**Concurrent Zero Knowledge without Complexity Assumptions**

*Daniele Micciancio and Shien Jin Ong and Amit Sahai and Salil Vadhan*

**Abstract: **We provide unconditional constructions of concurrent statistical zero-knowledge proofs for a variety of non-trivial problems (not known to have probabilistic polynomial-time algorithms). The problems include Graph Isomorphism, Graph Nonisomorphism, Quadratic Residuosity, Quadratic Nonresiduosity, a restricted version of Statistical Difference, and approximate versions of the (coNP forms of the) Shortest Vector Problem and Closest Vector Problem in lattices.

For some of the problems, such as Graph Isomorphism and Quadratic Residuosity, the proof systems have provers that can be implemented in polynomial time (given an NP witness) and have \tilde{O}(log n) rounds, which is known to be essentially optimal for black-box simulation.

To our best of knowledge, these are the first constructions of concurrent zero-knowledge protocols in the asynchronous model (without timing assumptions) that do not require complexity assumptions (such as the existence of one-way functions).

**Category / Keywords: **foundations / zero knowledge

**Date: **received 23 Aug 2005, last revised 25 Aug 2005

**Contact author: **shienjin at eecs harvard edu

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Version: **20050826:005207 (All versions of this report)

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