Concurrent Knowledge Extraction in the Public-Key Model

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.

This work was supported in part by the National Basic Research Program of China Grant Nos.2007CB807900, 2007CB807901, the National Natural Science Foundation of China Grant Nos.60553001, 60703091, and the QiMingXing Program of Shanghai.