Statistically Hiding Commitments and Statistical Zero-Knowledge Arguments from Any One-Way Function

  • Authors:
  • Iftach Haitner;Minh-Huyen Nguyen;Shien Jin Ong;Omer Reingold;Salil Vadhan

  • Affiliations:
  • iftach@microsoft.com;mnguyen@eecs.harvard.edu and shienjin@eecs.harvard.edu and salil@eecs.harvard.edu;-;omer.reingold@weizmann.ac.il;-

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 2009

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Abstract

We give a construction of statistically hiding commitment schemes (those in which the hiding property holds against even computationally unbounded adversaries) under the minimal complexity assumption that one-way functions exist. Consequently, one-way functions suffice to give statistical zero-knowledge arguments for any NP statement (whereby even a computationally unbounded adversarial verifier learns nothing other than the fact that the assertion being proven is true, and no polynomial-time adversarial prover can convince the verifier of a false statement). These results resolve an open question posed by Naor et al. [J. Cryptology, 11 (1998), pp. 87-108].