After demonstrating its applicability to the major classic nonabelian protocols, we use this method to cryptanalyze the Triple Decomposition key exchange protocol, the only classic group theory based key exchange protocol that could not be cryptanalyzed by earlier methods.

Note: Substantial extension of earlier version. Includes detailed specifications, complexity analyses, and experimental results. Introduction thoroughly revised.

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Publication info
Preprint. MINOR revision.
nonabelian algebraic cryptographygroup theory-based cryptographybraid-based cryptographyTriple Decomposition key exchangeCommutator key exchangeCentralizer key exchangeBraid Diffie--Hellman key exchangealgebraic span cryptanalysis.
Contact author(s)
tsaban @ math biu ac il
2018-02-12: last of 2 revisions
2014-01-15: received
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      author = {Adi Ben-Zvi and Arkadius Kalka and Boaz Tsaban},
      title = {Cryptanalysis via algebraic spans},
      howpublished = {Cryptology ePrint Archive, Paper 2014/041},
      year = {2014},
      note = {\url{}},
      url = {}
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