Paper 2010/149

On Small Subgroup Non-confinement Attack

Feng Hao


The small subgroup confinement attack works by confining cryptographic operations within a small subgroup, in which exhaustive search is feasible. This attack is overt and hence can be easily thwarted by adding a public key validation: verifying the received group element has proper order. In this paper, we present a different aspect of the small subgroup attack. Sometimes, the fact that an operation does not fall into the small subgroup confinement may provide an oracle to an attacker, leaking partial information about the long-term secrets. This attack is subtle and reflects structural weakness of a protocol; the question of whether the protocol has a public key validation is completely irrelevant. As a concrete example, we show how this attack works on the Secure Remote Password (SRP-6) protocol.

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Publication info
Published elsewhere. Unknown where it was published
Key exchangePAKESRP-6
Contact author(s)
haofeng66 @ gmail com
2010-03-21: received
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Creative Commons Attribution


      author = {Feng Hao},
      title = {On Small Subgroup Non-confinement Attack},
      howpublished = {Cryptology ePrint Archive, Paper 2010/149},
      year = {2010},
      note = {\url{}},
      url = {}
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