On the (Im)Possibility of Arthur-Merlin Witness Hiding Protocols

The concept of witness-hiding suggested by Feige and Shamir is a natural relaxation of zero-knowledge. In this paper we identify languages and distributions for which many known constant-round publiccoin protocols with negligible soundness cannot be shown to witnesshiding using black-box techniques. In particular, our results imply that it is impossible to prove that parallel repetition of 3-Colorability or Hamiltonicity is witness-hiding for distributions that support instances with exactly one witness, if the proof of security is by a black-box reduction that is independent of the choice of the commitment scheme used in the protocol. This lower bound conceptually matches an upper bound of Feige and Shamir that uses such a black-box reduction to show that parallel repetition of 3-Colorability or Hamiltonicity is witness-hiding for distributions with "two independent witnesses". We also consider black-box reductions for 3-Colorability or Hamiltonicity that depend on a specifi...

• Type: Conference
• Year: 2009
• Where: TCC
• Authors: Iftach Haitner, Alon Rosen, Ronen Shaltiel
• Keywords: Black-box Reduction, Black-box Reductions, Black-box Techniques, Cryptography, TCC 2009