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Paper: The role of help in Classical and Quantum Zero-Knowledge

Authors:
André Chailloux
Iordanis Kerenidis
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URL: http://eprint.iacr.org/2007/421
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Abstract: We study the role of help in Non-Interactive Zero-Knowledge protocols and its relation to the standard interactive model. In the classical case, we show that help and interaction are equivalent, answering an open question of Ben-Or and Gutfreund (\cite{BG03}). This implies a new complete problem for the class SZK, the Image Intersection Density. For this problem, we also prove a polarization lemma which is stronger than the previously known one. In the quantum setting, we define the notion of quantum help and show in a more direct way that help and interaction are again equivalent. Moreover, we define quantum Non-Interactive Zero-Knowledge with classical help and prove that it is equal to the class of languages that have classical honest-Verifier Zero Knowledge protocols secure against quantum Verifiers (\cite{Wat06, HKSZ07}). Last, we provide new complete problems for all these quantum classes. Similar results were independently discovered by Dragos Florin Ciocan and Salil Vadhan.
BibTeX
@misc{eprint-2007-13701,
  title={The role of help in Classical and Quantum Zero-Knowledge},
  booktitle={IACR Eprint archive},
  keywords={cryptographic protocols / cryptography, zero knowledge protocols, help model, quantum},
  url={http://eprint.iacr.org/2007/421},
  note={ andre.chailloux@ens-lyon.fr 13826 received 9 Nov 2007},
  author={André Chailloux and Iordanis Kerenidis},
  year=2007
}