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Concurrent Knowledge Extraction in the Public-Key Model

  • Andrew C. Yao
  • Moti Yung
  • Yunlei Zhao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6198)

Abstract

Knowledge extraction is a fundamental notion, modeling machine possession of values (witnesses) in a computational complexity sense and enabling one to argue about the internal state of a party in a protocol without probing its internal secret state. However, when transactions are concurrent (e.g., over the Internet) with players possessing public-keys (as is common in cryptography), assuring that entities “know” what they claim to know, where adversaries may be well coordinated across different transactions, turns out to be much more subtle and in need of re-examination. Here, we investigate how to formally treat knowledge possession by parties (with registered public-keys) interacting over the Internet. Stated more technically, we look into the relative power of the notion of “concurrent knowledge-extraction” (CKE) in the concurrent zero-knowledge (CZK) bare public-key (BPK) model where statements being proven can be dynamically and adaptively chosen by the prover.

We show the potential vulnerability of man-in-the-middle (MIM) attacks turn out to be a real security threat to existing natural protocols running concurrently in the public-key model, which motivates us to introduce and formalize the notion of CKE, alone with clarifications of various subtleties. Then, both generic (based on standard polynomial assumptions), and efficient (employing complexity leveraging in a novel way) implementations for \(\mathcal{NP}\) are presented for constant-round (in particular, round-optimal) concurrently knowledge-extractable concurrent zero-knowledge (CZK-CKE) arguments in the BPK model. The efficient implementation can be further practically instantiated for specific number-theoretic language.

Keywords

Commitment Scheme Common Input Cryptology ePrint Archive Concurrent Session Random Tape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Andrew C. Yao
    • 1
  • Moti Yung
    • 2
  • Yunlei Zhao
    • 3
  1. 1.ITCSTsinghua UniversityBeijingChina
  2. 2.Google Inc. and Columbia UniversityNew YorkUSA
  3. 3.Software SchoolFudan UniversityShanghaiChina

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