Paper 2006/378

A New Key Exchange Primitive Based on the Triple Decomposition Problem

Yesem Kurt


We present a new key exchange primitive based on the decomposition problem over non-commutative groups. Different from the key establishment schemes that rely on the decomposition problem where the problem is decomposing an element into three parts where the middle piece is known, our scheme relies on decomposing an element into three parts, all unknown. We call this problem "Triple Decomposition Problem". This seems to be a harder problem because it requires quadratic systems to be solved instead of linear systems. We discuss the new primitive over two different protocols. The underlying problems in the two protocols differ slightly. We discuss the system and the underlying problems in one of the protocols in detail over braid groups. We manage to provide a setting which resists against linear algebra attacks and length based attacks.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Key ExchangeNon-commutative cryptographyBraid GroupCryptographic Protocol
Contact author(s)
yesem kurt @ pomona edu
2006-11-03: received
Short URL
Creative Commons Attribution


      author = {Yesem Kurt},
      title = {A New Key Exchange Primitive Based on the Triple Decomposition Problem},
      howpublished = {Cryptology ePrint Archive, Paper 2006/378},
      year = {2006},
      note = {\url{}},
      url = {}
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