Paper 2005/447

A new key exchange protocol based on the decomposition problem

Vladimir Shpilrain and Alexander Ushakov


In this paper we present a new key establishment protocol based on the decomposition problem in non-commutative groups which is: given two elements w, w_1 of the platform group G and two subgroups A, B of G (not necessarily distinct), find elements a in A, b in B such that w_1 = a w b. Here we introduce two new ideas that improve the security of key establishment protocols based on the decomposition problem. In particular, we conceal (i.e., do not publish explicitly) one of the subgroups A, B, thus introducing an additional computationally hard problem for the adversary, namely, finding the centralizer of a given finitely generated subgroup.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Contact author(s)
shpil @ groups sci ccny cuny edu
2005-12-08: received
Short URL
Creative Commons Attribution


      author = {Vladimir Shpilrain and Alexander Ushakov},
      title = {A new key exchange protocol based on the decomposition problem},
      howpublished = {Cryptology ePrint Archive, Paper 2005/447},
      year = {2005},
      note = {\url{}},
      url = {}
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