## Abstract

Zero Knowledge Proofs (ZKPs) are one of the most striking innovations in theoretical computer science. In practice, the prevalent ZKP methods are, at times, too complicated to be useful for real-life applications. In this paper we present a practically efficient method for ZKPs which has a wide range applications. Specifically, motivated by the need to provide an upon-demand efficient validation of various financial transactions (e.g., the high-volume Internet auctions), we have developed a novel secure and highly efficient method for validating correctness of the output of a transaction while keeping input values secret. The method applies to input values which are publicly committed to by employing generic commitment functions (even input values submitted using tamper-proof hardware solely with input/ output access can be used.) We call these: strictly black box [SBB] commitments. Hence these commitments are typically much faster than public-key ones, and are the only cryptographic/ security tool we give the poly-time players, throughout. The general problem we solve in this work is: Let SLC be a publicly known staight line computation on n input values taken from a finite field and having k output values. The inputs are publicly committed to in a SBB manner. An Evaluator performs the SLC on the inputs and announces the output values. Upon demand the Evaluator, or a Prover acting on his behalf, can present to a Verifier a proof of correctness of the announced output values. This is done in a manner that (1) The input values as well as all intermediate values of the SLC remain information theoretically secret. (2) The probability that the Verifier will accept a false claim of correctness of the output values can be made exponentially small. (3) The Prover can supply any required number of proofs of correctness to multiple Verifiers. (4) The method is highly efficient. The application to financial processes is straight forward. To this end (1) we first use a novel technique for representation of values from a finite field which we call "split representation", the two coordinates of the split representation are generically committed to; (2) next, the SLC is augmented by the Prover into a "translation" which is presented to the Verifier as a sequence of generically committed split representations of values; (3) using the translation, the Prover and Verifier conduct a secrecy preserving proof of correctness of the announced SLC output values; (4) in order to exponentially reduce the probability of cheating by the Prover and also to enable multiple proofs, a novel highly efficient method for preparation of any number of committed-to split representations of the n input values is employed. The extreme efficiency of these ZK methods is of decisive importance for large volume applications. Secrecy preserving validation of announced results of Vickrey auctions is our demonstrative example.

Original language | English (US) |
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Title of host publication | Automata, Languages, and Programming - 39th International Colloquium, ICALP 2012, Proceedings |

Pages | 738-749 |

Number of pages | 12 |

Edition | PART 1 |

DOIs | |

State | Published - 2012 |

Event | 39th International Colloquium on Automata, Languages, and Programming, ICALP 2012 - Warwick, United Kingdom Duration: Jul 9 2012 → Jul 13 2012 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 1 |

Volume | 7391 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 39th International Colloquium on Automata, Languages, and Programming, ICALP 2012 |
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Country/Territory | United Kingdom |

City | Warwick |

Period | 7/9/12 → 7/13/12 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science